R E S E A R C H
A p r i l
2 0 0 8

Evidence on the Prospects of
Expanding Treatment to
Drug-Involved Offenders

R E P O R T

To Treat or Not To Treat:

Avinash Singh Bhati
John K. Roman
Aaron Chalfin

research for safer communities
Going to Scale in the Treatment of Drug-Involved Criminal Offenders

URBAN INSTITUTE

Justice Policy Center

Copyright © April 2008
This document was prepared under grant # 2005-DC-BX-1064 awarded by the National
Institute of Justice, U.S. Department of Justice. Points of view in this document are those
of the authors and do not necessarily represent the official position or policies of the U.S.
Department of Justice or of other staff members, officers, trustees, advisor groups, or
funders of the Urban Institute.

URBAN INSTITUTE
Justice Policy Center
2100 M STREET, NW
WASHINGTON, DC 20037
www.urban.org

The views expressed are those of the authors, and should not
be attributed to The Urban Institute, its trustees, or its funders.

TO TREAT OR NOT TO TREAT:
EVIDENCE ON THE PROSPECTS OF EXPANDING
TREATMENT TO DRUG-INVOLVED OFFENDERS

Avinash Singh Bhati
John K. Roman
Aaron Chalfin

Justice Policy Center, The Urban Institute
2100 M Street, N.W., Washington, D.C. 20037

April 2008

Contents
Acknowledgments

ix

Abstract

xi

Executive Summary
1

2

xiii

Background and Motivation
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Prior Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Drug-Crime Nexus . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Criminal Justice System Interventions with Drug-Involved
Offenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Therapeutic Jurisprudence and Drug Courts . . . . . . . .
The Research Design
2.1 Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Data Sources and Uses . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Arrestee Drug Abuse Monitoring (ADAM) . . . . . . .
2.2.2 National Survey on Drug Use and Health (NSDUH)
2.2.3 Drug Abuse Treatment Outcome Study (DATOS) . .
2.2.4 Summary of the Elements of the Synthetic Data Set .

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3

Estimation Strategy
3.1 A Profile’s Prevalence in the Population of Arrestees . . . . . . . .
3.2 Simulated Counterfactual . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Simulated Eligibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Drug Court Survey Data Describing Eligibility Criteria
3.3.2 Estimating the Size of the Drug-Court Eligible Population
3.3.3 Estimating the Number of Individuals Currently Receiving Drug Treatment . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Cost and Benefit Estimates . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Treatment Price Estimates . . . . . . . . . . . . . . . . . . . .
3.4.2 Drug Court Price Estimates . . . . . . . . . . . . . . . . . . .
3.4.3 Estimates of the Benefits from Crime Reduction . . . . .
3.5 Key Assumptions and Caveats . . . . . . . . . . . . . . . . . . . . . .

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Findings
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4.1 Prevalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Crimes Avertable by Treatment . . . . . . . . . . . . . . . . . . . . . 48
4.3 Cost-Effectiveness of Treating Currently Eligible Drug Court
Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Simulated Cost-Effectiveness of Expanding Criminal Justice System–
Based Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.1 Simulation 1: Adding Individuals with Other Pending
Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.2 Simulation 2: Adding Individuals with Prior Violence . . 60
4.4.3 Simulation 3: Adding Individuals with Prior Failed Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4.4 Simulation 4: Adding Individuals with Co-Occurring
Alcohol Problems . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.5 Simulation 5: Expanding Eligibility to Include all Arrestees 66

5

Discussion

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6

References

A Mathematical Appendix
A.1 Interpolation Technique . . .
A.2 Prevalence Estimation . . . . .
A.3 Computing Variance . . . . . .
A.4 Empirical Similarity Weights

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List of Tables
2.1

Synthetic data profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Percent of responding adult drug courts considering individuals
eligible for participation, by select attributes . . . . . . . . . . . . .
3.2 Population of arrestees eligible for drug courts . . . . . . . . . . . .
3.3 Estimated number of individuals receiving each treatment modality in drug courts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Costs associated with four treatment modalities . . . . . . . . . . .
3.5 Administrative costs for drug courts . . . . . . . . . . . . . . . . . .
3.6 Price for four treatment modalities . . . . . . . . . . . . . . . . . . .
3.7 Cost of offending, pre-sentence . . . . . . . . . . . . . . . . . . . . . .
3.8 Probability that an offender is sentenced to probation, jail, or
prison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Estimated number of months an offender is sentenced to probation, jail or prison, and total sentencing costs . . . . . . . . . . . . .
3.10 Estimates of the total cost to society. . . . . . . . . . . . . . . . . . .

12

3.1

4.1
4.2
4.3

The estimated prevalence of potential clients nationwide. . .
Estimated number of crimes avertable annually by treating
tential clients under inpatient treatment modalities. . . . . .
Estimated number of crimes avertable annually by treating
tential clients under outpatient treatment modalities. . . . .

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po...
po...

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4.4

Cost benefit analysis of treating eligible drug courts clients in
available drug dourt treatment slots. . . . . . . . . . . . . . . . . . .
4.5 Cost benefit analysis of treating all eligible drug court clients
(retaining all eligibility restrictions). . . . . . . . . . . . . . . . . . .
4.6 Cost benefit analysis of treating all eligible drug court clients
without regard to current offense (retaining other eligibility restrictions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Cost benefit analysis of treating all eligible drug court clients
without regard to past violence (retaining other eligibility restrictions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Cost benefit analysis of treating all eligible drug court clients
without regard to past treatment (retaining other eligibility restrictions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Cost benefit analysis of treating all eligible drug court clients
without regard to co-occurring alcohol problems (retaining other
eligibility restrictions). . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Cost benefit analysis of treating all drug involved arrestees (with
no eligibility restrictions). . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures
2.1

Graphical depiction of the synthetic dataset. . . . . . . . . . . . . .

19

3.1

Graphical depiction of the treatment effects computation. . . . .

25

A.1 Successfully recovering hiddens signals using empirical similarity weights: An example. . . . . . . . . . . . . . . . . . . . . . . . . . .

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Acknowledgments
The authors would like to thank those who assisted our efforts in collecting,
preparing and analyzing the data used in this study. Michael Kane, Bogdan
Tereshchenko, Aaron Sundquist, Jay Reid and Will Jurist provided exceptional
assistance preparing the data sets for analysis. Adele Harrell and Terrence Dunworth contributed to the conceptual development of the core hypotheses tested
in this study. Shelli Rossman kindly allowed us to coordinate cost data collection with the MADCE. Nancy La Vigne provided excellent comments on the
final narrative.
We also wish to thank three anonymous reviewers for their comments on
the technical matters. We would like to thank Janice Munsterman, Jennifer
Handley and Marilyn Moses at the National Institute of Justice who monitored
this project for the patience and guidance.
Despite their guidance, all remaining errors are our own.

ix

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Abstract
Despite a growing consensus among scholars that substance abuse treatment is
effective in reducing offending, strict eligibility rules have limited the impact of
current models of therapeutic jurisprudence on public safety. This research effort was aimed at providing policy makers some guidance on whether expanding
this model to more drug-involved offenders is cost-beneficial.
Since data needed for providing evidence-based analysis of this issue are not
readily available, micro-level data from three nationally representative sources
were used to construct a synthetic dataset—defined using population profiles
rather than sampled observation—that was used to analyze this issue. Data from
the National Survey on Drug Use and Health (NSDUH) and the Arrestee Drug
Abuse Monitoring (ADAM) program were used to develop profile prevalence
estimates. Data from the Drug Abuse Treatment Outcome Study (DATOS)
were used to compute expected crime reduction benefits of treating clients with
particular profiles. The resulting synthetic dataset—comprising of over 40,000
distinct profiles—permitted the benefit-cost analysis of a limited number of simulated policy options.
We find that roughly 1.5 million arrestees who are probably guilty (the population most likely to participate in court monitored substance abuse treatment)
are currently at risk of drug dependence or abuse and that several million crimes
could be averted if current eligibility limitations were suspended and all at-risk
arrestees were treated. Under the current policy regime (which substantially
limits access to treatment for the population we are studying) there are about

xi

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55,000 individuals treated annually—about 32,000 are at risk of dependence and
23,500 at risk of drug abuse. In total, about $515 million dollars is spent annually
to treat those drug court clients yielding a reduction in offending which creates
more than $1 billion dollars in annual savings. Overall, the current adult drug
court treatment regime produces about $2.21 in benefits for every $1 in costs,
for a net benefit to society of about $624 million. Every policy change simulated
in this study yields a cost-effective expansion of drug treatment. That is, removing existing program eligibility restrictions would continue to produce public
safety benefits that exceed associated costs. In particular, removing all eligibility
restrictions and allowing access to treatment for all 1.47 million at risk arrestees
would be most cost effective—producing more than $46 billion in benefits at a
cost of $13.7 billion.

Executive Summary
The primary goal of this research is to determine the size of the drug-involved
offender population that could be served effectively and efficiently by partnerships between courts and treatment. Despite a growing consensus that substance
abuse treatment promotes desistance, few arrestees receive sufficient treatment
through the criminal justice system to reduce their offending. Strict eligibility
rules and scarce resources limit access to treatment, even in jurisdictions that
embrace the principles of therapeutic jurisprudence. The result is that existing
linkages between the criminal justice system and substance abuse treatment are
so constrained that at best only small reductions in crime can be achieved.
The limited access to treatment for the criminal offender population appears
to be based on subjective judgments of both the risks of treating offenders in
the community and the benefits of treatment. Risks are assumed to be high
for most offenders, and the benefits of treatment are assumed to be low. As a
result, almost all drug-involved arrestees are determined to be ineligible for participation in community-based treatment programs. An important question for
the nation’s drug policymakers is whether a substantial expansion of substance
abuse treatment would yield benefits from reduced crime and improved public
safety. A related question is whether evidence-based strategies can be developed
to prioritize participation, given limited resources.
Previous efforts to address these questions have been constrained by limitations in extant data, as well as by substantial econometric challenges to combining those data. The development of new modeling techniques now allows

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disparate data sources to be combined and critical values to be imputed for missing observations. Thus, in this paper we are able to combine data from several
prior studies to simulate the effects of treatment on an untreated cohort of arrestees. That is, using existing data on the drug use patterns of arrestees and
data predicting outcomes from the treatment of similar cohorts, we are able to
predict not only how much crime could be prevented through treatment of an
arrestee population, but also which arrestees (based on their attributes) are the
best (and worst) candidates for community-based treatment.
We use evidence from several sources to construct a synthetic dataset to estimate the benefits of going to scale in treating drug involved offenders. We
combine information from the National Survey on Drug Use and Health (NSDUH) and the Arrestee Drug Abuse Monitoring (ADAM) program to estimate
the likelihood of drug addiction or dependence problems and develop nationally representative prevalence estimates. We use information in the Drug Abuse
Treatment Outcome Study (DATOS) to compute expected crime reducing benefits of treating various types of drug involved offenders under different treatment modalities. We find that 1.5 million arrestees who are probably guilty (the
population most likely to participate in court monitored substance abuse treatment) are at risk of abuse or dependence. We estimate that roughly 1.15 million
potential clients are at risk of drug dependence and roughly 322,000 are at risk
of abusing drugs. We find that several million crimes would be averted if current
eligibility limitations were suspended and all at-risk arrestees were treated. Our
estimates are smaller than other studies, because we restrict our study sample to
those both at risk of abuse and dependence and to those likely to be found guilty,
since this is the population most likely to become eligible for criminal justice
system-based substance abuse treatment. Although our estimates are therefore
smaller than other published estimates, the distribution of client attributes is
similar.
We find that substance abuse treatment in each of the four DATOS domains
substantially reduces recidivism among this population. For those at risk of drug

xv
dependence, long-term residential reduces recidivism by 34%, short-term inpatient by 19%, outpatient methadone by 20%, and outpatient drug free by 30%.
For those at risk of drug abuse, recidivism reductions are large (27%). Outpatient drug free is the most effective modality, reducing recidivism by 33%.
Long-term inpatient reduces recidivism by 27%, short-term inpatient by 20%
and outpatient methadone by 16%. The pattern of offending reduction is generally similar for those at-risk of drug abuse as it is for those at risk of dependence,
where the largest reductions occur for the most prevalent (but least costly) crime
types. Small (or no) reductions in crime are observed for the most serious
crimes. These findings are also consistent with previous estimates.
We find that under the current policy regime (which for the most part limits access to treatment for the population we are studying to drug courts) there
are about 55,000 individuals treated annually, about 32,000 are at risk of dependence, and 23,500 are at risk of drug abuse. In total, we estimate that about $515
million dollars is spent annually to treat those drug court clients and that this
yields a reduction in offending which creates more than $1 billion dollars in annual savings. Overall, we estimate that the current adult drug court treatment
regime produces about $2.21 in benefit for every $1 in costs, for a net benefit to
society of about $624 million. The benefit-cost ratio is higher for those at risk
of abuse (2.71) as compared to those at risk of dependence (1.84), even though
the abuse group is less prevalent in the drug court population. We estimate that
there are about twice as many arrestees eligible for drug court (109,922) than
there are available drug court treatment slots (55,365). We simulate the effects
of treating all of these currently eligible in the four treatment modalities studied by DATOS, and find that the costs of treating these additional clients about
doubles, to slightly more than $1 billion. We find that the expansion of drug
treatment to this larger population remains cost-effective, although the benefitcost ratio is fractionally reduced to 2.14 from 2.21. In total, this expansion of
treatment yields a benefit to society of more than $1.17 billion dollars.
We also simulate several expansions of criminal justice system-based treat-

xvi
ment which allow many arrestees into treatment who are currently not eligible.
We estimate that expanding treatment access to those with a pending case is cost
beneficial, with a about $1.65 billion in total benefits. In particular, allowing
those with a pending case who are at-risk of drug dependence is especially beneficial, with a benefit to cost ratio 4.13:1. We find that allowing those with past
violence into court supervised treatment is as cost-beneficial as current practice,
with a benefit to cost ratio of 2.15. While the addition of those at risk of abuse
with prior violence is cost-beneficial (3.14:1) adding those at risk of drug dependence with prior violence is much less cost-beneficial (1.38:1). Expanding the
program to include those with a history of failed treatment is also cost-beneficial
(2.09:1), especially for those at risk of drug abuse (2.29:1).
Allowing those with co-occurring alcohol problems into court supervised
treatment yields is cost-beneficial for the entire group treated (1.73:1). However,
again, these aggregate numbers mask important differences in the responsiveness
of this new population to treatment. For those at risk of dependence, the results
are better, with the newly added group estimated to have a benefit to cost ratio
of 1.43:1. However, adding those with co-occurring alcohol problems who are
at risk of drug dependence is not cost-effective (0.70:1).
Finally, we consider allowing access to court-supervised treatment for all arrestees, without restriction. Treating all at-risk arrestees would cost more than
$13.7 billion and return benefits of about $46 billion. We find that this approach
would be cost-effective, with a benefit of $3.36 for every dollar in cost.

Chapter 1
Background and Motivation
1.1.

INTRODUCTION

Recent innovations in the criminal justice system have linked intensive criminal justice system surveillance with substance abuse treatment. The goal of this
justice-treatment partnership is to improve outcomes for drug-involved offenders and to reduce the burden of chronic drug use on private citizens, the police,
courts, and corrections. These interventions, labeled therapeutic jurisprudence,
are designed to identify and treat drug-involved offenders in the community in
lieu of incarceration. The programs take many forms. There is widespread use
of diversion programs that provide short-term pre-trial services to large numbers of low-risk arrestees. These programs may either incorporate direct judicial
monitoring or may add more strenuous treatment requirements to the conditions of community supervision. More intensive and long-term treatment is
managed by a judge on a separate court calendar. These programs, generally
known as drug courts, serve a more serious but narrowly targeted population.
Although these programs exist is many, if not most, jurisdictions, only a fraction
of the drug-involved arrestee population receives these programs. Proponents of
these interventions often discuss ‘going to scale’ and making them available to
the entire population of eligible offenders.

1

2

To Treat or Not to Treat

Despite the prominence of these initiatives, few arrestees who meet the clinical criteria for drug abuse or drug dependence receive intensive, long-term substance abuse treatment in the community in lieu of incarceration. Pre-trial diversion programs treat relatively large numbers of offenders, and many drug
involved offenders receive at least a pre-trial referral to treatment. However, the
dosage and duration of these programs is generally very limited. The more intensive adult drug court is a promising model for reducing recidivism. However,
while there are drug courts operating in most mid- and large-sized counties in
the US, most are very small and serve less than 100 clients annually. Thus, only a
small number of drug-involved arrestees receive intensive long-term treatment in
lieu of incarceration. There are few reliable estimates of the number of arrestees
who annually enroll in and/or complete a court supervised treatment program.
Using data from a census of drug courts conducted as part of the Multi-Site
Adult Drug Court Evaluation (MADCE), we estimate that fewer than 30,000
adult arrestees were enrolled in drug courts in 2005, a trivial percentage of the
ten million individuals arrested each year (Rossman et al. 2007) Probation and
parole based treatment programs have also shown promise, but few large-scale
programs exist today.
The limited penetration of these programs is the result of several forces.
First, tradition holds that federal sponsorship of new programs is limited to
the funding of demonstration programs. So, while new programs can be implemented, identifying the resources to take these programs to scale is left to local
governments. Second, the programs themselves are costly. Even cost-effective
programs are more expensive to administer than business as usual, and thus require additional funding if they are to expand. Third, the beneficiaries of these
programs generally are not the same party who pays for the program. For example, while the costs of drug court are born almost entirely by the court system,
the court does not explicitly realize the benefits. Instead, the benefits of drug
courts tend to accrue to private citizens who have a reduced risk of victimization and to corrections departments who have to house fewer offenders and

Background and Motivation

3

recidivists. Thus, unless measures can be enacted that pool the risk (and the rewards) of these programs, there are substantial disincentives to implementation.
Fourth, the benefits of the program to date have largely been estimated at the
micro-level. Due to the small number of clients involved, much of the success of
the programs comes from reduced recidivism within a small group of offenders,
but not from a meaningful reduction of crime rates in the community (i.e., at the
macro-level). Finally, and as a result of the aforementioned factors, even though
there is a large and growing body of research that demonstrates the efficacy of
these initiatives, there is substantial reluctance across the political spectrum to
treat convicted (or convictable) offenders in the community in lieu of prison.
The goal of this research then is to determine what would happen if none of
these factors impeded a national investment in therapeutic jurisprudence. That
is, suppose that there were no obstacles to the implementation of effective treatment for drug-involved offenders. How many offenders enter the criminal justice system each year who would be clinically diagnosed as drug abusers or drug
dependent? How many crimes could be prevented is they received treatment?
Given that treatment benefits may vary across treatment modalities, how many
crimes could be reduced by each of the most common modalities? Given that
amenability to treatment varies by arrestee attributes, can better (and worse)
candidates for therapeutic jurisprudence programs be identified ex ante? How
much would the delivery of this treatment cost? How big are the benefits? In
sum, if access to treatment were expanded, how many crimes could be prevented
and what are the costs and benefits off doing so?
We use evidence from several sources to construct a synthetic dataset for
answering the question: what are the expected benefits of ‘going to scale’ in
treating drug involved offenders? To answer this question, we combine drug use
and criminal justice data from the National Survey on Drug Use and Health
(NSDUH) and the Arrestee Drug Abuse Monitoring (ADAM) program to estimate the prevalence of drug addiction or dependence in the arrestee population.
Expected outcomes from substance abuse treatment from the Drug Abuse Treat-

4

To Treat or Not to Treat

ment Outcome Study (DATOS) is used to predict the benefits from treatment
in terms of reduced crime. We find that about 1.5 million (probably guilty) arrestees are at risk of abuse or dependence and that several million crimes would
be averted if current eligibility limitations were suspended and all at risk arrestees were treated.
1.2.
1.2.1.

PRIOR RESEARCH
Drug-Crime Nexus

A substantial research literature links substance use and abuse to criminality
(Anglin and Perrochet 1998; Ball et al. 1983; Boyum and Kleiman 2002; Brownstein et al. 1992; Condon and Smith 2003; Dawkins 1997; DeLeon 1988a;
DeLeon 1988b; Harrison and Gfroerer 1992; Inciardi et al. 1996; Inciardi 1992;
Inciardi and Pottieger 1994; Johnson et al. 1985; MacCoun and Reuter 2001;
Miller and Gold 1994; Mocan and Tekin 2004). Psychopharmacologic effects
of substance use lead users to commit crimes while intoxicated and economiccompulsive effects lead users to commit crimes to gain resources to buy drugs
(Goldstein 1985). Violence associated with the drug trade, and victimization of
intoxicated, drug users contribute to drug-involved crime as well (Boyum and
Kleiman 2002; Goldstein 1985; MacCoun et al. 2003). Drug sellers are often
drug users (Reuter, MacCoun and Murphy 1990), and sellers who are incarcerated tend to be replaced by new suppliers (Freeman 1996; Blumstein 2000).
Young drug users and suppliers are most likely to be violent (Blumstein and
Cork 1996; MacCoun et al. 2003). Drug users are also more likely to be the victims of violence than non-drug users (Cottler, et al 1992), and criminal behavior
increases as the frequency and intensity of use increases (Anglin et al. 1999; Anglin and Maugh, 1992; Chaiken and Chaiken 1990; Stewart et al. 2000; Vito,
1989). Criminal incidence is highest for substance abusers while they are using
drugs, four to six times more than when they are not abusing narcotics (Ball et al.
1982; Gropper, 1985), a pattern that is even more pronounced among habitual

Background and Motivation

5

offenders (Vito 1989). Conversely, crime decreases as drug use declines, particularly when it is income-generating crimes that decrease (Anglin et al. 1999;
Chaiken and Chaiken, 1982; Degenhardt et al 2005; Inciardi 1987; Nurco et al.
1990; Speckert and Anglin, 1986).
A corresponding literature suggests treatment can be effective in reducing
demand and associated offending. Economic studies have found that treatment
is more cost-effective than incarceration (Caulkins et al. 1997; MacKenzie 2006;
Lipsey and Cullen 2007), that intensive long-term treatment is most effective
(NIDA 1999), that direct interaction with a judge is more effective for serious
drug users (Marlowe et al. 2004), and that violent offenses cause the greatest
economic damage to communities (Cohen 2003). The Drug Abuse Treatment
Outcome Studies (DATOS) found length of participation in treatment to be the
key predictor of success. While attrition rates from treatment are estimated from
40% to 90%, studies show that those who remain in treatment for a sufficient
period subsequently commit fewer crimes (French, et al 1993; Lewis & Ross,
1994; Simpson, et al. 1997). In particular, patients with more severe problems
reported better outcomes after 90 days of treatment (Simpson et al. 1999). After
one year of treatment, major outcome indicators for drug use, illegal activities,
and psychological distress were each reduced on average by about 50% (Hubbard
et al. 1997). Prevalence of arrest fell from 34% in the year before intake to
22% one year after enrolling in treatment (Simpson et al. 2002). The average
net economic benefit from an episode of long-term residential treatment was
$10,344 and $795 from an episode of outpatient treatment (Flynn et al. 1997).
The number of drug users has remained relatively stable over time (Rhodes,
et al 2000) suggesting a general aging of the cocaine and heroin-using population
(Golub and Johnson 1997). Despite this, drug users face a significant risk of arrest and incarceration: a part-time drug seller in Washington, D.C. has a 22%
risk of imprisonment in a given year, and spends about one-third of their criminal career incarcerated (Reuter et al. 1990; MacCoun and Reuter 2002). Mark
Kleiman (1997) estimates that heavy users of cocaine who are arrested annually

6

To Treat or Not to Treat

consume 60% of the cocaine in the United States. The Bureau of Justice Statistics estimates that about half of both federal prisoners and jail inmates abuse
or are dependent on drugs (Mumola & Karberg 2006; Karberg & James 2005).
Few, however, received treatment within the criminal justice system (Harrell
and Roman 2001; Marlowe 2003). Among incarcerated populations, only about
15 percent received drug treatment (Karberg and James 2005).
1.2.2.

Criminal Justice System Interventions with Drug-Involved
Offenders

Given the preponderance of evidence that treatment can be effective, over the
last three decades various criminal justice system innovations have emerged to
treat drug and alcohol abusing offenders in the community with criminal justice
system oversight. The first widespread intervention, Treatment Accountability
for Safe Communities (TASC), redirected drug offenders from the court system
into treatment facilities. TASC provided the link between the judicial system
and treatment services and offered participation incentives in the form of case
dismissal for successful completion (Nolan 2001). An outcome evaluation of five
TASC programs found some evidence of reduced recidivism and drug use, but
the results were mixed (Anglin et al. 1999). In the late 1980s, a more rigorous
program, Intensive Supervision Probation (ISP), was developed to monitor drug
offenders in the community as an alternative to incarceration with the goal of reducing prison crowding and providing more thorough supervision than regular
probation (Tonry 1990). However, evaluation of the ISP program suggests that
the level and intensity of treatment was minimal and the program failed to affect
participant drug involvement. Overall, ISP resulted in increased incarceration
rates, although the effect may have been confounded by increased participant
scrutiny (Tonry 1990; Petersilia, et al. 1992; Turner, et al. 1992). Similar programs such as those mandated under Proposition 36 passed in California in 2001
and the Drug Offender Sentencing Alternative (DOSA) program in Washington
serve large numbers of offenders in several states, and these have generally been

Background and Motivation

7

found to yield better treatment and criminal justice outcomes (Aos et al. 2005;
Longshore et al. 2004).
1.2.3.

Therapeutic Jurisprudence and Drug Courts

While each of these programs has linkages to the criminal justice system, they
did not fully exploit the coercive powers of the criminal justice system to incentivize compliance with treatment protocols. Under the rubric of therapeutic jurisprudence, a more formal model of intensive court-based supervision, referred
to as drug treatment courts, emerged in the 1990s (Hora, Schma and Rosenthal
1999; Senjo and Leip 2001; Slobogin 1995; Wexler and Winick 1991). The therapeutic jurisprudence model posits that legal rules and procedures can be used to
improve psychosocial outcomes, an idea supported by a growing research consensus that coerced treatment is as effective as voluntary treatment (Anglin et al.,
1990; Belenko 1999; Collins and Allison 1983; DeLeon 1988a; DeLeon 1988b;
Hubbard et al. 1989; Lawental et al. 1996; Siddall and Conway 1988; Trone and
Young 1996). A number of studies have found that drug treatment court participation reduces recidivism rates (Finigan, 1998; Goldkamp and Weiland 1993;
Gottfredson and Exum 2002; Harrell and Roman 2002; Jameson and Peterson
1995; Peters and Murrin 2000; Wilson et al. 2006). In response, the model has
proliferated, and by 2005 there were about 600 adult drug courts in operation in
the United States, including most medium and large counties.
Despite the pervasiveness of the drug treatment court model, drug courts
routinely exclude most of the eligible population. A survey of adult drug courts
in 2005 (Rossman et al 2007) found that only 12% of drug courts accept clients
with any prior violent convictions. Individuals facing a drug charge, even if the
seller is drug dependent, are excluded in 70% of courts for misdemeanor sales
and 53% of courts for felony sales. Other charges that routinely lead to exclusion include property crimes commonly associated with drug use (theft, fraud,
prostitution), young offenders with marijuana charges, and current domestic
violence cases (only 20% accept domestic violence cases). Many also reject of-

8

To Treat or Not to Treat

fenders based on the severity of the users drug problem. However, eligibility
based on drug use severity is applied inconsistently—16% of drug courts exclude
those with a drug problem that is deemed too serious, while 48% reject arrestees
whose problems are not severe enough. Almost 69% exclude those with cooccurring disorders. Even among eligible participants, more than half of drug
courts (52%) report they cannot accept some clients who are eligible for participation due to capacity constraints. Given these criteria, we estimate that fewer
than 30,000 annually enroll in drug treatment courts. On the other hand, if the
Bureau of Justice Statistics estimates of dependence and abuse are correct, several
million individuals are arrested annually who use illegal substances (Mumola &
Karberg, 2006; Karberg & James, 2005).
Based on available evidence on the general crime reducing benefits that accrue by treating drug involved offenders, our research was motivated by the need
to provide policy makers some guidance on the prospects of going to scale. That
is, what crime reductions can we reasonably expect if more drug involved offenders received treatment? We explain our analytical strategy for exploring this
issue next.

Chapter 2
The Research Design
The most straightforward way to investigate this issue would be to identify and
assess a sample from the population of all arrestees nationwide who are probably
guilty and at risk of drug abuse or dependence. That is, since an admission of
guilt is generally required for enrollment into therapeutic jurisprudence based
programs, we would need to ensure that we sample from a population of guilty
arrestees. For each arrestee we would like to observe the number of crimes
(by type) that could be prevented if they were treated (under various treatment
modalities). Of course, such data do not exist. It is, however, possible to generate synthetic data that provide information on all the relevant quantities. If
appropriately constructed, analysis of these synthetic data provides a sound basis for making valid inferences about population characteristics. Our research
employs this strategy for estimating the number of potential clients and the
expected number of crimes avertable by treating these potential clients under
various treatment modalities.
To construct our sample, we define a potential client of a therapeutic jurisprudence program as any arrestee who is probably guilty of a crime and is
also at risk of substance abuse. To determine the nature of the arrestee’s substance use, we use the DSM-IV criteria to asses whether or not a drug involved
offender is at risk of being dependent on drugs or of abusing drugs. We also
9

10

To Treat or Not to Treat

include a set of client attributes (e.g., age, race, or gender) as traits to be included
in the design of the synthetic data, e.g. as attributes along which dependency
may vary.
We perform all of our analyses on profiles that represent types of individuals,
rather than on individual observations. Because we combine information from
multiple data sources, we can not observe information about the same individuals describing their risk, dependence and responsiveness to treatment. Since
we can observe common attributes–socio-demographic characteristics, and information about substance abuse and criminal histories across datasets–we create simulated (synthetic) profiles. These profiles, which are combinations of all
attributes, are then used in the analysis in much the same way individual observations would be used had that information been available.
From these multiple data sources, we develop an exhaustive set of ‘profiles’,
where each profile is one possible combination of all of the potential client’s attributes. For example, if we simply collected data on age, race and number of
prior arrests, we would develop one profile for young male arrestees with few
prior arrests, one profile for young male arrestees with many priors, etc. Hence,
the synthetic data used in this analysis includes a profile for every client permutation, allowing us to quantify the effect of drug treatment on every combination
of client attributes and characteristics.
We use simulation models to estimate outcomes for each profile, conditional
on receiving each of four possible treatment modalities (described below). We
use data from studies linking client traits and characteristics to outcomes to identify expected outcomes for each of these profiles. Since not all of the profiles
are represented in the outcomes data (from DATOS), we estimate expected outcomes for all client profiles. Putting all of these approaches together, we are
able to model expected outcomes from treatment for a wide variety of potential
clients.

The Research Design

2.1.

11

SYNTHETIC DATA

A great deal of attention has recently been paid to the potential of using synthetic data as a way of archiving data regarding individual behavior without
actually providing sensitive micro-data (Abowd and Woodcock 2001). In that
literature, the main purpose of synthetic data is to replace the actual micro data
with a scientifically valid replacement, allowing for the robust estimation of outcomes without violating the confidentiality of individuals represented by the
data. One valuable extension of this approach is the use of many synthetic data
sets to generate expected outcomes, which allows for the modeling of statistical uncertainty and the generation of standard errors and confidence intervals
around outcomes. The method has been in general use in statistics for more
than 25 years for handling missing data and has recently been formalized for the
synthetic data problem (Reiter 2002, 2003; Ragunathan et al. 2003).
Our motivation for using synthetic data is slightly different. We use this design for the purpose of bringing together information from several disparate data
sources. Data for this study were developed from the National Survey on Drug
Use and Health (NSDUH) and the Arrestee Drug Abuse Monitoring (ADAM)
program—to estimate the likelihood of various arrestee profiles having drug addiction or dependence problems—and from the Drug Abuse Treatment Outcome Study (DATOS)—to compute expected crime reducing benefits of treating
various profiles of drug involved offenders under different treatment modalities.
In order to do so, we defined a detailed exhaustive set of client attributes (based
on availability across these sources) as a base data set. The attributes that define
the synthetic database include all characteristics available for all the databases
used in this study. We began by creating a synthetic data set of 40,320 client
profiles with the attributes and categories listed in table 2.1.
The base synthetic data set is a cross combination of all of these attributes.
Each profile in the dataset is a list of attribute combinations that represents one
row in this data set. For example, one profile could be a white male, aged 25
years, who is arrested for a drug offense, who does not have a violent past nor

12

To Treat or Not to Treat

Table 2.1: Synthetic data profiles.
Category

Attributes

Age
Race
Gender
Criminal History
Current Offense

Arrestee age (20, 25, 30, 35 40, or 45)
Arrestee race (Black, White, or Other)
Arrestee gender (Male or Female)
Number of prior arrests (0, 2, 5, 10, or 20)
Most serious charge at current arrest (Violent,
Drug, Property, or Other)
Any prior violent charges (Yes or No)
Any prior treatments (Yes or No)
Is arrestee currently under any criminal justice
supervision (Yes or No)
Is arrestee at risk of alcohol dependence or abuse
(Yes or No)
Non-MSA, Large MSA (more than 1 million residents), or Small MSA (less than 1 million residents)

Violent History
Treatment History
Criminal Justice Status
Alcohol problems
Geographic location

any past treatment, has two prior arrests, was not under active criminal justice
supervision at the time of arrest, and was arrested in a MSA with less than a
million residents. Another distinct profile could be for a female who has all the
same remaining features.
The next step is to determine how many individuals in the population are
represented by each profile. That is, the proportion of the population (the prevalence) of each profile. For each profile, a value is estimated that is used for
weighting the profile by its prevalence in the population of interest. Moreover,
since we are interested in assessing the prevalence of potential clients at risk of
drug dependence or abuse, we have generated prevalence estimates conditional
on drug dependence or abuse.
Independently of the profiles’ prevalence, we also generate estimates of the
expected crime reducing benefits of treating potential clients under various treatment modalities. This information is obtained from DATOS, and we interpolate all expected outcomes of treatment onto the profiles in the synthetic dataset.

The Research Design

13

We describe the interpolation technique as well as the steps taken to obtain
prevalence and treatment effect estimates in more detail in the following chapter.
Before that, we turn to a description of our main data sources and their intended
uses in constructing the synthetic data.
2.2.

DATA SOURCES AND USES

To populate the synthetic data columns, we rely on three main data sources.
We combine information from the National Survey on Drug Use and Health
(NSDUH) and the Arrestee Drug Abuse Monitoring (ADAM) program to estimate the likelihood of various arrestee profiles having drug addiction or dependence problems. We also use the same sources to develop prevalence estimates
of these profiles among arrestees nationally. We use information in the Drug
Abuse Treatment Outcome Study (DATOS) to compute expected crime reducing benefits of treating various types of drug involved offenders under different
treatment modalities. Each dataset is described in more detail below.
2.2.1.

Arrestee Drug Abuse Monitoring (ADAM)

ADAM data is used as the first step in defining the attributes used to construct
our profiles, that is as the first source of socio-demographic, treatment and criminal information that may be common among datasets that describe risk of drug
abuse or dependence. Since ADAM data is not representative, we use data from
NSDUH to re-weight our ADAM sample. Funded by the National Institute of
Justice, the Arrestee Drug Abuse Monitoring (ADAM) program is a research
program designed to estimate illicit drug use in the population of arrestees in
urban areas. Data on a stratified sample of arrestees were collected on a quarterly basis in 2000, 2001, 2002 and, again in 2003 in 39 selected metropolitan
areas in the United States. The sampling frame represents all facilities in the
target county and all types of offenders arrested and booked on local and state
charges within the past 48 hours. Self-reported and administrative data collected

14

To Treat or Not to Treat

include: (1) demographic data on each arrestee, (2) administrative criminal justice records, (3) case disposition, including accession to a verbal consent script,
(4) calendar of admissions to substance abuse and mental health treatment programs, (5) data on alcohol and drug use, abuse, and dependence, (6) drug acquisition data covering the five most commonly used illicit drugs, (7) urine test
results, and (8) for males, weights.
ADAM contains several items that make it particularly appealing for our
analysis. First, arrestees were asked about the total number of times they were
arrested in the prior 12 months. We use this quantity to estimate the prevalence
of arrestees nationwide (described in more detail below). The same domains are
also collected for a non-probabilistic sample of female arrestees.
Second, among respondents who said they used drugs or alcohol during the
last 12 months, arrestees were asked six questions about their substance use to
allow for a categorization of their risk of drug abuse or dependence following
Diagnostic Statistical Manual (DSM-IV) definitions. The DSM-IV distinguishes
between two types of drug problems, substance abuse disorder and substance
dependency disorder (which is commonly referred to as addiction). Substance
abuse disorder is based on the frequency of drug use, the use of drugs in particular situations, negative outcomes that can be linked to the use of drugs,
pronounced use of drugs in the face of evidence that drugs are contributing to
personal and interpersonal problems. By contrast, the conditions for substance
dependency disorder are broader. These include physical symptoms, such as tolerance and withdrawal, and patterns of behavior aimed at either unsuccessfully
reducing the influence of drugs or allowing for greater amounts of drugs to be
taken.1
Finally, ADAM contains detailed information on the current charge, the arrest history, criminal justice status, arrestee age, race, and gender, as well as an
1

Data from ADAM describing individual responses to DSM-IV items are not included in the
public release version of ADAM. Public data flag individuals as being at risk of drug dependence
or abuse. Similarly, they are flagged as being at risk of alcohol dependence or abuse. We use
these items to compute the probability of drug dependence or abuse.

The Research Design

15

indicator for the ADAM site. We use information from the Census to classify
each of the ADAM sites as belonging either to a large MSA (with over 1 million
residents), a small MSA (with fewer than 1 million residents), or a non-MSA.
Using all these items, we create the set of arrestee attributes for each profile. We
use ADAM data (in combination with NSDUH as described below) to predict
the probability that a particular profile is at risk of drug abuse or dependence.
The probability of drug abuse or dependence calculated from ADAM and NSDUH data were then joined with DATOS data to predict expected changes in
offending, conditional on treatment.
In sum, in our analysis, we used ADAM data to predict the probability that a
profile is at risk of drug abuse or dependence. However, since ADAM is not nationally representative, the prevalence of each profile is also not nationally representative for several reasons. For instance, we have combined the male and female samples in ADAM, which means our final sample is not representative even
of the 39 metropolitan areas included in ADAM. Moreover, because ADAM is
a study mainly of metropolitan areas, it undercounts arrestees in smaller MSAs
and non-MSAs. In order to correct for these imbalances and to make ADAM
data more representative of all arrestees nationwide, we utilize another data set
(NSDUH) to re-weight ADAM data. The item that is re-weighted using NSDUH is the prevalence of each profile in the population.
The probability that a profile is at risk of drug abuse or dependence is still
calculated from ADAM, but the weight assigned to each profile (how often it appears in the population) is adjusted using NSDUH. In re-weighting the ADAM
data, we are motivated by making the sample of arrestees in the ADAM data
more representative of arrestees nationwide. What we attempt is different from
what, for example, Rhodes and his colleagues (Rhodes at al. 2007) computed.
Rhodes et al. (2007) are primarily interested in computing the arrest rate among
chronic drug users. Our primary interest lies in computing the prevalence of
risk of drug dependence or abuse among arrestees nationwide.

16
2.2.2.

To Treat or Not to Treat

National Survey on Drug Use and Health (NSDUH)

Funded by the United States Department of Health and Human Services, the
National Survey on Drug Use and Health (NSDUH) series (formerly titled National Household Survey on Drug Abuse) measures the prevalence and correlates of drug use in the United States. The NSDUH data represents the civilian,
non-institutionalized population of the United States age 12 and older. The survey covered substance abuse treatment history and perceived need for treatment,
and (as is the case for ADAM) includes questions from the Diagnostic and Statistical Manual (DSM) of Mental Disorders to apply diagnostic criteria.
Moreover, the data provide detailed information on illegal involvement, which
allows us to select observations from NSDUH that resemble the population in
ADAM, and thus the population of interest in the study. Using information
on illegal involvement over the last 12 months, we sub-set the data to include
only those individuals who were arrested and booked at least once during the
last year. Additionally, we restricted our NSDUH sample to adults who were
18 years and older. From the initial respondent pool of 55,031, we select about
10,347 observations for use in our study.
Based on a set of elements common to ADAM and NSDUH, we computed
new ADAM weights to re-weight the current ADAM sample to exploit the more
representative data in the NSDUH sample. The items we include in the reweighting include age, race, gender, current offense, flags indicating risk of drug
dependence, risk of drug abuse, a flag indicating risk of alcohol dependence or
abuse, and geographic location (non-MSA, large MSA, or small MSA). We estimate the probability that an observation in the combined NSDUH and ADAM
datasets is in ADAM. We then use this predicted probability to compute a weight
which is applied to the profile’s prevalence among all arrestees nationwide. Define ti = 1 if the observation is from ADAM (the convenient sample) and ti = 0 if
it is from NSDUH (a sample representing the target population more closely).
Then define wi = Pr(ti = 0|xi )/ Pr(ti = 1|xi ) ∀i ∈ Nc where Nc is the size of
the ADAM sample. One may further compute functions of these weights, e.g.,

The Research Design

17

normalized to 1, before using it to re-weight the convenient sample for analysis. After re-weighting, we confirmed that the re-weighted ADAM sample did
resemble the NSDUH data, at least on the attributes utilized in the exercise.
From that point onwards, we utilized the re-weighted ADAM data for all our
analysis.
2.2.3.

Drug Abuse Treatment Outcome Study (DATOS)

Funded by the National Institute on Drug Abuse (NIDA), the Drug Abuse
Treatment Outcome Studies (DATOS) began in 1990 with the goal of evaluating
substance abuse treatment outcomes. DATOS is a longitudinal study of 10,010
adults entering 96 participating treatment programs in eleven statistically representative cities from 1991 to 1993. DATOS evaluated the effectiveness of four
common treatment modalities on four primary topical domains: (1) cocaine
use, (2) HIV risk behaviors, (3) psychiatric co-morbidity and (4) criminal behavior. Treatment modalities included Outpatient Methadone Treatment (OMT),
Long-Term Residential (LTR), Outpatient Drug-Free (ODF), and Short-Term
Inpatient (STI). Data were collected at baseline and 3, 6, 12, and 60 months after
completion of treatment.
Data from DATOS were used to estimate the crime-reducing benefits of
treating drug involved offenders. That is, we wanted to link each profile, weighted
by its prevalence in the population, to the expected change in criminal offending
that would occur if that profile were treated. We perform the exercise by treatment modality so that we obtain estimates of the crime reducing benefits to be
expected conditional on arrestee attributes, treatment modality, and risk of drug
dependence or abuse. Moreover, we were able to obtain detailed crime reducing
benefits for all crimes as well as select sub-types (including drug related, fraud &
forgery, burglary, larceny, robbery, aggravated assaults, and sexual assaults).
DATOS contains detailed information on illegal activities one year prior to
treatment intake, the complete history of illegal activities prior to that, the illegal activities in the year following intake, and detailed information on our

18

To Treat or Not to Treat

attributes of interest. However, DATOS represents only participants entering
treatment—there are no counterfactual data. That is, there is no comparison
group studied which would generate information about expected offending for
non-participants. Thus, no data from DATOS are available that directly predict
how much crime was prevented by treatment. Therefore, we must interpolate
expected outcomes using information about expected offending predicted by
client attributes. We therefore generate a simulated counterfactual from these
data in order to estimate the crime reducing benefits to be expected from treatment. A technical discussion of the interpolation approach can be found in
Appendix I.
2.2.4.

Summary of the Elements of the Synthetic Data Set

Figure 2.1 graphically depicts the kind of data file we populated using data from
a various sources described above.
Each row in the figure represents one of the 40,320 profiles that are a crosscombination of observable attributes. The first column, “Profile’s Prevalence in
the Population of Arrestees” is a value developed from ADAM and NSDUH.
The next two columns use ADAM data to predict the expected proportion of
that profile that would be expected to be at risk of drug abuse and at risk of
drug dependence. The following columns describe the expected reduction in
the number of crimes, conditional on treatment. Each of the four treatment
modalities in DATOS are measured independently, and estimates are created for
both groups of drug-involved offenders (those at risk of abuse and those at risk
of dependence). Once these estimates are created, the total number of crimes
avertable by treatment is estimated by summing across profiles, weighting each
profile by its prevalence.
The next section describes the estimation strategy used to generate the values in figure 2.1. Once the cells in figure 2.1 were populated, we then calculated
the expected costs of delivering treatment in each modality (and an additional
cost to represent the costs to the court system of administering the program).

Dependence
SOURCE:
Re-weighted ADAM

@ Risk of
Dependence

@ Risk of
Abuse

@ Risk of
Dependence

@ Risk of
Abuse

@ Risk of
Dependence

@ Risk of
Abuse

Crime Type II

@ Risk of
Dependence

Crime Type II

@ Risk of
Abuse

Crime Type II

Treatment Modality 4
Outpatient Drug Free

Crime Type II

Treatment Modality 3
Outpatient Methadone

Crime Type II

Treatment Modality 2
Short-Term Inpatient

Crime Type II

Treatment Modality 1
Long-term Residential

Crime Type II

Crime Type I

Crime Type I

Crime Type I

Figure 2.1: Graphical depiction of the synthetic dataset.

…

Profile 2

Profile 1

Profile's
Prevelance
in the
Population
of Arrestees
Abuse

Expected Benefits that Accrue by Treating a Particular Profile Under …

Crime Type II
Crime Type I

SOURCE:
DATOS

Crime Type I

Crime Type I

Crime Type I

Crime Type I

Probability
that a
particular
profile will be
at risk of drug
…

The Research Design

19

20

To Treat or Not to Treat

We also translate the number of crimes into monetized values to account for
the variation in harms to victims and cost to the criminal justice system that is
a function of the severity of the particular crimes that are prevented by treatment. A description of the method to develop these costs and benefits follows
the section on estimation.
Finally, once the synthetic data were prepared, and all outcomes were estimated for each profile (that is, the reduction in offending for each profile, for
those at risk of drug abuse and dependence, and for each of the various treatment
modalities) we ran simulation models to compare a set of policy options to inform policy. That is, it is not enough to simply say that a profile will experience
x outcomes conditional on receiving y treatment, we must compare those outcomes to current policy, and to a set of possible policies. In particular, we are
interested in simulating an expansion of drug court-like programs, since these
programs have been demonstrated to deliver services of sufficient dosage that it
is reasonable to expect that they would yield results similar to the expected outcomes predicted by the DATOS study. The simulation models consider several
possible expansions of the drug court model, and these expansions are mainly
achieved by sequentially relaxing current drug court eligibility rules. A description of eligibility rules follows the description of the simulation models, which
in turn is followed by a section describing the findings.

Chapter 3
Estimation Strategy
In this section, we describe how the prevalence estimates were computed and
how the benefits from reducing new crimes by treating drug involved offenders
were derived. We also list a set of key assumptions that go into our analysis.
All of our estimation is based on using the empirical similarity between the
profiles and raw data sources. We explain the estimation and use of these similarity weights in details in Appendix IV. In short, the expected value of any
quantity (for example, the prevalence or the treatment effect) for a particular
profile is the weighted average of the same quantity across all observations in
the raw dataset. The weights reflect the empirical similarity of the profile to the
raw data set observations. This technique allows us to interpolate values from
the raw datasets onto the synthetic dataset, while allowing the functional form
of the links be very flexible.
3.1.

A PROFILE’S PREVALENCE IN THE POPULATION OF
ARRESTEES

Returning to figure 2.1, the first column, the profile’s prevalence in the population of arrestees is an estimate of the annual number of arrestees nationwide for
each of the 40,320 profiles in the dataset.

21

22

To Treat or Not to Treat

As noted in the previous chapter, we utilize a re-weighted version of the
ADAM dataset for estimating the prevalence of particular profiles in the population of interest. Unfortunately, the ADAM dataset contains information on
the number of arrests each year but not the number of arrestees. However, the
re-weighted ADAM dataset does provide information on the number of times
individuals were arrested in the year prior to the current booking. We use the
concept of a re-capture rate to convert the number of arrests into number of
arrestees. Note that if, for a particular profile, we have a low recapture rate then
the number of arrestees will be approximately equal to the number of arrests
(since they are being recaptured infrequently). On the other hand if, for a particular profile, we have a very high recapture rate then the number of arrestees will
be relatively low (since the same arrestees are being recaptured several times).
First, we estimate the number of bookings per year nationwide of a particular profile by interpolating this quantity from the re-weighted ADAM. Profiles
that are more similar to high booking rate observations in ADAM will have
higher interpolated booking rates than will profiles that are less similar to these
high booking rate observations. In a similar manner, we calculate the recapture
rate for each of these profiles. Once we estimate the re-capture rate, we can then
calculate the number of arrestees (as apposed to arrests). Note that the number
of arrestees is an appropriately scaled down (by the recapture rate) version of the
number of arrests per profile.
Finally, the estimated number of arrestees can then be combined with the
rate of risk of dependence and abuse to calculate the number of arrestees in each
profile that are in each condition. And thus, in this step we are able to fill in data
for the first three columns in figure 2.1. A detailed description of this process is
provided in the mathematical appendix.
3.2.

SIMULATED COUNTERFACTUAL

The next step in the analysis is to calculate the crime reduction benefits that can
be expected from treating drug involved offenders. There are several ways one

Estimation Strategy

23

can generate this quantity. First, and optimally, if we could randomize individuals into the treatment and control groups, then the difference between their
outcomes (say, recidivism) could provide us an average treatment effect. Or, in
the absence of randomization, we could use some quasi-experimental design and
use observational data to recover treatment effects. There exists an extensive
literature on establishing causal effects from observed data. Reviewing that literature is beyond the scope of this paper (see the exchange between Heckman
(2005a,b) and Soble (2005) for an extensive review of the issues and controversies
surrounding causal analysis). The common thread in all of the non-experimental
approaches to generating the treatment effect estimates is the need for an appropriate counterfactual. Since the same individual cannot be observed under
treatment and not under treatment, we need some way to generate an estimate
of what would have happened to treated individuals had they not been treated.
There are three essential components to the development of the counterfactuals. First, we have observed outcomes (e.g., recidivism) that we wish to compare. Second, we potentially have a set of observed attributes (e.g., age, race,
gender, etc.) that may be relevant to take into account when comparing those
who do and do not receive treatment. Finally, there is the unknown—what we
don’t know or see about the individual—that may be relevant for computing an
appropriate counterfactual. Experimental methods are designed to mitigate the
effect of unobserved states and traits to allow comparisons across those who do
and do not receive treatment. Typically, all available evidence is used to make
sure that the groups are as comparable as possible either by matching them,
weighting them, or randomly assigning them, and then multivariate regression
(or some variant thereof) is used to account for heterogeneity.
In this research effort, we take a different approach to estimating the crime
reducing benefits of treating drug involved offenders. We use data only on a sample of individuals receiving various forms of treatment. However, rather than
seek to identify an appropriate comparison group to compare the outcomes of
the treated group with, we simulate a sample of identical twins for each individ-

24

To Treat or Not to Treat

ual based on their attributes. What we are missing for this sample is the outcome
(e.g. recidivism) that would have been observed in the absence of treatment. We
simulate this quantity.
One of the most consistently documented criminological associations is the
link between prior and future criminal activity (Nagin and Paternoster 1991).
Individuals who were criminal in the past have a strong likelihood of being
criminal in the future. Although criminologists do not speak with one voice
about the explanation for this persistence in, and more interestingly desistance
from, criminal activity (Piquero et al. 2003), the theoretical debate underlying
this linkage centers on the causal interpretation attributed to the link between
past and future crime (Nagin and Paternoster 1991). None, however, deny that
this link exists. In a similar manner, it is a well established fact that the offending rate evolves non-monotonically—first increasing then decreasing—with age
(Farrington 1986). In this research effort, we utilize this link between past and
future offending as a way to generate plausible counterfactuals.
DATOS provides us information on how many crimes individuals committed one year prior to intake and then during the first year post-intake. A simple
comparison of the pre-intake and post-intake offending rate would be an incorrect way of assessing the effects of treatment precisely because of the age-crime
link noted above. Hence, despite knowing how much crime individuals committed post-intake, we lack an appropriate counterfactual to compare this number
to—how many crimes they would have committed had they not been treated.
To estimate this counterfactual, we model the link between the pre-intake offending rate and various individual attributes. Crucial among these are clients’
age and criminal history. Then, we use this model to project what the clients’
offending rate would have been had they aged by a year and increased their criminal history by a particular amount. We augment the criminal history by the
observed pre-intake offending rate. This yields a simulated offending rate one
year out for an arrestee who moved one year further along the age crime curve
and one who had a higher criminal history but did not receive treatment. We

Annual offending
rate at intake

Age Effect

AGE AT INTAKE

1 YEAR

Treatment effect: Reduction in the
annual offending rate from what
was anticipated

Criminal History Effect

The Factual

The Counterfactual

AGE

Age-crime curves (with low and high criminal history)
estimated from pre-treatment data

Figure 3.1: Graphical depiction of the treatment effects computation.

OFFENDING RATE

Anticipated annual offending rate at
age at intake + 1 years and more
criminal history

Estimation Strategy

25

26

To Treat or Not to Treat

treat this estimate as the simulated counterfactual. We then compare these simulated counterfactuals (for each profile) with the actual offending rates during the
one-year follow-up period to compute the treatment effect. Figure 3.1 provides
a graphical presentation of how we define the treatment effect.
Since the counterfactual is an exact replica (twin) of our sample members
so that all attributes are identical (with the only exception being that the twin
has aged by one year and has acquired some more criminal history) we control
for all observed and unobserved differences. We define the difference between
the factual and the counter-factual as the treatment effect. Note that the links
between offending and age as well as offending and criminal history are both
flexible functional form. As such, depending on who the individual is and how
old the individual is, the counterfactual could have a higher, lower or stable. The
advantage of this strategy over conventional quasi-experimental designs is that
we do not have to adjust the control group to make it comparable to the treatment group: every observable (and unobservable) attribute is identical. Thus,
we have generated an expected outcome for the treatment group one year into
the future by exploiting the relationship between their current offending behavior, age, criminal history, and other attributes.
Expected treatment effects were developed for each offender profile in our
synthetic dataset. Moreover, estimates were generated conditional on drug dependence or abuse and conditional on treatment modality.
3.3.

SIMULATED ELIGIBILITY

As discussed earlier, the drug court is the place within the criminal justice system
where long-term, high dosage treatment is most likely to be delivered. While
other substance abuse diversions exist in the criminal justice system, only drug
courts are designed to oversee the delivery of treatment that is consistently of
sufficient duration and dosage to modify behavior as predicted by DATOS. We
therefore use the drug court as a model for the delivery of services within the
criminal justice system.

Estimation Strategy

27

For the purposes of our study, the adult drug court model provides two
important pieces of information. The first important piece of information provided by drug courts concerns who is likely to be served if criminal justicebased substance abuse treatment goes to scale. From our synthetic data we are
able to create estimates of the benefits of serving different profiles with varying
attributes. However, these profiles are artificial, and do not reflect real-world
decision-making about the trade-offs between prosecuting substance abusing offenders who are likely to be found guilty and be sentenced, or, deferring prosecution while these offenders are treated in the community. Operational drug
courts, however, make explicit policy choices between serving and prosecuting
drug-involved offenders based on observable offender attributes. These choices
are reflected in choices about who is, and is not, eligible for drug courts. We use
this information to estimate a conditional eligibility probability for each profile
and assess whether current eligibility rules lead to a net benefit. We then incrementally relax those eligibility rules to simulate whether individuals who are
currently not eligible for drug courts can be efficiently treated.
Second, drug courts give us a place to observe the expected costs of delivering services to drug-involved offenders. That is, the expansion of substance
abuse treatment would likely yield two additional sources of cost—the cost associated with the direct provision of treatment, and the costs of coordinating
and monitoring service delivery. In this study, we use extant data on treatment
costs, as described later. We also estimate the costs of drug court that are associated with supervising offenders and model those expenses in our cost model.
In sum, we do not observe treatment costs from extant drug courts, only the
costs of supervision, and derive treatment cost estimates from other sources.
The discussion that follows describes the survey data used to stratify profiles by
eligibility rules. The section that follows describes drug court cost.

28
3.3.1.

To Treat or Not to Treat

Drug Court Survey Data Describing Eligibility Criteria

Data on adult drug court eligibility were gathered from a survey of 600 drug
courts in 2005 administered as part of the Multi-Site Adult Drug Court Evaluation (MADCE) conducted by the Urban Institute, RTI International and the
Center for Court Innovation. The web-based survey queried drug court administrators about 70 different characteristics of court operation. Several of these
items pertained to their court’s eligibility criteria. Other data include the location, size and demography of their drug court, which we used to identify the
probability that a profile would be served by each type of drug court. The survey sample includes all adult drug courts that had been in operation at least one
year during FY 2005. In total, 378 (63%) of adult drug courts responded to the
survey.
For this portion of the study, we sought to estimate the probability that each
profile would be eligible for drug court participation. In order to estimate the
probability of drug court eligibility for each profile, relevant survey questions
were mapped to attributes that correlate to eligibility in the synthetic dataset.
In most cases, there was a variable in the survey that measured an identical construct as a variable in the synthetic dataset. For instance, the survey reports that
many drug courts exclude as potential participants anyone with prior violence,
and prior violence is also observable in the synthetic data. Across all adult drug
courts, dozens of eligibility restrictions can be found. Some of those eligibility
rules are subjective, and others are not routinely recorded in administrative data.
Thus, not all of those attributes are observable in the synthetic data. However,
we were able to identify six attributes (number of prior arrests, past violence,
past treatment, age, gender, and alcohol abuse) that are used to determine eligibility
However, several survey questions were not perfect matches, but a reasonable approximation could be developed. For instance, geographic location is categorized as urban, suburban, or rural in the synthetic data, but was defined as
MSA with > 1 million residents, MSA with < 1 million residents and non-MSA

Estimation Strategy

29

on the drug court survey. To make these variables comparable, we recoded MSA
> 1 million as “urban,” MSA < 1 million was coded as “suburban” and non-MSA
was coded as “rural.” Likewise, while the synthetic dataset specified numbers of
prior arrests, the drug court survey asked administrators about the number of
prior convictions offenders were allowed to have while retaining eligibility. To
create a consistent metric, the number of prior arrests was multiplied by 0.66,
the weighted average probability of conviction conditional upon arrest, for all
index crimes (following Harrell, Roman and Cavanagh 1998). We identified individuals with prior treatment history, who were determined to be ineligible if
the individual either failed to successfully complete prior treatment or were past
enrollees in drug court (regardless of the outcome). A court was classified as
excluding arrestees with an active criminal justice status if they exclude individuals with another pending criminal case, or individuals currently on probation
or parole. Table 3.1 describes the percentage of drug courts excluding offenders
with each of the six attributes. In total, we estimated eligibility probabilities for
all ten attributes used to construct the profiles. No drug court excluded based
on race, so those data are not included in table 3.1. Eligibility based on drug
use severity (at risk of abuse or at risk of dependence) and the availability of
treatment are discussed below.
There is substantial variation across offender attributes in the likelihood of
being excluded (found ineligible) for drug court. Only a handful of drug courts
exclude offenders on the basis of age. Though few drug courts exclude offenders
based on number of prior arrests, the overwhelming majority of drug courts
(88%) exclude offenders with a violent history. Approximately half of drug
courts exclude offenders with prior treatment history and about one third exclude offenders with a history of alcohol abuse. Half of all adult drug courts exclude offenders who are currently on probation or parole or have another open
criminal case. The overall percentage of arrestees who are excluded is high, because the presence of a single exclusionary attribute is generally sufficient for
an individual to not be accepted into drug court. In addition to limiting the

30

To Treat or Not to Treat

Table 3.1: Percent of responding adult drug courts considering individuals eligible for participation, by select attributes
Criteria

Pr(eligible)

Offender’s Age
Age <= 20
Age > 20
Offender’s Prior Criminal History
Number of Prior Arrests > 2
Number of Prior Arrests > 5
Number of Prior Arrests > 10
Number of Prior Arrests > 20
Current Most Serious Offense
Violent
Property
Drug
Other
Offender has past violence
Offender has past treatment history
Offender has active criminal justice status
Offender has alcohol abuse problems

0.99
1.00
0.98
0.93
0.85
0.85
0.37
0.94
0.99
0.93
0.12
0.51
0.50
0.66

Source: Urban Institute analysis of MADCE surveys.

number of individuals treated in drug court due to eligibility limitations, drug
courts also limit the number of people who are treated due to limitations on the
number of clients who can participate in a drug court at any one time; we return
to this topic below.
3.3.2.

Estimating the Size of the Drug-Court Eligible Population

The size of the drug court eligible population was estimated in three steps. In the
first step, a probability of eligibility for each profile in the synthetic database was
estimated. To do this, we estimated the probability that each profile would be
found to be eligible for drug court by multiplying the conditional probabilities

Estimation Strategy

31

of treatment for each of the ten characteristics along which the synthetic dataset
was stratified. Each profile’s probability of drug court eligibility is based on the
assumption that each characteristic is statistically independent. So, for example,
we would observe that a profile included those with past violence (which had
a 88% likelihood of exclusion) and included individuals with alcohol problems
(which a 34% chance of exclusion). Thus, the conditional probability of exclusion was 92% on those two characteristics alone. This process was then repeated
for the other five eligibility restrictions.
The second step in the eligibility estimation process was to weight the probabilities in the first step by the probability that an arrestee at risk of drug abuse
and dependence. Based on responses to the MADCE survey, all drug courts
were assumed to accept those at risk of drug abuse (those offenders with less serious substance abuse problems) as eligible for drug courts. Thus, for this group,
there was no decrease in the probability that a profile was eligible. However,
many drug courts (61.5%) exclude those with the most serious drug problems.
So, we multiply the probability that a profile is eligible by 38.5% for all profiles
in order to estimate the number at risk of drug dependence who are eligible for
drug court participation.
The third step is to adjust these probabilities by a scaling factor to account
for the limited number of drug court treatment slots. That is, even though most
arrestees at risk of drug abuse or dependence are ineligible for participation in
drug courts based on the eligibility criteria described above, there are still more
individuals eligible for drug court than there are drug court placements. On
average, we estimate that 16% of profiles for arrestees at risk for drug abuse are
eligible for drug court. We estimate that 6% of profiles for arrestees at risk for
dependence are eligible for drug court. Though there is considerable variation,
for both groups more than half of profiles have less than a 10% probability of
drug court eligibility. Combining both at risk populations, the weighted average probability of drug court eligibility was 7%, for a total of 109,921 drug court
eligible arrestees. Again, there are too few drug court slots to treat all of those

32

To Treat or Not to Treat

109,921 eligible, so we must scale down the eligible number into order to estimate the size of the population that is both eligible and for whom a treatment
slot is available.
To complete the third step and estimate the number of drug court eligible
arrestees, we first estimated the number of drug court slots (109,921) using the
survey of drug court administrators. Next, we multiply the probability that a
profile is eligible in the second step, by the probability that an eligible profile
would actually secure one of the scarce drug court slots. We are then able to
make two important estimates—the number of individuals who are eligible for
drug court, and the number of eligibles who actually receive treatment under a
drug court regime.
Among drug courts that responded to the survey, the average number of
participants currently enrolled was 93. In order to devise a national estimate
of the number of drug court clients annually enrolled, we assume that 93 is
the average number of drug court clients. Thus, we assume that the average
drug court that responded to the survey is the same as average drug court that
did not respond to the survey. Rossman et al. (2008) reports that drug courts
from larger jurisdictions were more likely to respond than drug courts from
smaller jurisdiction, so this is probably a conservative assumption. Finally, the
number of enrollees per court per year (93) was multiplied by 600, which is the
population of adult drug courts in operation in 2005 that had been in operation
for at least one year. Rossman et al. (2008) report substantial efforts were made
to identify all drug courts meeting these criteria, and that it is likely that some of
the non-responding drug courts were not currently in operation, so this is also
probably a conservative assumption. Thus, we estimate that there were 55,365
adult drug court participants in 2005.
As shown in table 3.2, there were substantially more arrestees eligible for
drug court than there were treatment slots. To estimate the number of at-risk
arrestees who were actually treated in drug court, we weight the eligible population by the probability a slot would be available. Since the number of available

33

Estimation Strategy

Table 3.2: Population of arrestees eligible for drug courts

Size of the at-risk population
Size of the drug court-eligible
population
Estimated number of drug
court slots
Percentage of drug court
eligible arrestees who were
treated at drug court
Percentage of all arrestees who
are eligible and treated at drug
court

Urban

Rural

Suburban

Overall

525,224
39,238

485,223
36,250

460,891
34,433

1,471,338
109,921

18,998

25,106

11,261

55,365

48.4%

69.3%

32.7%

50.4%

3.6%

5.2%

2.4%

3.8%

Source: Urban Institute analysis of MADCE surveys.

slots and the drug court eligible population both vary by the size of their jurisdiction, we calculate these probabilities by type of the jurisdiction.
In summary, of the almost 1.5 million arrestees at risk of drug abuse or dependence, 109,921 (about 7%) met drug court eligibility requirements. Of the
109,921 eligibles, approximately half (55,364) were actually enrolled in a drug
court program. In aggregate, just 3.8% of the at-risk arrestee population was
treated in drug court.
3.3.3.

Estimating the Number of Individuals Currently Receiving Drug
Treatment

In order to estimate the cost-effectiveness of treating arrestees, we must determine what type of treatment would be received. There are no existing estimates
of the number of individuals in drug court who receive each of the four treatment modalities considered in this paper. As such, we relied on estimates of
the number of individuals receiving each of the four treatment modalities nationwide, irrespective of delivery via drug court. To create these estimates, we
multiplied the number of drug court slots by the proportion of individuals na-

34

To Treat or Not to Treat

Table 3.3: Estimated number of individuals receiving each treatment modality in drug courts

Long-term Residential
Short-term Residential
Outpatient Methadone
Outpatient Drug-Free
Total

Urban

Rural

Suburban

Overall

1,221
2,339
3,396
12,042
18,998

1,613
3,091
4,488
15,913
25,105

724
1,386
2,013
7,138
11,261

3,558
6,816
9,897
35,093
55,364

Source: Urban Institute analysis of MADCE surveys.

tionwide who receive each of the four treatment modalities. Thus, we implicitly
assume that treatment delivered through drug courts follows the same distribution of treatment modalities nationally. Table 3.3 displays these results by
regional type.
Across all three regional types, outpatient drug-free therapy was, by far,
the most common service offered to substance-involved individuals, comprising
63% of treatments. Methadone (18%) was the second most common treatment
followed by short-term residential (12%) and long-term residential (6%). As we
incrementally relax the eligibility restrictions to test the cost-effectiveness of different policy regimes later in this paper, the same approach is used. So, for
example, when we consider the cost-effectiveness of treating all drug court eligibles, regardless of whether there is currently a treatment slot, we would apply
the same weighting scheme as described above to estimate the distribution of
those drug court eligibles across treatment modalities.
3.4.

COST AND BENEFIT ESTIMATES

In the language of cost-benefit analysis, the eligibility estimates described in the
preceding section are quantities. That is, first we estimate how many individuals
would be found in each policy regime (e.g., where we could consider the costeffectiveness of treating only those who are eligible for drug court, all who are

Estimation Strategy

35

eligible for drug court regardless of treatment availability, all at-risk arrestees,
or some other combination). Then, we estimate how many crimes would be
averted if those policy regimes were implemented. The simulation results are
described in the next section. Once we have estimated these quantities they
must be multiplied by the price of each outcome to estimate the cost or benefit
that results. That is, the cost of treating any given profile is the product of the
price of the outcomes and the number of outcomes.
Price therefore has two components. The first component is the value of the
resources that must be added in order to implement that policy regime (this is
commonly referred to as the cost, but in cost-benefit parlance the net cost refers
to the product of prices and quantities). In our models, there are two prices
associated with each policy regime (e.g., two kinds of resources consumed in
administering each policy). There are the prices associated with each of the four
treatment modalities and there are the prices associated with the criminal justice
system’s oversight of treatment. We estimate the first set of prices from extant
data for each of the four treatment modalities. We estimate the second set of
prices from a survey of a small sample of drug courts undertaken as part of this
study and the MADCE. It is worth noting that the drug court prices are just
the price of criminal justice oversight. Treatment prices are not included in the
estimate of the price of criminal justice oversight, they are estimated separately.
Second, there are the prices associated with changes in the number of crimes.
That is, if a policy regime results in fewer crimes, than the price is the savings
to private citizens (from reductions in the number of victimizations) and to the
criminal justice system (from reductions in the number of offenses investigated
and the number of offenders processed through the system). If the policy leads
to additional crimes, than the prices will reflect the loss to private citizens who
experience more victimizations and to the criminal justice system which must
investigate more crime and process more offenders. We label these prices as
benefits, and note that depending on the outcome of the simulations, the benefits
may be positive or negative.

36

To Treat or Not to Treat

In the section that follows, we first describe how the costs of the DATOS
treatment modalities were estimated. This is followed by a discussion of the
estimation of costs of drug court administration. Finally, we describe how the
benefits of changes in the policy regimes from reductions (or increases) in the
number of crimes were estimated.
3.4.1.

Treatment Price Estimates

The cost of each new policy regime is divided into two categories: (1) the cost of
providing four different drug treatment modalities (long-term residential treatment, short-term residential treatment, outpatient methadone treatment and
outpatient drug-free treatment) and (2) the administrative cost of drug court as
a conduit for delivery of these treatment services. Data on the cost of treatment
modalities is drawn from DATCAP, a data collection instrument and interview
guide designed in the early 1990s to assess treatment programs along a set of
standard accounting and economic principles. Resource categories include personnel, supplies and materials, contracted services, buildings and facilities and
other miscellaneous items (Bradley French and Racal 1994; Roebuck French and
McClellan 2003). Roebuck, French and McClellan gathered information on 53
outpatient and 32 residential (inpatient) programs between 1993 and 2002, calculating average costs for a number of adult treatment modalities including longand short-term residential treatment, outpatient methadone treatment and outpatient drug-free treatment. Table 3.4 details the average costs for each of these
modalities.
The cost of methadone treatment (over an average of 99 weeks) is $8,609.
The cost of long-term residential treatment (20 weeks) is $16,448 and the cost of
short-term residential treatment (3 weeks) is $3,287. All costs have been translated into 2007 dollars, using the Consumer Price Index as a deflator.

37

Estimation Strategy

Table 3.4: Costs associated with four treatment modalities
Average length Economic Price per
of stay (weeks)
treatment episode
Long-term Residential
Short-term Residential
Outpatient Methadone
Outpatient Drug-Free

20
3
99
17

$16,448
$3,287
$8,609
$3,557

Source: Roebuck, French and McClellan gathered information on 53 outpatient and 32 residential (inpatient) programs between 1993 and 2002.

3.4.2.

Drug Court Price Estimates

To estimate the price of treatment delivery using a drug court as the delivery
mechanism, we conducted phone interviews with fifteen drug court administrators located in New York, Florida, South Carolina, Illinois and Washington
State.1 In order to estimate personnel costs, drug court administrators were
asked to provide fully-loaded salaries of personnel involved in drug court who
were not directly involved in the provision of treatment. In addition, administrators were asked to estimate the percentage of each staff member’s time that
was allocated to drug court. The costs of monitoring offenders was estimated as
the product of the number of drug tests administered per offender by the number of offenders given the average length of enrollment in drug court. Finally,
the costs of offender fines and sanctions were considered. These costs included
fees and fines paid for by drug court clients as well as the cost of jail days assigned
as a punishment for failure to comply with court rules.
Table 3.5 lists the per-individual costs of drug court, excluding the cost of
treatment. These costs include (1) personnel not directly involved in treatment,
e.g. not including drug court clinical staff, (2) drug and alcohol testing and
fees and (3) fines and jail terms during the course of drug court. The costs of
treatment are not included in these estimates. Capital costs are also not included
1

This portion of the study was done in conjunction with the MADCE. The fifteen sites
represent a sample of the 23 drug courts participating in that study (67%).

38

To Treat or Not to Treat

Table 3.5: Administrative costs for drug courts
County

Average Price

Osceola (FL)
Volusia – Deland (FL)
Volusia – Daytona (FL)
Fulton (GA)
York (SC)
Auburn (NY)
Wayne (NY)
Kane (IL)
Finger Lakes (NY) (misdemeanor)
Finger Lakes (NY) (felony)
Cook (IL)
Syracuse (NY)
Thurston (WA)
King – Seattle (WA)
King – Kent (WA)

$2,313
$9,826
$9,826
$4,003
$3,160
$5,516
$8,390
$4,087
$3,528
$7,260
$5,071
$1,477
$6,905
$3,830
$3,830

Weighted (by size) Average

$4,060

Source: Urban Institute survey of drug court administrators.

in these estimates. After weighting to account for variation in drug court size,
the average price of drug court is $4,060.
Table 3.6 describes the price of four treatment modalities that will be used to
simulate the costs of going to scale. These are just $4,060 (from table 3.5) added
to the cost estimates provided in table 3.4.
We note that it is possible that our price estimates may overestimate the true
average price of treatment if drug courts were substantially expanded. Many of
the costs of treating drug court clients are fixed and do not vary (or vary minimally) with the size of the drug court. For example, a drug court is likely to
have a single drug court coordinator and a single judge even if the population of
the court increases substantially. In the presence of fixed costs, average costs will
decline as the number of clients enrolled increases. Since increasing the scale of

39

Estimation Strategy

Table 3.6: Price for four treatment
modalities
Modality
Long-term Residential
Short-term Residential
Outpatient Methadone
Outpatient Drug-Free

Price
$20,508
$7,347
$12,669
$7,617

Source: Urban Institute analysis of
Roebuck, French and McClellan and
MADCE survey data.

drug court entails increasing drug court enrollments, the cost of treating drug
court clients is not expected to increase linearly. Instead, the cost per client is
expected to diminish at the margins. Thus, the real price of drug court plus
treatment may be lower if the average size of the drug court increases substantially. However, we cannot model this change in price since we cannot observe
this in our data (even the largest drug courts in our sample are smaller than the
average drug court would have to be if every drug involved arrestee were eligible
for treatment). This results in a conservative bias if any. That is, if a change in
policy regime yields a positive benefit to cost ratio it will have done so using
what are likely to be the upper bound of expected prices. If prices were actually
lower, the benefit to cost ratio would increase.
3.4.3.

Estimates of the Benefits from Crime Reduction

The purpose of treating drug-involved arrestees is to reduce anti-social behaviors, including crime. If this occurs, the burden on the public and governmental
agencies from offending will be reduced. Thus, the critical benefits to consider
in our models are those associated with reduced offending. There are two potential groups of beneficiaries of reduced offending: (1) potential victims (private
citizens) whose welfare is enhanced as the number and severity of offending by
drug involved offenders is reduced and (2) public agencies (and taxpayers) which

40

To Treat or Not to Treat

will consume fewer resources in the investigation and processing of offenders if
there are fewer crimes committed as a result of treatment.
Estimating the benefits to public agencies from reduced crime is relatively
straightforward. First, we estimate the average unit costs to two public agencies—
police agencies and departments of correction—of investigating, arresting, and
incarcerating offenders. Data on the cost of arrest were drawn from estimates
in Roman, Woodard, Harrell and Riggs (1998). Data on the cost of supervision
come from a variety of sources. Data on the probability of conviction given
arrest and the probability of being assigned prison, jail or probation given a conviction comes from DuRose and Langan (2004). Data on the cost of state prison
comes from the Bureau of Justice Statistics (Stephan 2001). Data on the daily
cost of jail is derived from estimates in Roman and Chalfin (2006).
We repeat the same process for the estimation of benefits to private citizens.
Benefits to private citizens occur when the number and/or severity of crimes are
reduced. To estimate these benefits, we first estimate the unit price of a victimization. The unit price of a victimization has two components: tangible and intangible costs. Tangible costs of crime include direct costs of victimization such
as medical bills, rehabilitation costs, and lost wages from being unable to work
and are estimated from data on victim injuries. Intangible costs include psychological harm associated with victimization, including fear, pain, and suffering
and are estimated using the sizes of jury awards made by civil juries. We use extant estimates of the costs of victimization to estimate the benefits of drug treatment delivered via drug court. The cost of harms to victims for aggravated assault, other assaults, robbery, burglary, larceny/theft, stolen property offenses,
fraud and drug offenses are drawn from five sources extant economics of crime
literature: Cohen (1988), Cohen, Miller and Rossman (1993), Miller, Cohen and
Wiersma (1996), Rajkumar and French (1997) and McCollister (2007). In order
to reduce the degree to which final results are sensitive to changes in the choice of
monetized harms, for each offense category, an average of extant estimates was
taken. These estimates are reflected in the column entitled ‘Cost to Victims’ in

41

Estimation Strategy

Table 3.7: Cost of offending, pre-sentence

Aggravated Assault
Robbery
Burglary
Larceny/Theft
Stolen Property
Drug Offenses

Cost to

Cost of

Pre-sentence Cost

Victim

Arrest

Detainment

Adjudication

$47,009
$30,253
$2,643
$819
$819
$31

$2,603
$2,563
$2,563
$675
$675
$675

$1,080
$1,080
$1,080
$1,080
$1,080
$1,080

$5,502
$5,502
$5,502
$2,751
$2,751
$5,502

Source: The costs of crime to victim, both tangible and intangible are estimated
as the average of estimated prices from Cohen (1988), Cohen, Miller and Rossman
(1993), Miller Cohen and Wiersma (1996), Rajkumar and French (1997). Estimates
of the cost of arrest are from Roman, Woodard, Harrell and Riggs (1998). For
offenses not reported, we assume an arrest cost of $675. Data on the length of
pre-sentence detainment come from Roman, Woodard, Harrell and Riggs (1998).
These data are not available by offense. Roman, Woodard, Harrell and Riggs (1998)
report a per minute trial cost of $3.50. We assume a mean adjudication length of
40 hours for murder and rape; 10 hours for larceny and stolen property offenses
and 20 hours for all other offenses. Data on the daily cost of jail are from Roman
and Chalfin (2006).

table 3.7. The expected costs of supervision have been expressed in net present
value, discounted at a rate of 5% per annum.
Next, we estimate the cost of incapacitating convicted offenders. First, we
calculate the likely disposition for a convicted offender (table 3.8), since the costs
of probation, jail and prison vary, following Durose and Langan (2004).
We then calculate the expected time served for each sentence type (table 3.9).
These expected sentence lengths are then multiplied by the average expected
percentage of the sentence to be served to yield the expected length of stay, by
sentence type, by crime (not shown).
The data in tables 3.7, 3.8 and 3.9 can then be combined in table 3.10, to show
the total expected cost of crimes to both victims and public agencies. Costs at
each stage of processing are multiplied by the probability that the stage had a
positive outcome (e.g., the costs of arrest are only counted for those cases where

42

To Treat or Not to Treat

Table 3.8: Probability that an offender is sentenced to probation, jail, or prison
Prison
Aggravated Assault
Robbery
Burglary
Larceny/Theft
Stolen Property
Drug Offenses

Jail

Probation

42% 29%
71% 15%
46% 26%
36% 31%
36% 31%
38% 27%

29%
14%
28%
33%
33%
35%

Source: Data on the probability of each type of sentence
is developed from Durose and Langan (2004).

Table 3.9: Estimated number of months an offender is sentenced to probation, jail or prison, and total sentencing costs
Probation
(mos)
Aggravated Assault
Robbery
Burglary
Larceny/Theft
Stolen Property
Drug Offenses

54
91
50
34
34
45

Jail Prison % Sentence
(mos) (mos)
Served
7
11
7
6
6
6

39
52
40
36
36
36

66%
58%
49%
52%
52%
43%

Cost of
Sentence
$22,736
$43,932
$20,378
$13,062
$13,062
$11,609

Source: Data on the cost of incarceration in state prisons comes from Stephan (2001).
Data on the daily cost of jail comes from Roman and Chalfin (2006).

$47,009
$30,253
$2,643
$819
$819
$803
$31

56%
26%
13%
18%
16%
16%
0.025%

56%
26%
13%
18%
18%
43%
20%

$2,603
$2,563
$2,563
$675
$675
$675
$675

$5,502
$5,502
$5,502
$2,751
$2,751
$5,502
$1

$22,736
$43,932
$20,378
$13,062
$13,062
$13,593
$1

Cost of
Cost of
Cost of
Arrest Adjudication Sentencing

$54,436
$36,066
$4,233
$2,095
$2,095
$2,280
$33

Total Cost
to Society

Source: Data on the probability a committed crime is reported is estimated from Sourcebook of CJS 2002, p 275 Table 4.19.
Probability of an arrest is derived from Crime Reported to Police (BJS). Data on the probability of each type of sentence and
the percentage of time served come from Durose and Langan (2004).

Aggravated Assault
Robbery
Burglary
Larceny/Theft
Stolen Property
Fraud
Drug Offenses

Cost to Prob of
Prob of
Victims a Report an Arrest

Table 3.10: Estimates of the total cost to society.

Estimation Strategy

43

44

To Treat or Not to Treat

an arrest was made).
The first column of table 3.10 is the cost to victims of a crime, which is the
same data as shown in table 3.7, and is the total cost to private citizens from a single criminal incident of each type. The other columns in table 3.10 describe the
costs to the criminal justice system from each crime. Unlike private costs, public costs vary by the likelihood that the average case proceeds to each subsequent
stage of processing. The total costs to the criminal justice system then are the
sum of the conditional probability of an event (multiplied by the price of each
event). That is, the criminal justice costs only occur if an event occurs; for instance, if a crime is not reported, than there are no criminal justice system costs.
So, for instance, the total cost to the criminal justice system of a sexual assault
is $4,464 multiplied by the probability that a crime is reported (43%) multiplied
by the probability that an arrest is made, for a total of $845. The same process
is applied to expected cost of sentencing, so the average cost of sentencing per
committed crime is 67, 038 ∗ 0.43 ∗ 0.44, or $12,864.
Generally speaking, as the seriousness of the crime decreases, the proportion
of the social costs that fall on public agencies (as opposed to victims) decreases.
For example, while costs to victims comprise 87% of the cost of an aggravated
assault, they comprise just 38% of the cost of a theft. Thus, given that the effect sizes associated with the various treatment modalities are positive, potential
victims are expected to reap the greatest benefits of expanding drug treatment to
offenders whose offending is primarily violent. Public agencies are expected to
see the most savings if drug treatment is expanded to offenders whose offending
is comprised primarily of drug and property offenses. Next, we use data from
the impact analysis to estimate the number of arrests and convictions that were
prevented by drug treatment via drug court.
3.5.

KEY ASSUMPTIONS AND CAVEATS

There are several assumptions concerning the data and the model that should
be noted. First, the treatment effects we have computed from the DATOS

Estimation Strategy

45

data are based on underlying data that was reported regarding arrests (not offenses). Not every crime is reported and not every reported crime is cleared.
Therefore, prior to our analysis, we computed a scaling factor that converts the
number of arrests into the number of offenses. This scaling was based on available information on crime reporting rates and clearance rates. We obtained data
for the clearance rates from the 2003 Sourcebook of Criminal Justice Statistics
(http://www.albany.edu/sourcebook/) by gender and race groups. We obtained
the reporting rate from Hart and Rennison (2003). Details on the conversion
factors are available from the author upon request.
Second, the prevalence estimates we report are for potential clients that would
accept treatment if offered. In our experience with substance abuse diversion
and alternative to incarceration programs suggests that only those who are likely
to be found guilty are likely to enroll (since a plea is generally required for admittance). Thus, we need some way to identify potentially guilty clients. Every
year a proportion of arrests will be declined for prosecution and every year a
proportion of defendants will not be convicted. Hence, we created a scaling factor that converts the total number of arrestees for a particular profile into the
total number of arrestees who are probably guilty. To do so, we used data on
conviction rates and declination rates. These data were obtained and used at the
offense type level. Conviction rates were obtained from the 2003 Sourcebook
of Criminal Justice Statistics (http://www.albany.edu/sourcebook/) and declination rates were obtained from Chapter 2 of the 2003 Compendium of Federal Justice Statistics (http://www.ojp.gov/bjs/abstract/cfjs03.htm). Details on
these data are also available from the authors upon request.
Third, in both DATOS and the NSDUH, several of the questions needed
to compute a drug dependence or abuse score were either not available or were
worded slightly differently. For example, the question relating to whether or not
respondents had used drugs (or alcohol) to alleviate feelings of sadness, anger, or
boredom was not available. In our analysis, we have identified the closest proxy
for the variables used in ADAM. Despite the slightly different definitions, we

46

To Treat or Not to Treat

confirmed that our definitions did not create large imbalances in the data sets.
For example, across all data sets used, we found that, of respondents at risk of
drug dependence or abuse, the number at risk of dependence were about three
times as large as the proportion of respondents at risk of abusing drugs.
Fourth, once interpolated onto the synthetic data, we combine and transform our estimates in various ways. This necessitates the combination of their
variances as well. Combining the variances of two or more random variables is
straight forward if we can make the assumption that they are independent. In
our analysis, since the estimated variances are conditional on profile attributes,
we need only make the less restrictive assumption of conditional independence.
In other words, we assume that for all individuals of a particular profile, the
variation in, say, the prevalence of drug dependence is unrelated to variation in,
say, the expected treatment benefits. We recognize that this is a limiting assumption and that some of our variance estimates may be biased (either too small or
too large). Unfortunately, combining variance estimates across several thousand
profiles would be extremely complicated if we were to permit there to be covariances. Fortunately, the point estimates of all quantities should be unaffected
by this assumption.
Fifth, the results are very sensitive to the selection of a price of crime to victims. We modeled the data using Cohen et al. (1993) and Rajkumar and French
(1997) and found an overall benefit to cost ratio of 2.73:1 for the current drug
court regime. We re-ran the models using a blended estimate of the five most
cited estimates of the costs of crimes to victims and this results in a much smaller
estimate of the benefits of the current drug court regime of 2.14:1. Although
none of results changed, we note that the estimates are sensitive to price.
Finally, we note that there are three kinds of transformations we perform
on estimated quantities in the synthetic data that necessitate computing new
variances. These include scaling, summing and taking products. A description
of our approach can be found in the mathematical appendix.

Chapter 4
Findings
In this section, we discuss our findings. We begin with a discussion of the estimated prevalence of drug abuse and drug dependence, which constitute the
population of potential treatment clients, and then present findings regarding
the number of crimes avertable by going to scale.
4.1.

PREVALENCE

Table 4.1 presents our estimates of the number of individuals arrested annually
who are either at risk of drug dependence or of abusing drugs. We estimate that
roughly 1.15 million potential clients are at risk of drug dependence and roughly
322,000 are at risk of abusing drugs. Together this constitutes about 1.47 million
arrestees who are probably guilty and at risk of drug dependence or abuse. The
distribution of client attributes varies by the severity of drug problems. For
instance, 23% of those at risk of dependence are female, compared to 18.5% of
those at risk of abuse. The biggest difference between those at risk of abuse and
dependence concerns prior treatment. Slightly less than 40% of those at risk
of dependence have a prior treatment episode, compared to slightly more than
60% of those at risk of abuse. The other notable difference is that 44% of those
at risk of dependence also have problems with alcohol, compared with only

47

48

To Treat or Not to Treat

37% of those at risk of abuse. Since these latter two differences are currently
used to determine eligibility for criminal justice system-based treatment, those
differences will have important implications for the effectiveness of different
eligibility regimes. This is discussed in greater detail in the following section.
Our estimates are based on a population of potential clients for criminal
justice system-based treatment, and includes only those who are at risk of dependence or abuse, and likely to be found guilty. We are not attempting to
estimate the prevalence of drug use among arrestees. Thus, we expect our estimates of the number of potential clients (those at risk of drug abuse and drug
dependence) to be less than the total number of drug users in the arrestee population for two reasons. First, there are some arrestees who use drugs, and/or
are under the influence at the time of their arrest, but who are not at risk of
dependence or abuse. Second, not every arrestee is probably guilty, and therefore eligible for treatment under court supervision. Brecht et al. (2003) report
findings from a study testing similar hypotheses, but focuses on drug use among
arrestees, rather than just those at risk of abuse and dependence, and who are
probably guilty. Brecht et al. finds that nationwide nearly 6.4 million arrestees
are drug users. Moreover, they find that, among arrestees nationwide, the number of male drug users is nearly three times the number of female drug users.
In our analysis, the number of potential clients are lower but we find a similar
break down by gender (at least among clients at risk of drug dependence). In a
similar way, they also find that the prevalence of drug use remains fairly stable
among arrestee of all ages. Our analysis mirrors this finding, albeit on a smaller
scale.
4.2.

CRIMES AVERTABLE BY TREATMENT

Next, we estimate the reductions in recidivism rates to be expected by treating
potential clients under various modalities. We find that treatment in each of the
domains substantially reduces recidivism. For those at risk of drug dependence,
long-term residential reduces recidivism by 34%, short-term inpatient by 19%,

49

Findings

Table 4.1: The estimated prevalence of potential clients nationwide.
Clients at risk of dependence
Low
Mean
High

Clients at risk of abuse
Low
Mean
High

All
1,145,034 1,149,019 1,153,004 320,090 322,320 324,550
Gender
Male
878,933 882,668 886,403 260,674 262,833 264,992
Female
264,961 266,350 267,740 58,928 59,487 60,046
Race
Black
417,079 419,299 421,518 120,907 122,109 123,311
White
388,685 390,764 392,842 89,852 90,760 91,667
Other
336,381 338,956 341,532 107,807 109,451 111,096
Current Offense
Violent
191,877 193,387 194,898 74,962 75,909 76,856
Property
313,127 315,231 317,334 64,899 66,102 67,305
Drug
387,348 389,714 392,079 97,667 98,824 99,981
Other
248,795 250,687 252,579 80,348 81,485 82,622
Any Violent History
Violent History
616,959 620,136 623,313 169,804 171,526 173,248
No Violent History 526,477 528,883 531,289 149,376 150,794 152,212
Any Treatment History
Treatment History
692,490 695,608 698,727 125,848 127,407 128,966
No Treatment History 450,930 453,411 455,891 193,318 194,913 196,508
Any Alcohol Problems
Alcohol Problem
638,779 641,810 644,841 200,606 202,405 204,205
No Alcohol Problem 504,622 507,209 509,796 118,597 119,915 121,232
Geographic Location
Rural
381,142 383,590 386,039 100,192 101,633 103,073
Urban
383,593 385,815 388,037 74,171 75,076 75,982
Suburban
377,390 379,613 381,837 144,169 145,611 147,053
Current Age
Age: 20
170,093 171,410 172,726 48,167 48,858 49,548
Age: 25
177,994 179,336 180,679 47,670 48,335 49,000
Age: 30
177,591 178,985 180,379 48,472 49,152 49,832
Age: 35
170,339 171,767 173,196 46,648 47,334 48,020
Age: 40
157,345 158,962 160,579 43,025 43,896 44,767
Age: 45
146,106 147,829 149,552 42,460 43,566 44,673
Age: 50
139,063 140,730 142,397 40,112 41,179 42,246
Criminal History
Criminal History: 0 166,745 168,176 169,607 59,946 60,804 61,662
Criminal History: 2 178,123 179,582 181,040 62,602 63,456 64,310
Criminal History: 5 198,376 199,861 201,347 66,821 67,679 68,536
Criminal History: 10 241,259 242,791 244,323 71,517 72,390 73,263
Criminal History: 20 355,934 358,609 361,283 56,572 57,991 59,409
Source: Urban Institute analysis.

50

To Treat or Not to Treat

outpatient methadone by 20%, and outpatient drug free by 30%. Note that the
reductions are no uniform by crime type, and in particular the most serious have
the highest rates of recidivism. For in stance, only long-term residential reduces
recidivism for aggravated assault and robbery, and outpatient drug free actually
increases the number of aggravated assaults. For less serious crimes with higher
prevalence rates, the reduction in recidivism is generally large.
For those at risk of drug abuse, recidivism reductions are large, but the 27%
reduction in recidivism is not quite as great as the reduction in recidivism for
those at risk of drug dependence. The effectiveness of different modalities is
slightly different as well. Outpatient drug free is the most effective modality,
reducing recidivism by 33%. Long-term inpatient reduces recidivism by 27%,
short-term inpatient by 20% and outpatient methadone by 16%. The pattern
of offending reduction is generally similar for those at-risk of drug abuse as it
is for those at risk of dependence. One minor difference is that the recidivism
reductions for the most serious offenses is positive for all modalities, although
the recidivism reductions are very small, generally 1% or 2%.
The findings here generally corroborate what has been found elsewhere in
the literature. For example, Holloway, Bennett and Farrington’s (2006) metaanalysis results found that drug treatment may reduce offending by 29-36%.
More interesting, however, are findings regarding the total number of crimes
avertable by treating potential clients. Table 4.2 and table 4.3 provide these estimates.
A cautionary note on reading these tables. The modalities are conditioning
variables. Hence, the first three columns in table 4.2, for example, produces
the estimates (and upper and lower confidence bounds) of the expected crimes
avertable if every potential client at risk of drug dependence was treated under Modality 1 (long term residential) or under Modality 2 (short term inpatient). As such the number cannot be summed or aggregated across modalities.
Moreover, the number of all non-drug crimes avertable is not an aggregation of
all sub-crime types. Respondents were asked to identify the number of times

Source: Urban Institute analysis.

689,274,887
3,809,215
44,102
338,054
734,169
-25,553
48,933
-72,923

162,791,624 166,526,868 170,262,111
1,488,310
1,522,185
1,556,060
119,675
126,802
133,929
222,233
231,258
240,283
131,204
139,992
148,780
-25
1,354
2,732
-44,294
-40,561
-36,828
60,135
63,523
66,911

679,518,218
3,705,355
18,079
315,206
716,014
-28,147
43,212
-80,103

260,065,953
2,919,438
210,188
157,162
166,007
101,948
11,249
1,933

Modality 2: Short Term Inpatient
Drug
669,761,550
All Non-Drug
3,601,495
Fraud
-7,945
Burglary
292,359
Larceny
697,859
Robbery
-30,741
Aggravated Assault
37,490
Other Assaults
-87,284

255,738,040
2,860,013
203,498
149,074
155,715
97,549
9,622
-542

High

251,410,127
2,800,589
196,808
140,987
145,423
93,150
7,995
-3,018

High

Clients at risk of abuse
Low
Mean

Modality 1: Long Term Residential Treatment
Drug
1,012,217,240 1,024,164,494 1,036,111,748
All Non-Drug
6,967,517
7,048,988
7,130,460
Fraud
1,318,702
1,349,364
1,380,026
Burglary
912,634
942,097
971,561
Larceny
1,766,153
1,797,942
1,829,732
Robbery
148,311
154,299
160,287
Aggravated Assault
97,979
101,884
105,788
Other Assaults
-19,586
-12,826
-6,067

Clients at risk of dependence
Low
Mean

Table 4.2: Estimated number of crimes avertable annually by treating potential clients under inpatient treatment
modalities.

Findings

51

52

To Treat or Not to Treat

they were arrested for any crime and then subsequently the number of times
they were arrested for particular crime types. The estimates can, however, be
summed across risk criteria. For example, the total number of all non-drug
crimes avertable by treating offenders at risk of drug dependence or abuse under
modality 1 (long term residential treatment) is a little over 9.9 million (7,048,988
+ 2,860,013). Similarly, we expect that roughly 1.27 billion drug related crimes
could be averted by treating all offenders at risk of drug dependence or abuse
using long term residential treatment.
Benefits can be expected vary, of course, by treatment modality. For example, long term residential treatment is the most effective treatment modality—
would avert the most crimes if everyone at risk of dependence or abuse was
treated under it. However, the modality effectiveness rankings are crime typespecific. Notably, the lowest number of drug crimes are averted if all potential
clients are treated under modality 4 (outpatient drug free). On the other hand,
outpatient drug free is an effective modality for averting non-drug crimes. In
fact, if all offenders at risk of drug dependence were treated under this modality,
roughly 6.7 million non-drug crimes would be averted. Only 3.7 million and 3.3
million non-drug crimes would be averted if these same individuals were treated
under short term inpatient and outpatient methadone modalities respectively.
There are also several crime types for which the evidence is insufficient to
conclude any crime reductions. For example, among offenders at risk of dependence, it is unclear if short term inpatient treatment will reduce any frauds or
whether outpatient methadone will reduce any aggravated assaults. Similarly,
among offenders at risk of abusing drugs, it is unclear if short term inpatient
treatment or outpatient drug free can avert any robberies.
4.3.

COST-EFFECTIVENESS OF TREATING CURRENTLY ELIGIBLE
DRUG COURT PARTICIPANTS

The crimes avertable by treating individuals will vary depending on the subgroup that is selected for treatment. Additionally, not all individuals can or will

Source: Urban Institute analysis.

127,163,645
892,080
16,139
94,193
167,853
5,886
-13,387
111,245

134,805,945
925,981
22,417
102,094
177,491
7,357
-11,280
120,487

354,283,621 363,442,051 159,544,034 163,696,423 167,848,811
6,779,782
6,901,924
1,527,269
1,562,353
1,597,436
264,776
282,627
82,356
88,058
93,761
173,516
188,167
136,203
144,134
152,065
1,200,833
1,225,470
82,118
87,846
93,574
24,604
27,818
-1,213
407
2,026
-7,045
-2,532
11,548
13,244
14,940
317,778
326,508
135,005
143,929
152,852

119,521,345
858,179
9,861
86,291
158,215
4,415
-15,494
102,003

Modality 4: Outpatient Drug Free
Drug
345,125,191
All Non-Drug
6,657,640
Fraud
246,925
Burglary
158,866
Larceny
1,176,197
Robbery
21,390
Aggravated Assault
-11,558
Other Assaults
309,049

593,763,103
3,455,760
66,844
471,383
989,094
20,235
6,219
571,363

High

578,123,548
3,370,857
48,990
447,468
958,940
15,423
2,852
544,708

Clients at risk of abuse
Low
Mean

Modality 3: Outpatient Methadone
Drug
562,483,993
All Non-Drug
3,285,954
Fraud
31,135
Burglary
423,554
Larceny
928,786
Robbery
10,611
Aggravated Assault
-516
Other Assaults
518,054

Clients at risk of dependence
Low
Mean
High

Table 4.3: Estimated number of crimes avertable annually by treating potential clients under outpatient treatment modalities.

Findings

53

54

To Treat or Not to Treat

be treated under the same treatment modality. The associated costs and benefits
of treating those individuals will also vary. Therefore, to study the effectiveness
of treating drug involved offender, we run six simulations models. In these simulations, we begin with the full sample in table 4.1, and then put restrictions
on the sample to reflect the current policy regime. The first two describe the
currently eligible population for drug courts, and are discussed below. The next
four describe the effects of relaxing existing eligibility criteria, and these are discussed in the next section.
Table 4.4 describes the first simulation which describes the effectiveness of
the currently eligible drug court population. That is, although there are almost
1.5 million individuals arrested each year who are at risk of drug abuse and dependence, and who are likely to be found guilty, only a fraction of those arrestees
are currently being treated. Thus, we begin our simulations by estimating the
size of the population that is currently being treated by the criminal justice system. Since there are no national data to identify who is currently being treated,
we begin by identifying adult drug courts as the mechanism in the criminal justice system that is most likely to deliver the long-term intensive treatment for
which effect sizes are available from the DATOS study. We believe adult drug
courts are a reasonable population to study, since any large scale expansion of
treatment in the criminal justice system will require a significant infrastructure
to manage, and the adult drug court management model is the most reasonable
candidate.
Thus, we begin in table 4.4 by estimating the size of the population that
is currently treated in adult drug courts. We find that there are about 55,000
individuals treated annually, about 32,000 of which are at risk of dependence,
and 23,500 are at risk of drug abuse. Our estimates suggests that by far the most
common treatment modality is out-patient drug free, which is consistent with
the drug court literature. In total, we estimate that about $515 million dollars is
spent annually to treat those drug court clients.
We find that there is a substantial reduction in criminal offending that results

1.84
248,627,369

1.95
281,675,271

2.56
339,070,917

2.08
554,651,149

2.21
624,223,730

2.34
693,794,936

2.71
2.86
375,596,361 412,119,665

1.73
215,580,233

Net BC Ratio
Net $ Saved

174,003
35,398,083
24,247
19,691
35,950
-322
-2,088
279
656,080,414 1,105,256,814 1,136,696,776 1,168,136,740
21,740,872
49,687,880
52,484,962
55,282,088
46,663,534
71,662,023
77,506,484
83,351,072
15,131,850
69,369,787
72,342,089
75,314,391
-11,681,056
-19,178,456
-15,396,575
-11,615,055
-86,997,983 -199,585,945 -184,476,281 -169,368,240
-7,249,007
-10,518,107
810,859
12,140,259
633,688,624 1,066,693,997 1,139,968,313 1,213,241,254

169,929
34,445,357
23,020
18,310
34,531
-427
-2,274
19

73,488,167
50,435,232
126,299,462
269,223,458
519,446,318

639,119,284
20,383,360
43,685,407
13,795,785
-13,412,585
-95,656,411
-12,847,150
595,067,689

165,854
33,492,631
21,793
16,929
33,112
-532
-2,460
-242

72,964,468
50,075,815
125,399,413
267,304,888
515,744,583

3,583
6,865
9,969
35,345
55,762

High

71,338
19,881,225
9,535
11,024
7,223
-324
-1,073
-167

72,440,768
49,716,398
124,499,363
265,386,318
512,042,847

30,752,734 31,049,494 31,346,255
21,105,728 21,309,396 21,513,064
52,852,778 53,362,801 53,872,824
112,662,456 113,749,636 114,836,816
217,373,696 219,471,328 221,568,959

3,558
6,816
9,898
35,093
55,365

Overall
Mean

69,060
19,367,251
8,940
10,320
6,585
-372
-1,179
-295

3,532
6,767
9,827
34,841
54,968

Low

1,528
2,928
4,252
15,076
23,785

1,514
2,900
4,212
14,934
23,560

Clients at risk of abuse
Mean
High

1,500
2,873
4,172
14,791
23,335

Low

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
99,072
100,868
102,665
66,782
Drug
14,639,353 15,078,106 15,516,858
18,853,277
Fraud
13,448
14,080
14,711
8,345
Burglary
7,313
7,990
8,667
9,617
Larceny
27,165
27,946
28,727
5,947
Robbery
-112
-55
2
-420
Agg. Assaults
-1,174
-1,095
-1,015
-1,286
Oth. Assaults
182
314
446
-424
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
483,098,660 497,577,492 512,056,326 622,158,155
Fraud
30,662,010 32,101,602 33,541,217
19,025,870
Burglary
30,954,659 33,821,077 36,687,538
40,707,364
Larceny
56,910,047 58,546,304 60,182,541
12,459,740
Robbery
-4,033,261
-1,983,991
66,001 -15,145,195
Agg. Assaults -95,269,483 -88,819,870 -82,370,258 -104,316,462
Oth. Assaults 7,926,752 13,658,009 19,389,266 -18,444,859
Total (Benefits) 510,249,384 544,900,624 579,552,630 556,444,613

Number of clients treated under different modalities
LT Residential
2,033
2,044
2,055
ST Inpatient
3,894
3,915
3,937
OP Methadone
5,655
5,686
5,717
OP DrugFree
20,050
20,160
20,269
Total (clients)
31,633
31,805
31,977
Total costs under different modalities
LT Residential 41,688,034 41,914,973 42,141,912
ST Inpatient 28,610,670 28,766,419 28,922,168
OP Methadone71,646,586 72,036,612 72,426,637
OP DrugFree 152,723,862 153,555,252 154,386,642
Total (costs)
294,669,151 296,273,255 297,877,359

Clients at risk of dependence
Low
Mean
High

Table 4.4: Cost benefit analysis of treating eligible drug courts clients in available drug dourt treatment
slots.

Findings

55

56

To Treat or Not to Treat

from drug court treatment. Notably, 34.4 million drug crimes are prevented annually. We count as a drug crime each drug transaction (so a drug deal would
count as two crimes, one for the buyer and one for the seller). This reduction in
drug offending leads to more than one billion dollars in savings. Notably, since
the likelihood of arrest is trivial, this reduction in offending leads to little savings
to the criminal justice system, but produces large benefits to private citizens. Reductions in other property crimes leads to significant savings, with almost $200
million in savings from reductions in fraud, burglary and larceny. However,
drug court treatment does not reduce crimes in all categories. Notably, there
are more than 400 additional robberies and 2,200 additional assaults, that would
not have occurred in the absence of drug court. Increases in the crimes result in
about $200 million dollars in negative benefits.
Overall, we estimate that the current adult drug court treatment regime produces about $2.21 in benefit for every $1 in costs, for a net benefit to society of
about $624 million. Interestingly, the benefit-cost ratio is higher for those at risk
of abuse (2.71) as compared to those at risk of dependence (1.84), even though
the abuse group is less prevalent in the drug court population. Much of this is
due to much greater reductions in drug crimes and larceny.
Our benefit-cost ratio is similar to other published estimates. For instance,
Aos et al. (2005), using a meta analytic design, estimates $2.83 in benefit for every
dollar in new cost. It turns out that the benefit-cost ratio is sensitive to which
estimates of the price of victimization are used in the benefits calculations. If
we rely on data from Miller et al. (1993) and Rajkumar and French (1997), our
estimate of the benefit-cost ratio is 2.76, which is very close to the Aos et. al,
estimate. Our decision to use the average of published costs to victims yields a
lower—and therefore more conservative estimate.
Next, we simulate the effects of expanding the number of treatment slots for
eligible drug court clients so that all currently eligible drug court clients can be
treated. Recall that we found that there were more than twice as many arrestees
eligible for drug court (109,922) than there are currently available drug court

3,010
5,767
8,375
29,693
46,845
61,735,649
42,369,431
106,101,153
226,168,179
436,374,412

83,016,643
56,974,664
142,675,449
304,130,970
586,797,726

62,250,361
42,722,679
106,985,755
228,053,822
440,012,617

3,035
5,815
8,445
29,940
47,235

Net BC Ratio
Net $ Saved
1.72
418,866,901

1.82
479,428,498

1.92
539,992,491

2.43
624,519,672

2.57
692,240,163

7,019
13,446
19,527
69,232
109,225

Low

2,182,362,842
105,930,715
153,705,775
144,863,112
-24,685,013
-368,778,972
2,228,556
2,195,627,015

342,345
66,132,207
46,461
36,311
69,147
-684
-4,546
51

144,863,521
99,420,431
248,967,765
530,706,637
1,023,958,354

7,064
13,532
19,652
69,674
109,922

Overall
Mean

2.03
2.14
1,043,386,573 1,171,668,661

2,126,077,895
100,827,528
143,068,839
139,443,577
-31,838,704
-396,818,686
-19,905,623
2,060,854,826

1,245,972,802
45,955,042
95,550,874
31,772,917
-18,441,628
-180,956,615
-16,242,403
1,203,610,988
2.71
759,960,074

334,863
64,426,603
44,223
33,798
66,560
-883
-4,892
-458

149,191
37,756,752
20,156
22,573
15,166
-511
-2,231
-373

62,765,085
143,945,340
43,075,937
98,790,280
107,870,380
247,389,746
229,939,512
527,342,887
443,650,915 1,017,468,254

3,061
5,863
8,515
30,188
47,626

Clients at risk of abuse
Mean
High

4,048
7,755
11,262
39,928
62,993

Low

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
194,032
197,334
200,636
140,831
145,011
Drug
28,495,085
29,288,073
30,081,060
35,931,518
36,844,135
Fraud
26,219
27,381
28,543
18,004
19,080
Burglary
13,802
15,026
16,251
19,997
21,285
Larceny
53,741
55,155
56,568
12,819
13,992
Robbery
-187
-81
25
-695
-603
Agg. Assaults
-2,255
-2,112
-1,970
-2,637
-2,434
Oth. Assaults
425
679
933
-883
-628
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
940,337,808
966,506,397
992,674,987 1,185,740,087 1,215,856,445
Fraud
59,778,408
62,428,634
65,078,906
41,049,120
43,502,081
Burglary
58,422,427
63,607,132
68,791,922
84,646,412
90,098,643
Larceny
112,588,149
115,548,929
118,509,709
26,855,428
29,314,183
Robbery
-6,760,932
-2,924,953
911,388
-25,077,772
-21,760,060
Agg. Assaults -182,902,612 -171,343,439 -159,781,833 -213,916,074 -197,435,533
Oth. Assaults 18,497,495
29,551,534
40,605,138
-38,403,118
-27,322,978
Total (Benefits) 999,960,743 1,063,374,235 1,126,790,217 1,060,894,084 1,132,252,780

Number of clients treated under different modalities
LT Residential
4,009
4,028
ST Inpatient
7,679
7,717
OP Methadone
11,152
11,207
OP DrugFree
39,540
39,734
Total (clients)
62,380
62,686
Total costs under different modalities
LT Residential 82,209,691
82,613,160
ST Inpatient 56,420,850
56,697,752
OP Methadone141,288,593
141,982,010
OP DrugFree 301,174,708
302,652,815
Total (costs)
581,093,842
583,945,737

Clients at risk of dependence
Low
Mean
High

2.26
1,299,952,564

2,238,647,788
111,033,948
164,342,796
150,282,625
-17,530,240
-340,738,448
24,362,735
2,330,401,205

349,827
67,837,812
48,699
38,824
71,734
-486
-4,201
560

145,781,728
100,050,601
250,545,829
534,070,483
1,030,448,641

7,109
13,618
19,776
70,116
110,618

High

Table 4.5: Cost benefit analysis of treating all eligible drug court clients (retaining all eligibility restrictions).

Findings

57

58

To Treat or Not to Treat

treatment slots (55,365). In table 4.5, we simulate the effects of treating all who
meet current eligibility standards (regardless of whether a treatment slot in drug
court is available) in the four treatment modalities studied by DATOS. We find
that the costs of treating these additional clients about doubles, to slightly more
than $1 billion. We find that the expansion of drug treatment to this larger
population remains cost-effective, although the benefit-cost ratio is fractionally
reduced to 2.14 from 2.21. In total, this expansion of treatment yields a benefit
to society of more than $1.17 billion dollars.
4.4.

SIMULATED COST-EFFECTIVENESS OF EXPANDING CRIMINAL JUSTICE SYSTEM–BASED TREATMENT

In the next five simulations, we incrementally relax existing drug court eligibility requirements to model the cost-effectiveness of expanding criminal justice
system-based treatment to individuals who are currently excluded from drug
courts.
4.4.1.

Simulation 1: Adding Individuals with Other Pending Charges

Beginning with the same group described in table 4.5 (everyone eligible for
drug court regardless of whether there would be a treatment slot in the current regime), we first relax the assumption about current charges that currently
restrict drug court eligibility. From table 3.1, about half of drug courts restrict
eligibility to those arrestees who do not have a current charge pending in court.
In table 4.6, we relax this restriction, and allow drug courts to enroll into treatment any arrestee, regardless of whether they have some other pending charge.
This change in eligibility has little impact on the number of individuals entering drug court. Because the presence of any ineligible characteristic causes
an arrestee to be excluded from drug court, few additional arrestees become
eligible. We suspect that exclusions for active criminal justice cases is highly correlated with other grounds for exclusion, such as a past violence history. We

74,001,824
50,787,757
127,182,252
271,105,238
523,077,071

73,431,485
50,396,331
126,202,046
269,015,803
519,045,665

Net BC Ratio
Net $ Saved
2.02
692,611,484

2.15
780,972,766

2.27
869,335,740

2.51
784,043,567

8,250
15,805
22,953
81,378
128,386

2,289,287,763
110,859,300
183,975,958
156,454,286
47,114,458
-272,990,341
338,917,596
2,853,619,020

409,082
69,372,356
48,623
43,462
74,680
1,306
-3,365
7,791

170,234,729
116,832,796
292,571,654
623,653,903
1,203,293,081

8,301
15,902
23,094
81,877
129,173

Overall
Mean

2.81
2.23
2.37
954,661,827 1,476,655,051 1,650,325,940

2,228,193,866
105,315,457
172,058,920
150,181,164
32,732,059
-308,640,451
292,778,260
2,672,619,277

1,275,739,482 1,308,183,511
46,863,348
49,501,992
101,425,347
107,484,929
27,397,342
30,403,038
10,112,185
15,595,299
-175,461,749 -155,016,209
106,354,290
125,617,838
1,392,430,244 1,481,770,397
2.66
869,353,174

400,059
67,521,026
46,191
40,647
71,686
908
-3,805
6,730

74,572,177
169,197,886
51,179,192
116,121,206
128,162,480
290,789,698
273,194,720
619,855,436
527,108,570 1,195,964,226

3,636
6,966
10,116
35,866
56,585

Low

177,520
39,641,925
21,711
25,392
14,512
432
-1,911
2,888

172,690
38,658,772
20,554
23,961
13,077
280
-2,163
2,445

3,608
6,913
10,039
35,592
56,152

Clients at risk of abuse
Mean
High

3,581
6,859
9,961
35,318
55,719

Low

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
232,199
236,392
240,585
167,860
Drug
29,845,406
30,713,584
31,581,762
37,675,620
Fraud
26,794
28,068
29,343
19,397
Burglary
18,118
19,502
20,885
22,529
Larceny
60,043
61,602
63,162
11,643
Robbery
779
1,026
1,273
128
Agg. Assaults
-1,390
-1,202
-1,015
-2,415
Oth. Assaults
4,728
5,346
5,964
2,002
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
984,898,413 1,013,548,280 1,042,198,148 1,243,295,454
Fraud
61,090,776
63,995,952
66,901,060
44,224,681
Burglary
76,693,071
82,550,611
88,408,237
95,365,850
Larceny
125,789,540
129,056,944
132,324,327
24,391,624
Robbery
28,102,267
37,002,273
45,901,920
4,629,792
Agg. Assaults -112,731,540
-97,528,591
-82,324,021 -195,908,911
Oth. Assaults 205,687,518
232,563,306
259,439,529
87,090,742
Total (Benefits) 1,369,530,045 1,461,188,776 1,552,849,199 1,303,089,232

Number of clients treated under different modalities
LT Residential
4,670
4,692
4,715
ST Inpatient
8,946
8,989
9,033
OP Methadone
12,991
13,055
13,118
OP DrugFree
46,060
46,284
46,509
Total (clients)
72,667
73,021
73,375
Total costs under different modalities
LT Residential 95,766,401
96,232,904
96,699,408
ST Inpatient
65,724,876
66,045,039
66,365,202
OP Methadone 164,587,652
165,389,402
166,191,152
OP DrugFree 350,839,633
352,548,665
354,257,698
Total (costs)
676,918,561
680,216,010
683,513,459

Clients at risk of dependence
Low
Mean
High

2.51
1,823,997,567

2,350,381,658
116,403,052
195,893,165
162,727,365
61,497,219
-237,340,230
385,057,367
3,034,619,596

418,105
71,223,687
51,054
46,278
77,674
1,705
-2,926
8,852

171,271,584
117,544,394
294,353,632
627,452,418
1,210,622,029

8,351
15,999
23,234
82,375
129,960

High

Table 4.6: Cost benefit analysis of treating all eligible drug court clients without regard to current offense
(retaining other eligibility restrictions).

Findings

59

60

To Treat or Not to Treat

find that the number of arrestees enrolled in drug court would increase by only
a little more than 19,000, to a total of 129,173 arrestees if this exclusion criteria
was removed.
However, we find that allowing these arrestees to participate in treatment
significantly enhances the cost-effectiveness of drug courts. Treating these additional clients increases the total cost of drug court and treatment to a little more
than $1.2 billion. The benefits increase from about $2.196 billion to $2.854
billion, and the benefit-cost ratio increases from 2.14:1 to 2.37:1. Since there are
only 19,000 new eligibles, these changes in overall mean disguise the effectiveness
of treating this group. We estimate that the group of arrestees who are currently
ineligible because of a pending court case are a particularly cost-effective population to serve, with a benefit-cost ratio of 3.67:1. While both groups of new
eligibles (those at risk of drug dependence and those at risk of drug abuse) have
high benefit-cost ratios, the benefit-cost ratio for the 10,000 individuals who
are at-risk of drug dependence and previously had been excluded for a pending
charge is the highest for any sub-group in any of the simulations (4.13:1).
4.4.2.

Simulation 2: Adding Individuals with Prior Violence

In table 4.7, we return again to the population in table 4.5 (all eligible arrestees)
and relax the eligible exclusion for those with past violence. That is, we are
now studying the population that would be eligible for drug court if there were
enough slots, and allowing those with past violence to be eligible (we are once
again not allowing those with a current charge to be eligible). Since 88% of drug
courts exclude those with past violence, removing this exclusion leads to the
size of eligibles more than doubling, from 109,922 to 213,460 (but we note that
many who are excluded because of past violence are excluded on other grounds
as well). Total costs of treating this group are almost $2 billion. Benefits increase
substantially as well, to almost $4.3 billion. The overall benefit to cost ratio is
2.15, almost identical to the 2.14:1 ratio for the eligible group with the violence
restriction.

Net BC Ratio
Net $ Saved
1.50
562,967,489

1.61
691,420,902

13,631
26,112
37,921
134,446
212,110

Low
13,717
26,278
38,162
135,302
213,460

Overall
Mean

13,804
26,445
38,404
136,158
214,810

High

1.72
2.67
2.85
3.03
819,876,515 1,424,367,171 1,591,171,205 1,757,973,601

2,256,039,712
75,557,809
136,527,415
60,604,055
-29,920,714
-151,682,301
277,576,401
2,624,702,378

2,199,920,825
71,798,864
128,463,550
56,925,822
-45,812,115
-181,853,769
220,897,208
2,450,340,385

2.01
1,987,334,660

3,765,471,598
145,007,316
162,473,757
256,721,447
-104,060,148
-719,059,213
456,662,188
3,963,216,945

635,131
114,105,200
63,600
38,383
122,540
-2,885
-8,864
10,498

2.15
2,282,592,107

3,862,769,893
152,930,453
179,412,319
266,234,653
-75,835,257
-658,235,253
543,772,940
4,271,049,748

649,811
117,053,633
67,075
42,384
127,081
-2,103
-8,115
12,500

2.29
2,577,850,116

3,960,068,187
160,853,635
196,351,049
275,747,881
-47,610,005
-597,412,104
630,884,563
4,578,883,206

664,492
120,002,066
70,550
46,386
131,622
-1,320
-7,365
14,503

122,619,618
279,536,041
281,315,128
283,094,227
84,154,349
191,846,737
193,067,732
194,288,735
210,738,577
480,420,902
483,478,505
486,536,131
449,216,232 1,024,078,604 1,030,596,276 1,037,113,996
866,728,776 1,975,882,285 1,988,457,641 2,001,033,089
299,980
68,364,840
33,139
32,253
28,928
-830
-1,870
6,381

121,550,131
83,420,356
208,900,518
445,298,175
859,169,180

120,480,658
82,686,372
207,062,482
441,380,165
851,609,677

5,979
11,454
16,634
58,975
93,043

292,155
66,664,267
31,491
30,348
27,172
-1,270
-2,242
5,078

5,927
11,354
16,489
58,461
92,232

Clients at risk of abuse
Mean
High

5,875
11,254
16,344
57,947
91,420

Low

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
350,800
357,656
364,512
284,331
Drug
49,141,505
50,389,366
51,637,227
64,963,695
Fraud
33,758
35,584
37,410
29,842
Burglary
9,940
12,036
14,133
28,443
Larceny
97,124
99,909
102,694
25,417
Robbery
-1,174
-832
-490
-1,711
Agg. Assaults
-6,251
-5,873
-5,495
-2,614
Oth. Assaults
6,723
7,422
8,122
3,775
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
1,621,669,661 1,662,849,068 1,704,028,475 2,143,801,937
Fraud
76,967,328
81,131,588
85,295,826
68,039,988
Burglary
42,073,988
50,948,769
59,823,634
120,399,769
Larceny
203,473,858
209,308,831
215,143,825
53,247,588
Robbery
-42,356,992
-30,023,142
-17,689,291
-61,703,155
Agg. Assaults -507,032,354 -476,381,484 -445,729,803 -212,026,859
Oth. Assaults 292,444,608
322,875,732
353,308,162
164,217,580
Total (Benefits) 1,687,240,097 1,820,709,363 1,954,180,828 2,275,976,848

Number of clients treated under different modalities
LT Residential
7,756
7,790
7,825
ST Inpatient
14,858
14,924
14,990
OP Methadone
21,577
21,673
21,769
OP DrugFree
76,500
76,841
77,182
Total (clients)
120,690
121,229
121,767
Total costs under different modalities
LT Residential 159,055,383
159,764,996
160,474,609
ST Inpatient 109,160,365
109,647,375
110,134,386
OP Methadone 273,358,421
274,577,987
275,797,554
OP DrugFree 582,698,439
585,298,102
587,897,764
Total (costs)
1,124,272,608 1,129,288,461 1,134,304,313

Clients at risk of dependence
Low
Mean
High

Table 4.7: Cost benefit analysis of treating all eligible drug court clients without regard to past violence
(retaining other eligibility restrictions).

Findings

61

62

To Treat or Not to Treat

However, this similarity masks a critical difference among those with past
violence. For those at risk of abuse, removing the past violence exclusion increases the eligible population from 47,235 to 92,232. Adding this population is
very cost-effective. Overall, the benefit to cost ratio for the newly eligible group
of at-risk with past violence (3.14) is higher than the at-risk group in general
(2.85).
Conversely, relaxing the exclusion for prior violence for the population at
risk of drug dependence is much less cost-effective. For those at risk of drug
dependence, removing the past violence exclusion increases the eligible population from 62,686 to 121,229. Overall, the benefit to cost ratio declines from
1.82:1 to 1.61:1. Focusing only on those who become newly eligible reveals that
the benefit is much smaller than it appears in the overall means. New costs of
treating this added group are about $545 million, and benefits are $757 million,
for a benefit-cost ratio of 1.38:1. Put another way, even though the newly eligible population of those at risk of drug dependence is about 30% larger than
the newly eligible population of those at risk of drug abuse, the total benefits
are about 40% smaller. Adding those at risk of drug abuse with past violence
is significantly more cost-effective than adding those at risk of drug dependence
with past violence.
4.4.3.

Simulation 3: Adding Individuals with Prior Failed Treatment

Next, we return to the eligible population in table 4.5, and simulate the effect of
dropping the exclusion on past treatment. Many drug courts exclude individuals
who have a history of failed treatment, have failed drug court in the past, or
have participated in drug court in the past. In table 4.8, we estimate the effect
of allowing the arrestee group to enter into treatment, regardless of whether
they had failed treatment (or drug court) in the past. By dropping the past
treatment exclusion, about 38,000 additional arrestees become eligible for drug
court managed treatment. There is little change in the cost-effectiveness of drug
court as a result, which suggests it is cost-effective to treat this group. The benefit

3,705
7,098
10,308
36,547
57,659
75,987,963
52,150,852
130,595,702
278,381,444
537,115,962

118,636,627
81,420,806
203,893,262
434,624,567
838,575,261

Net BC Ratio
Net $ Saved
1.72
595,134,514

1.82
683,050,071

1.92
770,964,948

2.38
740,609,401

2.52
823,846,564

1,526,825,621
48,373,369
94,609,667
35,125,357
-42,460,862
-267,162,084
-29,463,662
1,365,847,404

175,287
46,267,443
21,216
22,351
16,766
-1,177
-3,294
-677

76,679,046
52,625,146
131,783,424
280,913,224
542,000,840

3,739
7,163
10,402
36,880
58,184

460,726
86,524,250
57,806
39,968
93,939
-1,922
-6,879
-508

193,522,261
132,815,125
332,594,462
708,967,639
1,367,899,488

9,436
18,077
26,253
93,077
146,844

Low

2,930,596,869
138,625,847
182,003,719
204,290,531
-58,745,383
-520,745,183
7,550,469
2,883,576,869

470,736
88,805,966
60,801
42,996
97,513
-1,629
-6,420
174

194,764,509
133,667,685
334,729,435
713,518,605
1,376,680,233

9,497
18,194
26,421
93,674
147,786

Overall
Mean

3,005,893,480
145,453,968
194,824,714
211,779,130
-48,159,290
-483,488,144
37,205,970
3,063,509,827

480,746
91,087,681
63,796
46,025
101,088
-1,335
-5,960
855

196,006,756
134,520,245
336,864,407
718,069,572
1,385,460,979

9,558
18,310
26,590
94,272
148,729

High

2.66
1.98
2.09
2.21
907,083,900 1,335,743,915 1,506,896,635 1,678,048,848

1,563,989,457 2,855,300,257
51,412,700
131,797,817
101,017,921
169,182,681
38,283,339
196,801,891
-37,040,143
-69,332,918
-246,878,778 -558,003,032
-16,814,877
-22,103,293
1,453,969,619 2,703,643,403

180,589
47,393,620
22,549
23,864
18,274
-1,027
-3,043
-387

77,370,130
53,099,439
132,971,145
283,445,005
546,885,719

3,773
7,227
10,496
37,212
58,708

Clients at risk of abuse
Mean
High

5,785
11,082
16,094
57,060
90,021

Low

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
290,741
295,449
300,157
169,985
Drug
41,382,984
42,538,523
43,694,061
45,141,266
Fraud
37,923
39,584
41,246
19,883
Burglary
19,131
20,646
22,161
20,837
Larceny
78,680
80,747
82,814
15,259
Robbery
-595
-452
-308
-1,328
Agg. Assaults
-3,335
-3,126
-2,917
-3,544
Oth. Assaults
460
851
1,242
-968
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
1,365,638,472 1,403,771,248 1,441,904,024 1,489,661,785
Fraud
86,463,733
90,252,478
94,041,268
45,334,084
Burglary
80,981,269
87,394,052
93,806,793
88,201,412
Larceny
164,834,537
169,165,175
173,495,791
31,967,354
Robbery
-21,450,614
-16,284,520
-11,119,148
-47,882,304
Agg. Assaults -270,557,642 -253,583,098 -236,609,366 -287,445,390
Oth. Assaults 20,008,285
37,014,131
54,020,847
-42,111,578
Total (Benefits) 1,425,918,040 1,517,729,464 1,609,540,208 1,277,725,363

Number of clients treated under different modalities
LT Residential
5,731
5,758
ST Inpatient
10,979
11,031
OP Methadone
15,944
16,019
OP DrugFree
56,530
56,795
Total (clients)
89,184
89,603
Total costs under different modalities
LT Residential 117,534,298
118,085,462
ST Inpatient
80,664,273
81,042,540
OP Methadone 201,998,760
202,946,011
OP DrugFree 430,586,194
432,605,381
Total (costs)
830,783,526
834,679,393

Clients at risk of dependence
Low
Mean
High

Table 4.8: Cost benefit analysis of treating all eligible drug court clients without regard to past treatment
(retaining other eligibility restrictions).

Findings

63

64

To Treat or Not to Treat

to cost ratio decreases slightly, from 2.14:1 to 2.09:1.
Again, the results vary by drug severity. That is, the newly added group at
risk of drug dependence has a benefit to cost ratio of 1.81:1, while the newly
added group at risk of drug abuse has a benefit to cost ratio of 2.29:1. Again, it
is important to illustrate that the group that is most benefited from a change to
one policy regime, may not be the group that benefits the most from a change
to a different policy regime.
4.4.4.

Simulation 4: Adding Individuals with Co-Occurring Alcohol Problems

Next, we again return to the eligible population in table 4.5, and this time we
simulate the effect of removing current exclusions on alcohol problems. About
one-third of drug courts exclude individual with a history of alcohol abuse, and
in table 4.9, we simulate the effect of including the eligible pool of treatment
clients. By dropping the alcohol problem exclusion, about 70,000 additional
arrestees become eligible for drug court managed treatment.
The results are mixed. Overall, adding this group reduces the benefit to cost
ratio from 2.14:1 to 1.73:1. However, again, these aggregate numbers mask important differences in the responsiveness of this new population to treatment.
The newly added group with a history of alcohol abuse adds $654 million in
new costs as well as $714 million in new benefits. Thus, the benefit to cost ratio
for this group is only 1.09:1. For those at risk of dependence, the results are
better, with the newly added group estimated to have a benefit to cost ratio of
1.43:1. However, adding those with a history of alcohol abuse and a risk of drug
abuse may not be cost-effective. While the mean expected benefit to cost ratio is
0.70 to 1 for this group. Thus, adding those with co-occurring alcohol problems
who are at risk of drug abuse is cost-effective. Adding those with co-occurring
alcohol problems who are at risk of drug dependence is not cost-effective.

11,576
22,177
32,206
114,184
180,142

1.77
726,292,699

1.64
473,619,785

1.81
602,147,881

1.98
730,675,363

1.73
1,232,068,523

1.60
1,007,169,906

1.67
629,920,643

Net BC Ratio
Net $ Saved
1.57
533,550,121

2,980,699,093
154,102,350
342,463,415
259,984,765
-35,369,566
-810,585,146
18,863,774
2,910,158,685

105,836,486
235,843,155
237,406,188
72,636,016
161,860,129
162,932,845
181,894,470
405,328,704
408,014,989
387,731,328
864,009,977
869,736,139
748,098,300 1,667,041,965 1,678,090,161

11,500
22,031
31,994
113,432
178,956

2,895,152,860
145,549,272
320,256,970
251,106,658
-43,875,010
-875,730,209
-18,248,670
2,674,211,871

104,888,811
71,985,623
180,265,761
384,259,527
741,399,722

5,161
9,886
14,357
50,903
80,308

Overall
Mean

644,604
90,324,215
67,589
80,903
124,098
-981
-9,993
434

103,941,136
71,335,230
178,637,052
380,787,726
734,701,144

133,132,735
91,369,545
228,806,805
487,730,973
941,040,058

5,115
9,798
14,229
50,448
79,589

Low

631,935
87,731,905
63,837
75,657
119,860
-1,217
-10,796
-420

5,068
9,709
14,100
49,992
78,870

Clients at risk of abuse
Mean
High

6,492
12,436
18,060
64,032
101,020

Low

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
354,779
360,237
365,695
277,155
284,367
291,578
Drug
40,492,375
41,711,729
42,931,083
47,239,530
48,612,486
49,985,442
Fraud
37,026
38,810
40,595
26,811
28,778
30,746
Burglary
31,379
33,665
35,951
44,278
47,238
50,199
Larceny
90,931
93,222
95,513
28,929
30,876
32,823
Robbery
-125
-3
118
-1,092
-977
-863
Agg. Assaults
-4,078
-3,801
-3,523
-6,718
-6,192
-5,667
Oth. Assaults
1,315
1,661
2,007
-1,734
-1,227
-720
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
1,336,248,381 1,376,487,064 1,416,725,747 1,558,904,478 1,604,212,029 1,649,519,581
Fraud
84,419,850
88,487,689
92,555,483
61,129,422
65,614,661
70,099,922
Burglary
132,826,714
142,503,014
152,179,271
187,430,256
199,960,401
212,490,589
Larceny
190,500,717
195,300,174
200,099,630
60,605,941
64,684,592
68,763,284
Robbery
-4,505,004
-119,378
4,266,247
-39,370,006
-35,250,187
-31,131,089
Agg. Assaults -330,799,182 -308,290,026 -285,779,247 -544,931,027 -502,295,121 -459,659,215
Oth. Assaults 57,199,465
72,242,546
87,285,627
-75,448,134
-53,378,772
-31,309,410
Total (Benefits) 1,465,890,942 1,566,611,082 1,667,332,757 1,208,320,929 1,343,547,603 1,478,773,663

Number of clients treated under different modalities
LT Residential
6,432
6,462
ST Inpatient
12,321
12,379
OP Methadone
17,893
17,977
OP DrugFree
63,440
63,736
Total (clients)
100,086
100,553
Total costs under different modalities
LT Residential 131,902,019
132,517,377
ST Inpatient
90,524,899
90,947,222
OP Methadone 226,691,652
227,749,229
OP DrugFree 483,222,252
485,476,612
Total (costs)
932,340,821
936,690,439

Clients at risk of dependence
Low
Mean
High

1.86
1,456,968,062

3,066,245,327
162,655,405
364,669,860
268,862,914
-26,864,842
-745,438,461
55,976,217
3,146,106,420

657,273
92,916,525
71,340
86,149
128,336
-745
-9,190
1,287

238,969,221
164,005,561
410,701,275
875,462,301
1,689,138,358

11,652
22,323
32,418
114,935
181,328

High

Table 4.9: Cost benefit analysis of treating all eligible drug court clients without regard to co-occurring
alcohol problems (retaining other eligibility restrictions).

Findings

65

66
4.4.5.

To Treat or Not to Treat

Simulation 5: Expanding Eligibility to Include all Arrestees

Finally, we simulate the effects of treating all arrestees at risk of drug dependence
or at risk of drug abuse. That is, in table 4.10 we estimate the costs and benefits
of treating all 1.47 million arrestees with a serious drug problem who are likely
to be found guilty each year. The results suggest doing so would be very costeffective. For the entire group, the costs of treatment would exceed $13.7 billion.
The benefits are estimated at more than $46 billion. Overall, the benefit to cost
ratio is 3.36:1, meaning that for every dollar in costs, there are more than three
dollars in benefits. The results suggest that treating those who are currently
excluded will be substantially more cost-effective than current practice or any
limited expansion of current eligibility.

4.24
9,796,861,814

4.01
9,029,179,797

3.77
8,261,498,407

Net BC Ratio
Net $ Saved

3.31
24,811,224,952

5,549,430,293
213,026,807
653,233,470
251,457,508
342,175,454
295,442,715
5,515,396,088
12,820,162,334

5,393,134,402
199,245,871
619,071,043
236,589,125
279,344,514
131,920,577
5,172,398,098
12,031,703,631

3.18
23,330,768,029

1,557,254
168,164,554
93,433
154,319
120,027
9,487
3,642
126,788

2.12
11,950,310,365

94,151
180,367
261,934
928,671
1,465,123

Low

7,330,119
640,816,332
352,914
435,575
1,249,205
32,548
9,538
407,024

1,939,048,802
1,330,777,185
3,332,520,453
7,103,693,610
13,706,040,050

94,551
181,132
263,045
932,610
1,471,339

Overall
Mean

7,477,027
656,122,556
378,639
461,914
1,281,587
37,892
15,972
426,526

1,947,240,011
1,336,398,845
3,346,598,165
7,133,702,054
13,763,939,075

94,950
181,897
264,156
936,550
1,477,554

High

2.48
20,211,808,772

3.36
32,359,947,826

3.51
34,608,086,766

10,741,833,561 21,146,938,948 21,652,044,336
745,989,803
804,643,145
863,296,555
1,732,300,644 1,843,790,330 1,955,279,972
2,549,244,101 2,617,084,119 2,684,924,116
981,170,841 1,173,891,676 1,366,611,429
251,782,301
773,671,233 1,295,560,166
16,857,628,453 17,705,968,424 18,554,309,266
33,859,949,704 46,065,987,876 48,372,025,840

7,183,211
325,510,108
327,189
409,237
1,216,823
27,205
3,104
387,523

427,718,526 1,930,857,580
293,544,988 1,325,155,516
735,092,761 3,318,442,718
1,566,944,246 7,073,685,118
3,023,300,520 13,648,140,932

1,520,967
163,428,315
87,389
146,249
112,930
7,745
1,626
118,903

424,779,165
291,527,691
730,041,066
1,556,175,912
3,002,523,834

20,856
39,954
58,023
205,717
324,550

High

Total Treatment Benefits (Number of Crimes Averted)
All Non-Drug
5,698,532
5,809,152
5,919,773
1,484,679
Drug
166,818,032
477,388,017
487,958,001
158,692,076
Fraud
245,844
265,525
285,206
81,344
Burglary
271,059
289,327
307,594
138,178
Larceny
1,110,990
1,136,274
1,161,559
105,833
Robbery
21,202
24,803
28,404
6,003
Agg. Assaults
3,494
7,911
12,329
-390
Oth. Assaults
276,505
288,121
299,738
111,018
Total Treatment Benefits ($ Averted - only dollarizable crime categories)
Drug
5,504,995,050 15,753,804,547 16,102,614,043 5,236,838,510
Fraud
560,524,822
605,397,274
650,269,748
185,464,981
Burglary
1,147,392,070 1,224,719,286 1,302,046,503
584,908,575
Larceny
2,327,523,338 2,380,494,994 2,433,466,608
221,720,764
Robbery
764,657,627
894,547,162 1,024,435,976
216,513,215
Agg. Assaults 283,383,862
641,750,656 1,000,117,450
-31,601,561
Oth. Assaults 12,028,227,475 12,533,570,326 13,038,913,178 4,829,400,978
Total (Benefits) 22,616,704,243 34,034,284,245 35,551,863,506 11,243,245,461

421,839,790
289,510,386
724,989,348
1,545,407,530
2,981,747,054

1,519,521,484
1,042,853,858
2,611,505,404
5,566,757,808
10,740,638,554

20,713
39,680
57,624
204,303
322,320

Clients at risk of abuse
Mean

20,570
39,405
57,225
202,889
320,090

Low

74,094
141,943
206,134
730,833
1,153,004

Clients at risk of dependence
Mean
High

Number of clients treated under different modalities
LT Residential
73,582
73,838
ST Inpatient
140,962
141,452
OP Methadone
204,709
205,421
OP DrugFree
725,781
728,307
Total (clients)
1,145,034
1,149,019
Total costs under different modalities
LT Residential 1,509,017,790 1,514,269,637
ST Inpatient 1,035,645,129 1,039,249,493
OP Methadone2,593,453,370 2,602,479,387
OP DrugFree 5,528,277,588 5,547,517,698
Total (costs)
10,666,393,877 10,703,516,216

Low

Table 4.10: Cost benefit analysis of treating all drug involved arrestees (with no eligibility restrictions).

Findings

67

68

To Treat or Not to Treat

Chapter 5
Discussion
Our main motivation was to provide some answers to the question: What crime
reducing benefits can we reasonably expect if the therapeutic jurisprudence model
was extended to all offenders in need of treatment. Clearly information needed
to answer this question cannot be found in one place. Therefore, we designed
a synthetic data set—of 40,320 possible profiles—and using data from various
sources interpolated values conditional on profile attributes. We computed the
prevalence of the potential clients and computed the expected number of crimes
avertable by treating them under various modalities for each of the profiles in
our synthetic data. Moreover, for each of them, we computed precision estimates as well. Using combinations of several of the interpolated outcomes, we
estimate that nearly 1.5 million arrestees nationwide who are probably guilty
are either at risk of drug dependence or of abusing drugs. Moreover, several million crimes could be averted annually by treating these individuals. Although
our current work was motivated by a limited question, we believe the creating of
the synthetic data has several future benefits. Clearly, the prevalence estimates
and the conditional crime reducing benefits provide some guidance to policy
makers on the prospects of going to scale in therapeutic jurisprudence.
A more thorough analysis, however, would require additional pieces of information. For example, not every profile in our data set and not every treatment
69

70

To Treat or Not to Treat

modality costs the same. Hence, even if we could attach dollar estimates to
the crimes avertable by treatment, an important quantity to add to this data set
would the anticipated costs of treating individuals. Similarly, the counterfactual
currently is based on the absence of treatment. This may be statistically a clean
counterfactual, however from a policy perspective, the benefits of treating drug
involved offender should be compared against other policy options—e.g., incarcerating them. Clearly, incarcerating these offenders will avert some crimes (if
for no other reason than the mere fact that they are incapacitated). What is important for making informed policy choices is whether the addition reduction
in crimes, over and above those averted by treatment, are worth the additional
costs of incarcerating offenders.
As we continue to refine these data, we can create estimates of the costs and
benefits of treating varying offender profiles across available treatment modalities to estimate the optimal mix of treatment. In addition, the current drug court
eligibility assumptions (that, for example, those with violence in their current
charge should be excluded) are testable using this method. Estimates can also be
generated about the treatment capacity that would have to become available to
facilitate the additional demand for treatment.
We believe the synthetic data set we have designed is ideally suited to address
these future questions. Note that the additional variables of interest could be
interpolated onto the current dataset from any other data source. In a similar
manner, if in future researchers develop better estimates of the long term (post
graduation) crime reducing benefits of treatment, they can be interpolated onto
the synthetic data as well and built into the analysis.
A final future benefit of the synthetic data approach is that local jurisdictions that may not have the resources to conduct expensive studies of the potential costs and benefits of its policy options (regarding offenders at risk of drug
dependence or abuse) may be in a position to simply replace the prevalence estimates in the synthetic data with numbers that better reflect their jurisdiction.
Thereafter, they can utilize all the knowledge that has been interpolated onto

Discussion

71

the synthetic data from several data sources and, potentially, several scholars for
making informed decision relevant to their population.
These extensions are exciting and possible, at least in theory. Several are
currently under way. We hope that this article will help trigger interest in the
use of such detailed and large synthetic data, as a viable alternative to real microdata, for generating and assessing simulated evidence on the prospects of going
to scale in other interventions.

72

To Treat or Not to Treat

Chapter 6
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Appendix A
Mathematical Appendix
A.1.

INTERPOLATION TECHNIQUE

For all of the modeling work performed in this paper, we use a semi-parametric
interpolation technique. Since we are interested in generating a synthetic data
that resembles the evidence in several different sources as closely as possible, it
would be desirable to allow non-linear, flexible links among the attributes and
the estimated quantities. To do so, we utilize an approach which, like nonparametric regressions, computes expectations about an outcome as a weighted
average of observed outcomes. The weights reflect the empirical similarity of a
profile and an actual case in the data being used. The intuition behind this strategy is similar to the theory of case based reasoning among humans (Gilboa and
Schmeidler 1995, 1997, 2001). When we encounter a new situation, a heuristic approach to forming expectations is to think back on our experience and
assess the empirical similarity of this new situation to our experience. Gilboa,
Lieberman, and Schmeidler (2006) provide several examples of this form of reasoning in everyday decision-making, and lay out its axiomatic foundation. For
our analysis, we use the approach to merely interpolate data onto the synthetic
dataset.
One major advantage of the strategy is that we are able to uncover and use

81

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To Treat or Not to Treat

non-linear relationships without explicitly specifying complicated functional
forms. The learning strategy is a localized one that uncovers such non-linear
links, if they exist, automatically. It is similar, in spirit, to non-parametric regression and kernel based smoothing techniques (Silvernam 1986; Loader 1999;
Pagan and Ullah 1999; Fan and Yao 2003). A brief explication of our approach
follows.
Let xkn and xk m represent the values of the kth attribute of any two sample
members (indexed by n and m where both n, m = 1, . . . , N ). The empirical
similarity weights between units n and all other units can be defined as:
p mn =

exp −
m exp

k

−

θk (xk n − xk m )2
k

θk (xk n − xk m )2

(A.1)

where θk are shrinkage parameters that must be estimated with the evidence to
reflect the average amount of similarity in terms of the kth attribute. Our estimation procedure is similar to, and builds on, developments in the field of artificial intelligence (Huang, Kecman and Kopriva 2006). It falls under the general
class of learning models dubbed unsupervised learning algorithms. It is designed
to learn from the evidence (observed samples) to predict what can reasonably be
expected to happen in hypothetical or unobserved instances. In order to make
these predictions, the algorithm computes a similarity score for the hypothetical scenario to all scenarios already observed and makes the best guess based on
that. The choice of θk parameters is crucial in the analysis. Appendix IV explain
how these parameters are estimated and how the asymptotic standard errors for
θk , as well as related quantities, are estimated. Similar to human learning, they
are estimated by appropriately balancing the algorithm’s need to learn from the
evidence, not memorize it.
Once we have model estimates, i.e., once we have recovered the θˆk , we can
compute a host of interesting quantities from the available evidence. For example, we can simulate the expected outcome (say y) for a profile as follows. Let
the kth attribute for profiles j ∈ J be denoted by xk j . Armed with θˆk , we can

83

Mathematical Appendix

compute the empirical similarity of this profile to all observations in the real
data as
exp − k θk (xk j − xk m )2
pj m =
(A.2)
2
m exp −
k θk (xk j − xk m )
and use the empirical similarity between the profile and the observed sample
members to compute the expected outcome as
y m ˆp j m

yˆj =

∀ j ∈ J (profiles)

(A.3)

m

Note, however, that the parameters are estimated just once and used to compute the empirical similarity of each and every profile to all observations in the
sample. To see this, recall from (A.1) that the similarity between any two observations n or m is based only on xn and x m , and not any outcomes. Therefore,
once the algorithm has been trained (i.e., θˆk estimated) it can be used to interpolate any number of outcomes onto the synthetic dataset.
A.2.

PREVALENCE ESTIMATION

For each of the j = 1, . . . , J profiles, we are interested in estimating the annual
number of arrestees nationwide (a j ). If we had this information directly in the
re-weighted ADAM we could interpolate this variable directly onto the synthetic data. However, ADAM provides information on the number of times
individuals were arrested in the year prior to the current booking ( bi where
bi g t 1 ∀i ∈ N ). Using the empirical similarity between synthetic profiles and
ADAM sample members, we compute the expected number of arrests for particular profiles as bˆ j = i bi ˆpi j .
Note that individuals who are arrested more frequently ought to have a
larger share of all arrests nationwide. Therefore, we next re-scale b j to mimic
census numbers. This ensures that the total number of arrests across all profiles
sums to the total number of adult arrests nationwide.

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To Treat or Not to Treat

Next, suppose that we can estimate a profile specific annual recapture rate
(r j )—the proportion of all arrests in a year that are re-arrests. This would allow
us to convert the number of arrests into the number of arrestees as
a j = b j ∗ (1 − r j )

∀j ∈ J

(A.4)

The intuition behind this equation is straight forward. If the re-capture rate is
0 then it must be the case that the number of arrestees are exactly equal to the
number of arrests (since the probability of recapture is null). As the re-capture
rate increase, the number of arrestees would be an appropriately scaled down
version of the number of arrests. At the limit, the number of re-arrests will be
equal to b j − 1 (i.e., the number of arrests less 1) so that, with a re-capture rate
of r j =

b j −1
bj

, the number of arrestees a j is exactly 1 (i.e., all arrests are generated

by just 1 arrestee being recaptured several times).
We compute the expected re-capture rate also from the re-weighted ADAM
data using bi . Note that the number of recaptures (re-arrests) is bi − 1. If we
denote the hazard of a re-capture event at time t as hi (t ), then, by definition, the
probability of recapture within the 1 year period can be computed as
1

hi (t ) d t

1 − exp −
0

1

since the survival probability is defined as exp − 0 hi (t ) d t . Moreover, since
the hazard is an intensity function, the integrated hazard yields the number of
events within a year. Since bi is the total number of arrests within the year, we
1
have 0 hi (t ) d t = bi − 1 and, therefore, we can define ri = 1 − exp(1 − bi ). Using the empirical similarity between synthetic profiles and ADAM sample members, we can now compute the expected re-capture rate for a particular profile as
ˆr j = i 1 − exp(1 − bi ) ˆpi j . The expected number of arrestees of a particular
profile can now be computed by plugging in estimates of b j and r j into (A.4).
Furthermore, since ADAM has classifications for arrestees being at risk of

85

Mathematical Appendix

drug dependence or abuse, we can convert these into two binary outcomes.
Now, using the empirical similarity weights, we can generate estimates of the
ˆ j (d )) or
probability of an arrestee profile being at risk of drug dependence (π
ˆ j (a)). When combined with aˆj we obtained estimates of the numabuse (π
ˆ )) or abuse
ber of potential clients at risk of drug dependence (ˆ
ad j = aˆj π(d
ˆ
(ˆ
aa j = aˆj π(a)).
A.3.

COMPUTING VARIANCE

Formulas for computing the variance of the sum of independent random variables or scaled random variables are available in introductory statistics texts.
For the product of a set of independent random variables, denoting xˆ the expectation and x˜ the variance of a random variable, we use the following formula provided in Goodman (1962). If y = k xk , then yˆ = k xˆk and y˜ =
˜k + xˆk2 − k xˆk2 .
k x
A.4.

EMPIRICAL SIMILARITY WEIGHTS

Let pnm reflect the empirical similarity between unit m and n for all n, m =
1, . . . , N units in the training sample. Then we wish to link these weights to a set
of K attributes recorded, say, as xn = (xn1 , . . . , xnK ) for each unit.
The Euclidean distance between any to units, along the K different dimensions, may be computed as
φk n m = (xk n − xk m )2
so that we can compute the sum of p-weighted dis-similarity among the training
sample units as:
φk n m pn m
n

m

If we wish these weights to be a root-N consistent estimates of the diversity
among sample members, then a good sample analog of this quantity is σk2 / N

86

To Treat or Not to Treat

where
σk2 =

2

1

xk n − x k

N

n

is the observed sample variance of the kth attribute and x k its mean.
In order to ensure that the estimated weights provide this consistency, we
therefore convert this requirement into a set of constraints that the weights must
satisfy (in the sample). In other words, we require that
σk2 / N =

φk n m p mn
n

∀k ∈ K

(A.5)

m

If in addition, we wish to use the weights to compute expectations, we want
them to be normalized–i.e., sum to 1. This results in another set of constraints
1=

p mn

∀n ∈ N

(A.6)

m

What we now have is an ill-posed inversion problem: many more unknowns
(N ) than equations linking them (N + K). Typically, an infinite number of solutions will be consistent with the constraints. We need a way to choose among
them.
Information theory, an inter-disciplinary field that uses entropy and entropyrelated measures to quantify uncertainty, provides the philosophical justification
to make this choice. Edwin Jaynes, a physicist, argued in a series of influential paper that when faced with a problem that has an infinite number of solutions we should choose the solution that is least informative while satisfying the
constraints ( Jaynes, 1957a; Jaynes, 1957b). To operationalize such an agnostic
approach, Jaynes needed some way to quantify the lack of information. Fortunately, within the context of a problem in communication theory, Shannon
(1948) had, just a few years earlier, developed a precise definition of uncertainty
and termed it Information Entropy. Given a set of J proper probabilities, Shannon defined the uncertainty captured in them as H (w) = − j w j log w j . In
2

87

Mathematical Appendix

what has come to be known as the Maximum Entropy formalism, Edwin Jaynes
proposed to use Shannon’s Entropy as the criterion to maximize, subject to all
available constraints, in order to derive conservative inferences from the data.
The problem of assigning values to our similarity weights then can be formulated as a constrained maximization problem and solved by the method of
Lagrange. The primal Lagrange functions is:
=−

pnm log pnm +

ηn (1 −

nm

n

m

and solving the first order conditions
the solution:
p mn =

exp(−

k

∂
∂ p mn

φk mn θk )
k φk mn θk )

m exp(−

θk (σk2 / N −

p mn ) +
k

= 0 and

∂
∂ ηn

φk mn p mn )
nm

(A.7)
= 0 simultaneously yields

= Ω−1
exp(−
n

φk mn θk )

(A.8)

k

where θ1 , . . . , θK are the Lagrange Multipliers to be estimated and Ωn , termed
the partition function, ensures that the weights are properly normalized.
Note that this optimal solution can be inserted back into the primal to derive
the corresponding dual objective functions:
θk σk2 / N +

=
k

log Ωn

(A.9)

n

This is an unconstrained minimization problem in the unknown Lagrange
Multipliers that can be solved in a variety of software fairly easily. Note that
once the Lagrange Multipliers are estimated, they can be ported to the validations samples and similarity weights can readily be computed for each sample
member or can be used to assess the similarity/dissimilarity between a new observations (or a profile) and the entire training data.
Suppose we denote a new observations with the index j , i.e., this observations has attribute profile x j . Then we can compute how similar this individual

88

To Treat or Not to Treat

is to the training sample by plugging his/her attribute set into (A.8) to get:
ˆp j m = Ω−1
exp −
j

θk (xk j − xk m )2

∀m ∈ N

(A.10)

k

Since they are normalized, they will yield weights that can be applied to compute expectations using past outcomes for the training sample (i.e., ∀m ∈ N ).
Therefore, a data-driven expectations for an outcome for this individual can be
computed as:
ym p j m
(A.11)
yˆj =
m

The dual objective function (A.9) is an unconstrained optimization problem
in the parameter vector θ1 , . . . , θk . It falls under the general class of extremum
estimators. The consistency and asymptotic normality of these estimators can
be established under fairly general regularity conditions (Mittelhammer, Judge,
and Miller 2000,132–139). One way to assess the sampling variability of the
Lagrange Multipliers is to compute the negative inverted Hessian of the dual
objective function. That is,
ΣΘ = −

∂2
∂ Θ∂ Θ

−1

(A.12)

where Θ = (θ1 , . . . , θK ) . ΣΘ can be used to assess the sampling variability of
the Θ. But, more importantly, it can be used to construct asymptotic standard
errors around the various expectations derived in this paper.
Consider, for example, the quantity yˆj defined in (A.11). We have defined it
as the expected outcome for profile j . Since the algorithm has used a single data
set, we need a way to assess the sampling variability of this quantity. To do so, we
use the Delta-method (Greene 2000,357). Given an estimate of the asymptotic
covariance of Θ, we can approximate the covariance of any non-linear function

89

Mathematical Appendix

of it, e.g., yˆj , as follows:
y˜j =

∂ yˆj
∂Θ

ΣΘ

∂ yˆj

(A.13)

∂Θ

Using the definitions of yˆj from (A.11) and the definition of ˆp j m from (A.10),
we can derive
∂ yˆj
∂Θ

m

[x j − x m ]2 ˆp j m

y m ˆp j m

y m [x j − x m ]2 ˆp j m −

=−

m

(A.14)

m

and use that in (A.13) to approximate the asymptotic variance of each quantity
interpolated onto the synthetic data.
To show that the approach does successfully uncover hidden signals, even
from a small training data set (N = 200) with sufficient noise, we performed a
small simulation exercise. We generated data from the following process:
y = sin(2 × π × (1 − x)2 ) + ε

(A.15)

where x ∼ UNIFORM(0, 1) is some profile variable, y is some outcome variable, and ε ∼ NORMAL(0, 1).
After estimating the lagrange multiplier using only the information in the x
variable, we recovered the underlying signal. The true signal, the noisy data, and
the recovered signals are displayed in the figure A.1. As is evident, the algorithm
provides a very robust method for uncovering hidden relationships between the
variables—if such relationships truly exist.

90

Some Outcome Variable

To Treat or Not to Treat

True Signal
Recovered Signal
Noisy Data

Some Profile Variable

Figure A.1: Successfully recovering hiddens signals using empirical similarity
weights: An example.