SCIENCE ADVANCES | RESEARCH ARTICLE
SOCIAL SCIENCES

The population prevalence of solitary confinement
Hannah Pullen-Blasnik1*, Jessica T. Simes2, Bruce Western1
Solitary confinement is a severe form of incarceration closely associated with long-lasting psychological harm and
poor post-release outcomes. Estimating the population prevalence, we find that 11% of all black men in Pennsylvania,
born 1986 to 1989, were incarcerated in solitary confinement by age 32. Reflecting large racial disparities, the
population prevalence is only 3.4% for Latinos and 1.4% for white men. About 9% of black men in the state cohort
were held in solitary for more than 15 consecutive days, violating the United Nations standards for minimum
treatment of incarcerated people. Nearly 1 in 100 black men experienced solitary for a year or longer by age 32. Racial
disparities are similar for women, but rates are lower. A decomposition shows that black men’s high risk of solitary
confinement stems primarily from their high imprisonment rate. Findings suggest that harsh conditions of U.S.
incarceration have population-level effects on black men’s well-being.
INTRODUCTION

1

Columbia University, New York, NY, USA. 2Boston University, Boston, MA, USA.
*Corresponding author. Email: hannah.pullen-blasnik@columbia.edu

Pullen-Blasnik, Sci. Adv. 7, eabj1928 (2021)

26 November 2021

the harm experienced by incarcerated people with preexisting mental
illness (8–10). Evidence for negative mental health effects is consist­
ent with high rates of suicidality among those with histories of solitary
confinement (11). After prison, people who have been incarcerated
in solitary confinement also experience higher risks of new criminal
convictions, unemployment, and mortality (12–14).
The most harmful effects of solitary confinement have been reported for long periods of extreme isolation (15). Extended solitary
confinement has been found to be especially harmful to mental
health, associated with anxiety, depression, impulse control disorder,
social withdrawal, lethargy, apathy, self-harming, and suicidal behavior (15). Infamous cases of injustice have also involved lengthy
incarcerations in solitary confinement (16–18).
Acknowledging harms and threats to human rights accompanying
sustained solitary confinement, the United Nations Standard Minimum Rules for the Treatment of Prisoners prohibited “prolonged
solitary confinement” in excess of 15 consecutive days. Similar standards have recently been adopted in Colorado and New York (19, 20).
U.S. health organizations have opposed prolonged solitary confinement (21), focusing on the harms for those with serious mental
illness (22). Federal courts also recognized the harms, finding
certain forms of solitary confinement unconstitutional, notably for
incarcerated people with mental illnesses (23–26).
Given evidence of harmful effects and racial disparity, what is
the prevalence of solitary confinement in the general population for
men and women in different racial and ethnic groups? This paper
uses administrative data from the Pennsylvania Department of
Corrections to estimate the population prevalence of imprisonment
to age 30 and of solitary confinement to age 32 for men and women
in four racial/ethnic groups: non-Latino white, non-Latino black,
Latino, and any other race or ethnicity. Pennsylvania has the sixth
largest prison population among all 50 states, and its incarceration
rate and racial disparity in incarceration are approximately equal
to the national average (27, 28). Pennsylvania state prisons thus include a relatively large share of the U.S. prison population, and
patterns of racial disparity resemble the U.S. pattern more broadly.
We estimate the likelihood of having ever been imprisoned or held
in solitary confinement from age 18 to 32 for a birth cohort born
1986 to 1989. To study prolonged isolation, we also estimate the
likelihood by age 32 of being held in solitary confinement for up
to a year or longer. These estimates of cumulative risk describe
the prevalence of imprisonment and solitary confinement among
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Black men in the United States are imprisoned at disproportionately high rates. As the U.S. incarceration rate grew to historically high
levels in the early 2000s, this disparity has resulted in population
level effects. Data from the 1970s to 2000s indicate that 20 to 30% of
black men have been to prison by their mid-30s (1, 2). Although
period prevalence estimates describe the broad extent of incarceration, they convey little about prison conditions or racial disparities
in the severity of incarceration.
Solitary confinement involves intense isolation that differs substantially from the experience of incarceration in the general prison
population. Individuals are typically locked in their cells for 22 or
23 hours each day. Meals and toilet use take place inside the cell
with only an hour outside for, say, recreation or showers. Access to
rehabilitation programs, recreation activities, medical appointments,
commissary supplies, phone calls, and visitation is severely restricted
(3–5). Although conditions of solitary confinement vary across prisons
and jurisdictions, three characteristics have come to define its practice
in the United States: 22- or 23-hour confinement in a cell each day, severe
restrictions on prison activities such as visits or programming, and widespread use of long-term isolation (3–5). There are few detailed analyses
of the prevalence of solitary confinement, but national surveys providing point-in-time estimates indicate that about 4% of the state prison
population is held in solitary confinement on an average day (3, 5, 6).
Researchers also report racial disparities reflecting high rates of solitary confinement among incarcerated black and Latino people (7).
The official purposes of solitary confinement are typically divided
into punishment and prison management. As punishment, sometimes
called disciplinary custody, prison authorities use solitary confinement as a response to misconduct charges such as fighting or drug
use. For prison management, often called administrative custody,
authorities may use solitary confinement to separate those deemed
to pose a threat to staff or other incarcerated people or as protective
custody for those who feel or are determined to be unsafe in the
general prison population. Although the purposes of solitary confinement vary, prison conditions and restrictions are often similar
whether incarcerated in disciplinary or administrative custody (3).
Solitary confinement has been found to have a variety of negative effects. Much of the research has focused on mental health and

Copyright © 2021
The Authors, some
rights reserved;
exclusive licensee
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SCIENCE ADVANCES | RESEARCH ARTICLE
Pennsylvania residents by their early 30s. We find evidence of large
racial disparities, with black men far more likely to experience
imprisonment, solitary confinement, and long periods of solitary
confinement compared to other demographic groups. We decompose the disparity into components related to the disparity in
imprisonment and the disparity in solitary confinement conditional on imprisonment. Estimates of the prevalence of solitary
confinement for different racial and ethnic groups show how the
pains of imprisonment are unequally distributed in the population
and how imprisonment is disproportionately damaging for black
and Latino communities.
RESULTS

Table 1. First solitary charge. Percentage distribution of the recorded reasons for first-time solitary confinement for a Pennsylvania prison admission cohort,
born 1986 to 1989, by gender, race, and ethnicity.
White (%)

Black (%)

Latino (%)

Other (%)

Total (%)

58.3

43.8

50.6

52.7

49.8

  Violent misconduct

8.3

13.9

11.3

7.3

11.6

  Verbal threat

7.7

19.0

12.3

9.1

14.1

  Contraband

14.4

8.4

11.1

14.5

10.9

  Defiance

11.3

15.0

14.8

16.4

13.7

3247

4706

959

55

8967

44.5

25.0

12.8

12.5

35.9

  Violent misconduct

11.0

25.0

10.3

12.5

15.2

  Verbal threat

7.7

21.4

25.6

25.0

13.4

  Contraband

15.1

8.3

7.7

0.0

12.3

  Defiance

21.7

20.2

43.6

50.0

23.2

337

168

39

8

552

Men
Administrative
custody
Disciplinary custody:*

Sample size (N)
Women
Administrative
custody
Disciplinary custody:*

Sample size (N)

*In the case of multiple charges, the most severe charge is reported for disciplinary custody.

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The current analysis uses administrative records that provide data
on admissions to Pennsylvania prisons from 2007 until 2016 and
admissions to solitary confinement until 2018. We follow a birth
cohort, born 1986 to 1989, from age 18 until the oldest are aged 30
in 2016 (the final year for measuring imprisonment) and aged 32 in
2018 (the final year for measuring solitary confinement). We apply
demographic life table methods to these data to calculate the risk of
first-time imprisonment and solitary confinement at each year of
age, adjusting for the effects of mortality and migration in the population (29, 30). With estimates of the at-risk population experiencing
imprisonment or solitary confinement each year, we calculate a
cumulative risk that describes the proportion of the birth cohort
that has ever experienced the event by a given age. We report
estimates of the cumulative risks of imprisonment by age 30 and
solitary confinement by age 32 for Pennsylvania men and women,
born 1986 to 1989.

Table 1 describes the reasons for first-time solitary confinement
provided in prison administrative records for men and women in the
study birth cohort. The table reports administrative and disciplinary
custody status for first-time solitary cases and the official misconduct charge issued by prison staff in cases of disciplinary custody.
Around half of all incarcerated men and a third of women were first
sent to solitary confinement not for officially charged misconduct
but for administrative custody. For both men and women, rates of
administrative custody were higher for white people and lower for
black people. While prison misconduct charging can be arbitrary
and unprotected by due process, official reasons for disciplinary
custody in Pennsylvania were often not severe. Among those sent to
solitary confinement for disciplinary custody, a minority were charged
with violence by prison authorities. The most common categories of
charged misconduct included refusal to follow the orders of prison
staff (defiance), using abusive or obscene language (verbal threats),
and possession of contraband such as drugs or weapons. Black men
and women were more than twice as likely to be charged with verbal
threats leading to solitary confinement as white men and women.
Table 2 shows the age-specific and cumulative risks of imprisonment to age 30 and solitary confinement to age 32 for all Pennsylvania
residents in the study birth cohort. The cumulative risk describes
the number of people ever imprisoned or placed in solitary confinement for at least 1 day as a proportion of the cohort population,
adjusted for mortality and migration. The age-specific risk of firsttime imprisonment for an individual in the 1986–1989 birth cohort
peaks at age 22. By age 30, nearly 3% of the birth cohort in the state
has been admitted to prison at least once. About half of those incarcerated are estimated to have been placed in solitary confinement at least once for at least 1 day. The age-specific risk of solitary

SCIENCE ADVANCES | RESEARCH ARTICLE
Table 2. Life table results. Life table calculations for risk of incarceration by age 30 and solitary confinement by age 32, Pennsylvania (2007–2018).
Age

Prison incarceration

Solitary confinement

Age-specific risk (%)

Cumulative risk (%)

Age-specific risk (%)

Cumulative risk (%)

18

0.05

0.05

0.02

0.02

19

0.13

0.19

0.03

0.05

20

0.25

0.44

0.10

0.15

21

0.31

0.74

0.13

0.28

22

0.34

1.08

0.14

0.42

23

0.33

1.40

0.16

0.58

24

0.31

1.71

0.17

0.74

25

0.30

2.01

0.15

0.89

26

0.27

2.27

0.15

1.05

27

0.24

2.51

0.13

1.18

28

0.17

2.67

0.12

1.30

29

0.11

2.77

0.07

1.37

30

0.07

2.84

0.06

1.43

31

–

–

0.03

1.46

32

–

–

0.00

1.46

Pullen-Blasnik, Sci. Adv. 7, eabj1928 (2021)

26 November 2021

black women, whose rate of 0.4% is nearly three times the cumulative risk for white and Latina women.
Given the racial disparity in imprisonment and solitary confinement, how much of the disparity in solitary confinement results
from high risks of imprisonment among black and Latino men and
women versus high risks of solitary confinement once imprisoned?
We decompose the racial and ethnic disparity in the cumulative
risks of solitary confinement into components for the disparity in
incarceration in the general population and disparity in solitary
confinement, conditional on imprisonment (Table 4). For this decomposition, the total disparity between, say, black and white men
is defined as the log cumulative risk for black men minus the log
cumulative risk for white men. The total disparity in solitary confinement can be written as a function of the black-white disparity
in the cumulative risk of incarceration in the population and the
black-white disparity in solitary confinement among those who
are in prison.
Decomposing the disparity in solitary confinement shows that
90% of the relatively high rate of solitary confinement among black
and Latino men is related to the disparity in incarceration in the
population. The remaining 10% is related to the relatively high risk
of solitary confinement among black and Latino men in prison.
With less data for women, the results are more varied. However, a
notable fraction of the risk of solitary confinement is related to the
relatively high risk of solitary confinement in prison among incarcerated women of color.
Last, we report on the cumulative risk of solitary confinement for
different minimum durations. Figure 1 shows the cumulative risk of
solitary confinement from at least 1 day to more than 365 days for
men (A) and women (B). The vertical line indicates 15 days of
solitary confinement, the benchmark for prolonged solitary confinement designated by the United Nations. We estimate that 9% of all
black men born between 1986 and 1989 in Pennsylvania have been
incarcerated in solitary confinement for a period exceeding 15 days
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confinement peaks at 24 years, about 2 years older than the age of peak
imprisonment risk. We estimate that 1.5% of the state’s 1986–1989
birth cohort has been incarcerated in solitary confinement for at least
1 day by age 32.
Estimates of the prevalence of imprisonment in Pennsylvania
are similar to findings from national studies (30). Nearly one in five
(19.1%) black men in Pennsylvania, born 1986 to 1989, has been
imprisoned by age 30 compared to 6.6% of Latino men and fewer
than 3% of white men (Table 3). The relative risk of imprisonment
for black men is nearly seven times the risk for white men. Latino
men experience about twice the cumulative risk of imprisonment as
that estimated for white men.
We also find high rates and larger racial disparities for solitary
confinement. Among black men in Pennsylvania born in the
late 1980s, one in nine (11.1%) had been held in solitary confinement for at least 1 day by age 32. Nearly 60% of incarcerated
black men in the birth cohort also spent time in solitary confinement. In comparison, 3.4% of Latino men and 1.4% of white men
in the study birth cohort had been incarcerated in solitary confinement by their early 30s. The risk of solitary confinement by age 32
for black men is more than 8 times the risk for white men, and
Latinos are 2.5 times as likely as white men to have been held in
solitary confinement.
Cumulative risks of imprisonment and solitary confinement among
women are significantly lower than among men. Men are about
10 times more likely to go to prison than women. Among all women
in Pennsylvania, born 1986 to 1989, we estimate that one-half of 1%
had been sent to prison by age 30. Among black women in the study
birth cohort, 0.8% have been imprisoned by age 30, about twice the
prevalence of imprisonment as for white and Latina women. Solitary confinement is also used less often among incarcerated women
than incarcerated men. Nearly 0.2% of Pennsylvania women, born
1986 to 1989, have been in solitary confinement by age 32. The
highest cumulative risk of solitary confinement is estimated for

SCIENCE ADVANCES | RESEARCH ARTICLE
Table 3. Cumulative risk by race. Cumulative risk of incarceration by age 30 and of solitary confinement by age 32 for Pennsylvania men and women born
1986 to 1989 by race and ethnicity. Risk ratios show the race-specific risk compared to the risk for white individuals.
Imprisonment by age 30 (%)

Imprisonment relative risk ratio

Solitary confinement by
age 32 (%)

Solitary relative risk ratio

White

2.82

1.00

1.35

1.00

Men
Black

19.05

6.76

11.09

8.20

Latino

6.60

2.34

3.41

2.52

Other

0.62

0.22

0.29

0.22

Total

5.26

–

2.80

–

White

0.48

1.00

0.15

1.00

Black

0.83

1.72

0.40

2.75

Latina

0.42

0.88

0.16

1.10

Other

0.10

0.20

0.04

0.27

Total

0.48

–

0.17

–

Women

Table 4. Racial disparity in imprisonment and solitary confinement and decomposition results. Racial/ethnic disparities in cumulative risks of incarceration
and solitary confinement reported as the difference of logs and relative risks, and decomposition results for racial/ethnic disparities in the cumulative risk of
solitary confinement by gender in the Pennsylvania birth cohort, born 1986 to 1989.
Difference of logs

Relative risk

%

  Incarceration

1.91

6.76

90.8

   Solitary given incarceration

0.19

1.21

9.2

  Total solitary

2.10

8.20

100.0

0.85

2.34

92.0

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Men
Black-white disparity

Latino-white disparity
  Incarceration
   Solitary given incarceration

0.07

1.08

8.0

  Total solitary

0.93

2.52

100.0

  Incarceration

1.06

2.88

89.9

   Solitary given incarceration

0.12

1.13

10.1

  Total solitary

1.18

3.25

100.0

Incarceration

0.54

1.72

53.9

Solitary given incarceration

0.47

1.59

46.1

Total solitary

1.01

2.75

100.0

Incarceration

−0.13

0.88

−133.4

Solitary given incarceration

0.22

1.25

233.4

Total solitary

0.09

1.10

100.0

Incarceration

0.67

1.95

73.1

Solitary given incarceration

0.25

1.28

26.9

Total solitary

0.92

2.50

100.0

Black-Latino disparity

Women
Black-white disparity

Latino-white disparity

Black-Latino disparity

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12

15 days

Black
Latino
White
Other

0.3
0.2

6

'

0

' ·---.--- -.- - - -.- - -.0

100

200

A

:-_ ~ : .-:. -:-_

300

0.0

0.1

4

'

2

Cumulative risk (%)

8

0.4

10

Race/ethnicity

15 days

0.5

SCIENCE ADVANCES | RESEARCH ARTICLE

0
Duration (days)

100

200

300

B

Fig. 1. Solitary by duration. Cumulative risk at age 32 in Pennsylvania, by duration of solitary confinement in days and by race/ethnicity for men (A) and women (B).

Pullen-Blasnik, Sci. Adv. 7, eabj1928 (2021)

26 November 2021

by the relative risk of solitary confinement given incarceration, is
larger for men than women.
DISCUSSION

Among black men in Pennsylvania, born 1986 to 1989, one in nine
has been locked in solitary confinement in state prison by age 32.
The cumulative risk of solitary confinement for black men is three
times higher than for Latino men and more than eight times higher
than for white men. Although we find a similarly large racial disparity
for women, the overall prevalence of solitary confinement is more
than 90% lower than the prevalence for men.
Unusual by international standards, long periods of solitary
greater than 15 days are also relatively common in Pennsylvania.
Estimates indicate that 9% of all black men born 1986 to 1989 in
Pennsylvania have spent at least 15 consecutive days, and almost 1
in every 100 has spent at least 1 year, in solitary confinement by age
32. Racial disparity in the population prevalence of the duration of
solitary confinement persists through at least 1 year of solitary confinement, with black men more likely to be held for long stays than
any other racial/ethnic group.
A decomposition shows that the overrepresentation of black men
in solitary confinement in the Pennsylvania population is primarily
the result of the overall racial disparity in incarceration. Roughly
10% of the black-white cumulative risk of solitary confinement is
related to the racial disparity in solitary confinement inside prisons.
The decomposition results suggest that there may be greater potential to reduce the relatively high exposure of black men to solitary
confinement by lowering the prevalence of, and disparity in, incarceration in the population. The racial disparity that black men
and women experience increases for longer durations of solitary
confinement, and this, too, mostly results from the racial disparity
in imprisonment.
The current analysis is subject to several limitations. First, the
findings apply only to Pennsylvania, and it is unclear whether similar
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by age 32, compared to 2.7% of Latino men, and 1.1% of white men
in the same birth cohort. For men incarcerated in solitary confinement, about 80% are thus held for longer than the United Nations
limit on the minimum treatment of prisoners. Nearly 1 in 100 black
men in Pennsylvania in the study cohort has been locked in solitary
confinement for at least a full consecutive year by age 32, compared
to a cumulative risk of 0.2% for Latino men and 0.08% for white men.
Examining racial and ethnic disparity across durations of solitary confinement, we find that black men are about 8.2 times more
likely to spend at least a day in solitary confinement compared to
white men by age 32 (Fig. 2). That disparity increases to 10.6 times
for periods of solitary confinement of at least a year. The Latino-­
white ratios remain relatively stable across all durations of solitary
confinement. The black-Latino disparity grows with duration, indicating that black men are disproportionately likely to experience
long periods of solitary confinement. The relative risks of solitary
confinement given incarceration follow a similar pattern to the
overall solitary confinement disparity, increasing over longer durations for black men compared to white and Latino men. At all durations, the relative risk of solitary confinement in the population is
much higher than the relative risk of solitary confinement given
incarceration. Thus, most of the disparity in prolonged solitary
confinement in the population results from the racial/ethnic disparity in incarceration rather than the disparity in treatment within
the prison.
The pattern of increasing disparity is more varied for women
because prolonged periods of solitary confinement are less common
among all women (Fig. 2). The black-white disparity remains relatively high across all durations of solitary confinement for women,
peaking at 220 days, where the black-white ratio is 6.3. The Latina-­
white disparity remains relatively low across durations and decreases
for longer durations. Similar to the pattern observed for men, most
of the disparity in prolonged solitary confinement results from the
disparity in incarceration rather than the disparity in solitary given
incarceration. However, disparity in treatment in prison, indicated

SCIENCE ADVANCES | RESEARCH ARTICLE
Solitary given incarceration

8

8

2
0

0

2

:-

4

6

6

A

4

- ·- ·- ·---·-·- - -·-·-- ·-·. - -·-·-·-·-·- -200

300

0

100

200

300

0

100

200

300

6

8

4

I•

, •'

'"

4

6

B

8

10

12

100

12

0

10

Disparity ratio

Black−white ratio
Black−Latino ratio
Latino−white ratio

10

10

12

12

Solitary

0

100

200

2
0

0

2

~----- ·-',--,_
300

Duration (days)

rates and disparities would be found in other states. Because solitary
confinement is used in a similar way to other jurisdictions (31) and
rates of solitary confinement in the state mirror national levels (5),
we believe that similar patterns would likely be found elsewhere. Still,
racial disparities in imprisonment vary across states (28). States with
relatively high disparities in imprisonment would likely have higher
disparities in the risk of solitary confinement than those reported
here. Second, the data only allow us to explore prevalence from ages
18 to 32 and only within state prisons. Without data on solitary confinement in other types of incarceration such as jails, and more data
across the life course, the results underestimate the population prevalence of solitary confinement. Third, stratifying the analysis by
additional demographic measures such as education would likely
yield even greater disparity in the risk of solitary confinement because of the high rate of imprisonment among people with little
schooling. In particular, pervasive imprisonment among black men
with very little schooling (30) may be matched by pervasive solitary
confinement in this same segment of the population.
The evidence indicates that a high and disparate rate of imprisonment is closely associated with high rates of population-level
exposure to solitary confinement among black men. Because solitary confinement has harmful effects on health and well-being,
and federal courts have scrutinized conditions of extreme isolation, the pattern of imprisonment itself may have a social impact,
threatening public health and collective security against cruel and
unusual punishment guaranteed by the Constitution. Although
efforts to improve prison conditions may reduce the harms of
incarceration, our evidence indicates that large reductions in
black men’s absolute and relative exposure to solitary confinement
Pullen-Blasnik, Sci. Adv. 7, eabj1928 (2021)

26 November 2021

will depend on reducing the general level and racial disparity of
imprisonment.
MATERIALS AND METHODS

Pennsylvania has 23 state prisons, with 2 designated for women.
Prison conditions vary widely. The oldest prison in the system was
built in 1889, and 16 prisons opened after 1990 with the newest
facility having opened in 2018. All have solitary confinement units.
In solitary confinement—whether for disciplinary or administrative custody—incarcerated people are provided with basic supplies
for clothing, bedding, and hygiene, and staff provide food through
a slot in the door. Typical cells are about 3 meters by 2.5 meters and
include one or two fixed bunk beds, a toilet, and sink. These conditions are similar to those found nationwide (3, 5, 31).
Estimates of the cumulative risks of imprisonment and solitary
confinement are based on census data, vital statistics, and prison administrative records. The core data file records all prison admissions
and discharges from 2007 to 2016 in the state, with data on those
already admitted continuing through February 2018. The dataset
includes demographic and prison misconduct information and detailed records on the incidence and dates of solitary confinement.
We operationalize solitary confinement and duration using a combination of misconduct charge records and the admission and release dates that indicate when an incarcerated person entered and
left disciplinary or administrative custody. A solitary confinement
stay in this analysis includes all records where an individual was
held in solitary confinement for at least 1 day, thus avoiding
potential overinflation from temporary holds for transfers or court
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Fig. 2. Racial/ethnic disparity by duration of solitary confinement. Smoothed relative cumulative risks of solitary confinement and solitary confinement given
incarceration, for men (A) and women (B) by number of consecutive days in solitary confinement.

SCIENCE ADVANCES | RESEARCH ARTICLE
Table 5. Population race/ethnicity compositions. Percentage distribution of race/ethnicity of a Pennsylvania birth cohort, born 1986 to 1989, by gender for
the total state census population, the cohort admitted to prison by age 30 (2007–2016), and the cohort held in solitary confinement by age 32 (2007–2018).
White (%)

Black (%)

Latino (%)

Other (%)

Sample size (N)

State population
(2010)

74.2

12.4

8.0

5.3

345,222

Prison population
(2007–2016)

40.6

47.8

10.9

0.7

16,906

Solitary population
(2007–2018)

36.3

52.4

10.7

0.6

9061

State population
(2010)

74.3

12.9

7.3

5.6

336,982

Prison population
(2007–2016)

70.5

22.0

6.3

1.1

1626

Solitary population
(2007–2018)

61.6

30.1

6.9

1.4

562

Men

Women

Table 6. Solitary confinement exposure statistics. Solitary confinement
incarceration characteristics of a Pennsylvania prison admission cohort,
born 1986 to 1989, by gender and race/ethnicity.
Median
average time
in solitary
confinement
(days)

Median
cumulative
time in solitary
confinement
(days)

Men
White

47.9

26.5

48.0

Black

58.7

33.0

77.0
60.0

Latino

52.9

29.0

Other

47.4

26.0

30.0

Total

53.6

30.0

63.0

16,906

9061

9061

30.2

20.8

30.0

Sample size (N)
Women
White
Black

47.2

29.7

65.0

Latina

37.9

31.0

45.0

Other

44.4

24.0

41.5

Total

34.6

24.2

41.0

Sample size (N)

1626

562

562

appearances. Our analysis is confined to individuals born 1986 to
1989, allowing us to observe first-time imprisonment and solitary
confinement in Pennsylvania. With data from 2007 to 2018, the birth
cohort ages from 18 to 32. Time-invariant person-level identification numbers allow us to identify individuals across prison terms,
ensuring that first-imprisonment and first-solitary risk estimates
reflect the experiences of individuals, rather than distinct prison
admissions for the same person.
To calculate cumulative risks, we begin by estimating the age-­
specific risks of imprisonment and solitary confinement. At age
Pullen-Blasnik, Sci. Adv. 7, eabj1928 (2021)

26 November 2021

	​​r​ a​​  = ​S​ a​​  / ​​ Pˆ​​  a​​​	

(1)

The at-risk population is the observed population, Pa, minus all
those who have been in solitary confinement and survived to age a,
where survivors are those still living who have not left the state.
Population counts by gender, race/ethnicity, and cohort are obtained
from the 2010 U.S. Decennial Census and American Community
Survey (ACS). To adjust for migration and mortality, we calculate
annual Pennsylvania migration rates from the ACS and age-specific
mortality by race/ethnicity and gender from the CDC WONDER
Database. Following the 1986–1989 birth cohort from age 18, we
calculate age-specific risks for each year of age, the cumulative risk
of imprisonment to age 30 in 2016, and the cumulative risk of solitary confinement to age 32 in 2018.
To estimate the cumulative risk, the age-specific risks, ra, are used
~
to expose a hypothetical population of size, P
​​​  ​ ​ a​​​, at risk of being imprisoned and of going to solitary confinement for the first time. We
~
set the baseline population, P
​​​  ​ ​ 18​​​, called the radix in demographic life
table analysis, to 100,000 (29). Exposing a population to age-specific
~
~
risks yields the number going to solitary confinement, S​​​  ​ ​ a​​  = ​r​ a​​ ​​ P​ ​ a​​​,
at each year of age. The cumulative risk is given by the total ever in
solitary confinement as a proportion of the population. For the
cumulative risk of solitary confinement
~
 ​​ ​​ ​S​​  a​​
​∑ 32
a=18
─
	​
c = ​
​​	
(2)
~
​​ P​​  18​​
We also apply this method to estimate the cumulative risk of
imprisonment to age 30 and the cumulative risk of solitary confinement to age 32 by the duration of stay in solitary confinement for
minimum durations up to a year or more. For the duration calculations, we define first solitary confinement as the first solitary stint
that meets the duration threshold. For example, if an individual is
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Ever in solitary
confinement (%)

a = 18, 19,…32, the age-specific risk of solitary confinement, for
example, is estimated as the count of the number of people sent to
solitary confinement for the first time, Sa, divided by the population
at risk of first-time solitary confinement, P
​​​ ˆ​​  a​​​,

SCIENCE ADVANCES | RESEARCH ARTICLE

	​​​  Sr​​ = ​​  S∣Ir​​ × ​​  Ir​​​	

(3)

The black-white disparity, for example, can be written
​log ​​  SB​​ − log ​​  SW​​ = (log ​​  IB​​ − log ​​  IW​​ ) + (log ​​  S∣IB​​ − log ​​  S∣IW​​)​	 (4)
The first term on the right-hand side, logIB − log IW, is the
disparity in the cumulative risk of incarceration. The second term,
logS∣IB − log S∣IW, is the disparity in solitary confinement given
incarceration. The calculation of cumulative risks yields estimates of
Ir and Sr, which can be used to calculate the third decomposition
quantity, S∣Ir = Sr/Ir.
Because solitary confinement is experienced with some lag following incarceration, estimates of racial disparity are based on the
Pullen-Blasnik, Sci. Adv. 7, eabj1928 (2021)

26 November 2021

prevalence of imprisonment by age 30 but the prevalence of solitary
confinement by age 32. For the observed birth cohort, the first experience of solitary confinement occurs, on average, 1.3 years after
first incarceration. Of those who are held in solitary confinement,
77% have been placed in solitary within 2 years of their prison admission, and thus, a 2-year observation lag provides a good estimate
of the experienced lag time to first solitary stint.
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P. Dashtgard, N. Pifer, T. R. Blair, The body in isolation: The physical health impacts
of incarceration in solitary confinement. PLOS ONE 15, e0238510 (2020).
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held in solitary for 5 days at age 18 and for 15 days at age 20, their
first time in solitary confinement for 1 day or more would occur at
age 18; for 15 days or more would occur at age 20; and for longer
durations, such as 30 days or more, they would have no qualifying
solitary confinement experience.
Table 5 reports descriptive statistics for the racial/ethnic composition of the 1986–1989 birth cohort for the total Pennsylvania state
birth cohort population, the prison cohort population, and the cohort population that has spent at least 1 day in solitary confinement.
The prison-admitted birth cohort is 91% male, and the racial composition of the prison population varies by gender. Over half of the
prison admissions for men in the study cohort are black or Latino,
compared to under 30% among prison admissions for women.
Black men in this birth cohort are overrepresented in the prison
population and solitary confinement. While black men are only 12%
of the state cohort population, they make up 52% of the total cohort
population of men in solitary confinement.
Table 6 reports descriptive statistics for the Pennsylvania administrative data for the 1986–1989 birth cohort’s exposure to solitary
confinement. Over half of the men in the study cohort who have
been to prison have also been incarcerated in solitary confinement.
Nearly 60% of black men have been in solitary confinement for at
least 1 day, the highest solitary confinement rate among all race and
ethnic groups. Among those who have been in solitary confinement,
the median length of stay is 30 days. The median total number of
days that an individual in this birth cohort spends in solitary confinement during the study period is 63 days, with black and Latino
men spending more days overall in solitary confinement than white
men or men of another race. Solitary confinement is less common
for women in prison than it is for incarcerated men, and the women
spend less time in solitary confinement than men. Black and Latina
women stay longer in solitary confinement, with black women spending more than twice as many total days in solitary confinement
during the study period as white women.
Racial disparity in the cumulative risk of solitary confinement
can be decomposed with estimates of the cumulative risk of imprisonment (see Table 4). Calculations for the decomposition of racial
disparity require cumulative risks of imprisonment and solitary
confinement for each of the four race/ethnicity groups, r = B, W, L, O,
for black, white, Latino, and other. The cumulative risk of solitary
confinement, interpreted as a probability, Sr = p(Sr), is a function of
the probability of incarceration, Ir = p(Ir), and the probability of
solitary given incarceration, S∣Ir = p(Sr∣Ir)

SCIENCE ADVANCES | RESEARCH ARTICLE
31. Liman Program & ASCA, Time-in-cell: The ASCA-Liman 2014 national survey of
administrative segregation in prison, New Haven, CT: Yale Law School (2015).
Acknowledgments: We thank J. L. Jahn, S. Plummer, and N. Bardele for comments on the
manuscript. Thanks to K. Bradner and A. Lee for excellent research assistance. We
acknowledge the substantial assistance of the Pennsylvania Department of Corrections, which
provided access to administrative data used for the analysis. Funding: This study was
supported by NSF grant SES-1823846/1823854 (to B.W. and J.T.S.), Robert Wood Johnson
Foundation grant 77264 (to B.W. and J.T.S.), and Arnold Ventures grant (to B.W. and J.T.S.).
Author contributions: Conceptualization: J.T.S. and B.W. Methodology: H.P.-B. and
B.W. Investigation: H.P.-B. and J.T.S. Software: H.P.-B. Data curation: H.P.-B. and J.T.S. Formal
analysis: H.P.-B. and B.W. Visualization: H.P.-B. and B.W. Supervision: J.T.S. and B.W. Writing—

original draft: H.P.-B., J.T.S., and B.W. Writing—review and editing: H.P.-B., J.T.S., and B.W.
Competing interests: The authors declare that they have no competing interests. Data and
materials availability: Code used to produce the study are available at the Harvard Dataverse:
https://doi.org/10.7910/DVN/YMNPPM. Per our Data Use Agreement with the Pennsylvania
Department of Corrections, we are restricted from sharing the birth cohort data used in the
analysis. A version of the data can be provided by request pending a completed material
transfer agreement. Requests for the data should be submitted to bruce.western@columbia.edu.
Submitted 29 April 2021
Accepted 6 October 2021
Published 26 November 2021
10.1126/sciadv.abj1928

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ScienceAdvances
The population prevalence of solitary confinement
Hannah Pullen-BlasnikJessica T. SimesBruce Western

Sci. Adv., 7 (48), eabj1928. • DOI: 10.1126/sciadv.abj1928

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