Clusters of Jail Incarcerations in U.S. Counties: 2010–2018

Figures & data

Fig. 1 Purely spatial clusters calculated with county-level jail incarceration counts and the population of each county using the discrete scan statistic with Poisson distribution. The clusters are overlaid onto a choropleth map of the relative risk of jail incarceration in each county. The 20 clusters with the highest likelihood-ratios are labeled.

Table 1 The top 20 significant purely spatial clusters of jail incarceration for 2010–2018 based on the likelihood-ratio of the purely spatial scan statistic ($p<0.0001).$

Cluster	Locations in cluster	Likelihood-ratio	Observed to expected ratio	Relative risk	Population
1	774	256536.25	1.72	1.97	30,048,640
2	125	26673.79	2.14	2.16	1,669,095
3	2	25812.62	2.21	2.22	1,444,831
4	89	25254.90	1.86	1.88	2,712,077
5	53	11710.70	1.84	1.85	1,269,218
6	1	9602.25	33.45	33.47	3,442
7	1	7273.03	25.40	25.41	3,835
8	1	6017.53	4.63	4.64	52,765
9	1	4832.46	2.17	2.17	289,325
10	15	3941.37	1.88	1.88	406,748
11	1	3669.13	1.80	1.81	429,875
12	1	2982.16	16.50	16.50	2,954
13	2	2678.23	5.45	5.45	17,011
14	57	2259.86	1.31	1.32	1,552,997
15	17	2210.63	1.31	1.31	1,561,339
16	1	1876.87	18.17	18.18	1,609
17	22	1863.44	1.37	1.37	924,728
18	1	1819.33	1.78	1.78	223,532
19	22	1776.07	2.18	2.18	125,571
20	1	1669.58	31.83	31.83	641

Fig. 2 Retrospective space-time clusters calculated using the discrete scan statistic with poisson distribution. The 20 clusters with the highest likelihood-ratios are labeled.

Table 2 The top 20 significant retrospective space-time clusters of jail incarceration for 2010–2018 based on the likelihood-ratio of the retrospective space-time scan statistic ($p<0.0001).$

Cluster	Time	Locations in cluster	Likelihood-ratio	Observed to expected ratio	Relative risk	Population
1	2010–2013	724	105866.36	1.78	1.87	27,568,335
2	2012–2015	2	13503.12	2.33	2.33	1,444,831
3	2011–2014	196	12606.83	1.74	1.75	3,865,574
4	2011–2014	68	11715.34	1.89	1.90	2,673,430
5	2015–2018	1	7470.92	52.44	52.45	3442
6	2015–2018	90	7382.72	1.81	1.82	1,981,474
7	2013–2016	1	3445.27	26.68	26.69	3835
8	2010–2013	1	3433.90	2.21	2.21	429,875
9	2013–2016	1	3140.57	5.02	5.02	52,765
10	2011–2014	8	1910.09	1.60	1.61	847,414
11	2014–2017	1	1372.78	16.88	16.89	2954
12	2013–2015	8	1349.83	1.30	1.30	2,935,392
13	2012–2015	1	1325.79	1.64	1.64	531,510
14	2015–2018	10	1263.38	1.85	1.85	303,430
15	2011–2014	1	1229.11	1.98	1.98	223,532
16	2013–2016	37	1210.74	1.33	1.33	1,714,337
17	2010–2012	1	1184.63	1.76	1.76	482,939
18	2014–2017	3	1128.80	1.99	1.99	207,140
19	2015–2018	4	1038.59	3.19	3.19	47,119
20	2015–2018	22	964.10	2.32	2.32	125,571

Fig. 3 Prospective space-time clusters calculated using the discrete scan statistic with poisson distribution. The 20 clusters with the highest likelihood-ratios are labeled.

Table 3 The top 20 significant prospective space-time clusters of jail incarceration for 2010–2018 based on the likelihood-ratio of the prospective space-time scan statistic ($p<0.0001).$

Cluster	Time	Locations in cluster	Likelihood-ratio	Observed to expected ratio	Relative risk	Population
1	2015–2018	774	98263.16	1.71	1.80	30,048,640
2	2015–2018	152	11455.18	1.97	1.98	2,134,341
3	2015–2018	89	11058.92	1.86	1.87	2,712,077
4	2015–2018	2	8857.35	2.04	2.05	1,444,831
5	2015–2018	1	7470.92	52.44	52.45	3442
6	2015–2018	53	6346.86	1.95	1.96	1,269,218
7	2015–2018	1	3397.68	26.53	26.54	3835
8	2015–2018	1	2420.33	4.40	4.40	52,765
9	2015–2018	1	1858.33	2.08	2.08	289,325
10	2015–2018	2	1379.15	5.99	6.00	17,011
11	2015–2018	1	1369.85	16.81	16.81	2954
12	2015–2018	10	1263.38	1.85	1.85	303,430
13	2015–2018	17	1057.02	1.32	1.32	1,561,339
14	2015–2018	4	1038.59	3.19	3.19	47,119
15	2015–2018	2	1028.66	3.08	3.08	50,201
16	2015–2018	22	964.10	2.32	2.32	125,571
17	2015–2018	22	963.31	1.40	1.40	924,728
18	2015–2018	1	886.92	19.38	19.38	1609
19	2015–2018	1	818.14	2.61	2.61	61,625
20	2015–2018	5	758.64	1.32	1.32	1,120,060

Table 4 Parameter estimates from the negative binomial regression model.

Parameter	Estimate	Standard error	Wald’s 95% confidence limits	Wald’s ${\mathit{\chi }}^{\mathbf{2}}$	p-value
Black population percent ages 15–64 years	0.2075	0.0060	0.1958, 0.2193	1191.41	<0.0001
Republican voting percent	0.1772	0.0057	0.1661, 0.1883	980.13	<0.0001
Rate of poverty	0.1195	0.0048	0.1100, 0.1290	608.14	<0.0001
Latinx population percent ages 15–64 years	0.1167	0.0052	0.1065, 0.1269	503.11	<0.0001
Rate of uninsured	0.1282	0.0060	0.1164, 0.1400	455.90	<0.0001
Percent single parent homes	0.0873	0.0056	0.0763, 0.0982	244.57	<0.0001
Rate of violent crime	0.0713	0.0053	0.0608, 0.0818	178.29	<0.0001
Rate of unemployment	0.0391	0.0056	0.0281, 0.0501	48.33	<0.0001
Rate of opioid mortality	0.0251	0.0048	0.0156, 0.0345	26.81	<0.0001
Population density	–0.0144	0.0041	–0.0225, –0.0064	12.28	0.0005

Fig. 4 A Comparison map of locations in the original unadjusted spatial clusters and locations in covariate-adjusted spatial clusters. Red areas represent those which appeared only in the original significant spatial clusters. Yellow areas are clusters which appeared only after adjusting for the covariates. Orange areas or those which appeared in clusters both before and after covariate adjustment.

Table 5 Multivariate clusters of jail incarceration, republican vote, poverty, and black population %. (p < 0.0001).

Cluster	Number of locations in cluster	Relative risk
		Jail population	Poverty	Republican vote	Black population %
1	965	1.75	1.13	1.17	2.42
3	1	1.33	–	–	3.10
4	1044	1.03	1.00	1.25	–
8	1	1.08	1.19	–	2.03

Fig. 5 Purely spatial multivariate clusters of jail population, poverty, republican vote, and Black population.