Pragmatic Cluster Randomized Trials Using Covariate Constrained Randomization: A Method for Practice-based Research Networks (PBRNs)

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Figure 1.
Distribution of balance criterion in study 1. The full set of all possible randomizations is represented by the total area under the curve.
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Figure 2.
Distribution of balance criterion. The set of all possible randomizations (after applying stratification criteria) is represented by the total area under the curve.

Table 1. Study 1 County-Level Baseline Variables for Randomization

Variable	County-Level (Rural and Urban) Variables for Randomization (n = 16)		Differences in Raw Variables Between Study Groups^*
Variable	Mean (SD)	Minimum, Maximum	Optimal Randomizations (n = 14)	Remaining Randomizations (n = 126)
In CIIS (%)^{^†}	87.2 (7.7)	70, 100	<1 (1)	<1 (1)
Children aged 19–35 months, by county (n)	4,197 (4,432)	234, 12,354	223 (613)	1,264 (6,325)^{^‡}
Up to date at baseline (%)	40.8 (8.3)	27.0, 54.0	2.1 (5.0)	4.9 (15.0)^{^‡}
Hispanic ethnicity (%)^{^§}	22.3 (12.9)	6.0, 44.0	5.6 (11.3)	7.9 (23.3)
African American race^{^‖}	2.9 (2.7)	0, 10.0	<1 (1.0)	1.4 (4.5)
Average income ($)^{^¶}	53,481 (15,793)	29,738, 93,819	3,659 (9,702)	9,731 (27,131)^{^‡}
Pediatric–to–Family Medicine practices ratio	0.28 (0.25)	0, 1.0	0.20 (0.40)	0.15 (0.40)
CHCs (n)	4.4 (3.5)	0, 11	1.3 (2.8)	1.6 (4.8)

Data are based on baseline information on the counties from the Colorado Department of Public Health and Environment, the Colorado Immunization Information System (CIIS), and 2010 Census data.
↵* Data are means (maximums).
↵† Percentage of children between 0 and 4 years who had ≥2 immunization records in CIIS.
↵‡ P < .01, optimal vs remaining randomizations.
↵§ Population by ethnicity (Hispanic/Latino or not).
↵‖ Population by race (black or other).
↵¶ Population by income.
CHC, community health center; SD, standard deviation.

Table 2. Study 2 Practice-Level Baseline Variables for Randomization

Practice-Level and Clinical Variables Obtained from EHR Data	Practice-Level Variables for Randomization (n = 18 Practices)		Differences Between Study Groups on Raw Variables^*
	Mean (SD)	Minimum, Maximum	Optimal Randomizations (n = 172)	Remaining Randomizations (n = 1556)
FTE clinicians (n)	3.8 (3.1)	1, 12	1.0 (2.6)	1.3 (3.2)^{^†}
African American race (%)	2.9 (3.7)	<1, 15.0	1.2 (3.1)	1.4 (3.1)^{^‡}
Hispanic ethnicity (%)	16.6 (18.5)	<1, 68.0	3.6 (10.7)	3.9 (10.7)
Medicaid/Uninsured (%)	13.8 (8.6)	0, 30.0	1.8 (3.3)	3.0 (7.5)^{^†}
Have type 2 diabetes (%)	34.9 (18.4)	13.0, 100	8.4 (15.3)	9.1 (16.8)^{^†}
HbA_1c >9 (%)	9.1 (7.5)	0, 25	1.5 (4.8)	2.4 (8.1)^{^†}
Stage 4 CKD (%)	6.7 (4.5)	0, 15.6	<1 (2.6)	1.9 (5.6)^{^†}
BP >130/80^{^§} (%)	58.1 (14.2)	35.4, 1.0	5.7 (14.4)	5.8 (18.0)^{^†}
BP>140/90 mmHg^{^‖} (%)	31.2 (11.6)	0, 51.9	2.6 (6.2)	4.5 (14.8)^{^†}
Mean HbA_1c^{^¶}	7.02 (0.38)	6.63, 7.88	0.05 (0.15)	0.12 ( 0.33)^{^†}
Mean eGFR	49.4 (3.2)	45.2, 59.4	0.7 (2.2)	1.3 (4.0)^{^†}
Mean systolic BP	132.1 (3.8)	124.7, 138.6	0.8 (2.5)	1.6 (5.1)^{^†}

↵* Data are means (maximums).
↵† P < .01, optimal vs. remaining randomizations.
↵‡ P < .05, optimal vs. remaining randomizations.
↵§ Patients have either systolic blood pressure (BP) >130 or diastolic BP >80, or both.
↵‖ Patients have either systolic BP >140 or diastolic BP >90, or both.
↵¶ Includes diabetic patients only.
CKD, chronic kidney disease; eGFR, estimate glomerular filtration rate; FTE, full-time equivalent; SD, standard deviation.

Table 3. Study 1: County-Level Baseline Variables by Group for Worst Randomization from Optimal Set

Variable	County-Level Variables, Mean (SD)
Variable	Group 1	Group 2
In CIIS (%)^*	87.8 (10.1)	86.6 (5.0)
Children aged 19–35 months (n)	4,275 (4628)	4,118 (4546)
Up to date at baseline (%)	40.1 (8.8)	41.5 (8.3)
Hispanic ethnicity (%)	23.8 (14.8)	20.9 (11.6)
African American race (%)	2.5 (2.4)	3.3 (3.1)
Average income ($)	56,264 (18,004)	50,699 (13,877)
Pediatric–to–Family Medicine ratio	0.33 (0.33)	0.23 (0.15)
CHCs (n)	4.8 (4.5)	4.0 (2.4)

Table 4. Study 1: Practice-Level Baseline Variables by Group for Worst Randomization from Optimal Set

Variable	Practice-Level Variables, Mean (SD)
Variable	Group 1	Group 2
FTE clinicians (n)	3.9 (2.9)	3.6 (3.6)
African American race (%)	2.2 (1.2)	3.7 (5.2)
Hispanic ethnicity (%)	13.0 (3.6)	20.1 (2.1)
Medicaid/Uninsured (%)	13.1 (8.2)	14.4 (9.4)
Diabetic (%)	30.4 (11.6)	39.3 (23.3)
HbA_1c >9 (%)	10.3 (8.9)	8.0 (6.2)
Stage 4 CKD (%)	7.3 (3.8)	6.1 (5.3)
BP >130/80 (%)	55.4 (6.7)	60.1 (19.1)
BP >140/90 (%)	33.3 (6.5)	29.2 (15.4)
Mean HbA_1c	7.0 (0.4)	7.0 (0.4)
Mean eGFR	48.4 (2.4)	50.4 (3.6)
Mean systolic BP	132.3 (3.0)	131.9 (4.6)

BP, blood pressure; CKD, chronic kidney disease; eGFR, estimate glomerular filtration rate; FTE, full-time equivalent; SD, standard deviation.

County	Raw County-Level Variables for Study 1
County	Location	In CIIS (%)	Children Ages 19–35 Months (n)	Up to Date on Immunizations (%)	African American Race (%)	Hispanic Ethnicity (%)	Average Income ($)	Pediatric Practice—to– Family Medicine Practice Ratio	Community Health Centers (n)
1	Rural	94	366	37	2	44	35,988	1.00	1
2	Rural	85	1,274	39	0	23	67,565	0.08	0
3	Rural	85	614	42	5	12	35,879	0.33	3
4	Rural	93	1,720	39	1	18	63,617	0.33	6
5	Rural	82	242	31	1	6	59,118	0.20	0
6	Rural	80	350	27	3	15	57,179	0.00	3
7	Rural	94	401	49	1	38	29,738	0.20	3
8	Rural	103	234	37	1	39	37,350	0.00	1
9	Urban	93	3,779	51	4	35	52,923	0.15	11
10	Urban	89	11,807	51	10	17	58,302	0.45	6
11	Urban	83	9,453	54	2	7	93,819	0.61	1
12	Urban	70	12,354	29	8	13	54,839	0.26	10
13	Urban	93	10,008	50	2	13	63,857	0.34	3
14	Urban	85	5,343	36	2	10	53,502	0.18	7
15	Urban	82	3,143	38	3	39	39,570	0.27	7
16	Urban	84	6,056	43	1	28	52,457	0.10	8