TABLE 4.

Estimation of the average treatment effects with varying degrees of exposure-time treatment effect heterogeneity in 500 simulated data sets with binary outcomes. Each simulated data set represents a stepped-wedge CRT with E = 7 exposure-time periods, T = 8 steps, K clusters, and n_kt individuals per cluster per time periods. The Monte Carlo error associated with 95% coverage for 500 simulation iterations is 1.0%. We use Δ to denote the average treatment effect, $\widehat{\Delta }$ to denote its estimate, $\widehat{\mathbb{E}}(\cdot )$ and $\widehat{SD}(\cdot )$ to denote sample average and sample standard deviation across simulated experiments, and $\widehat{SE}(\cdot )$ to denote the estimated standard error.

								Bootstrap
							Model-based	Within cluster		Within cluster period
K	${\mathit{n}}_{\mathit{kt}}^{\mathbf{a}}$	Model	$\widehat{\mathbb{E}}(\widehat{\Delta })$	$\widehat{\mathbb{E}}({\widehat{\sigma }}_{\alpha })$	$\widehat{\mathbb{E}}({\widehat{\sigma }}_{\delta })$	$\widehat{\mathit{SD}}(\widehat{\Delta })$	$\widehat{\mathbb{E}}(\widehat{\mathit{SE}}(\widehat{\Delta }))$	$\widehat{\mathbb{E}}(\widehat{\mathit{SE}}(\widehat{\Delta }))$	Coverage (%)	$\widehat{\mathbb{E}}(\widehat{\mathit{SE}}(\widehat{\Delta }))$	Coverage (%)
g(e) = 0.173, Δ = 0.173, σα = 0.131, σδ = 0
14	34 [6–96]	1	0.179	0.101	-	0.105	0.103	0.103	94.2	0.102	93.8
14	34 [6–96]	4	0.175	0.095	-	0.136	0.129	0.130	93.2	0.128	93.2
14	34 [6–96]	5	0.177	0.102	0.026	0.111	0.108	0.107	93.6	0.106	92.4
42	100	1	0.174	0.127	-	0.039	0.038	0.037	93.6	0.036	94.8
42	100	4	0.174	0.126	-	0.054	0.053	0.048	90.4	0.048	90.8
42	100	5	0.173	0.126	0.009	0.040	0.040	0.038	93.8	0.038	94.2
42	500	1	0.175	0.128	-	0.019	0.018	0.018	93.2	0.018	93.6
42	500	4	0.175	0.128	-	0.028	0.028	0.027	92.8	0.027	92.4
42	500	5	0.175	0.128	0.004	0.019	0.019	0.019	94.2	0.019	94.0
g(e) = 0.173 + δe with δe ~ 𝓝(0, 0.3242), Δ = 0.173, σα = 0.131, σδ = 0.324
14	34 [6–96]	1	0.180	0.104	-	0.108	0.103	0.104	91.8	0.102	92.0
14	34 [6–96]	4	0.186	0.096	-	0.147	0.131	0.132	91.6	0.129	90.2
14	34 [6–96]	5	0.180	0.104	0.303	0.128	0.170	0.117	93.0	0.115	91.0
42	100	1	0.181	0.128	-	0.038	0.038	0.037	93.2	0.037	92.6
42	100	4	0.171	0.126	-	0.055	0.054	0.049	91.8	0.049	90.4
42	100	5	0.175	0.127	0.302	0.053	0.126	0.047	92.2	0.047	90.2
42	500	1	0.188	0.130	-	0.019	0.018	0.018	85.6	0.018	85.2
42	500	4	0.175	0.128	-	0.028	0.028	0.027	93.2	0.027	93.2
42	500	5	0.176	0.128	0.301	0.028	0.112	0.027	92.8	0.027	93.0
g(e) = (e − 2.853)/6.667, Δ = 0.173, σα = 0.131, σδ = 0.324
14	34 [6–96]	1	−0.251	0.170	-	0.120	0.116	0.117	5.4	0.115	5.2
14	34 [6–96]	4	0.185	0.093	-	0.143	0.130	0.131	92.2	0.129	92.6
14	34 [6–96]	5	0.027	0.114	0.228	0.167	0.172	0.148	79.6	0.146	78.0
42	100	1	−0.293	0.187	-	0.041	0.041	0.041	0.0	0.041	0.0
42	100	4	0.174	0.126	-	0.054	0.054	0.049	90.9	0.049	91.1
42	100	5	0.145	0.127	0.286	0.056	0.121	0.050	89.0	0.050	87.6
42	500	1	−0.337	0.196	-	0.019	0.018	0.019	0.0	0.019	0.0
42	500	4	0.175	0.128	-	0.029	0.028	0.027	92.6	0.027	92.2
42	500	5	0.167	0.129	0.296	0.029	0.110	0.027	91.2	0.027	91.2
g(e) = −0.563I(e = 1) + 0.294I(e > 1), Δ = 0.173, σα = 0.131, σδ = 0.324
14	34 [6–96]	1	−0.200	0.163	-	0.121	0.117	0.120	12.4	0.116	9.6
14	34 [6–96]	4	0.184	0.096	-	0.139	0.130	0.131	92.6	0.129	92.2
14	34 [6–96]	5	0.117	0.105	0.317	0.131	0.176	0.123	91.2	0.121	90.2
42	100	1	−0.254	0.185	-	0.042	0.041	0.042	0.0	0.041	0.0
42	100	4	0.172	0.125	-	0.055	0.053	0.048	90.4	0.048	89.6
42	100	5	0.160	0.126	0.304	0.054	0.126	0.047	90.4	0.047	89.8
42	500	1	−0.300	0.195	-	0.019	0.019	0.019	0.0	0.019	0.0
42	500	4	0.174	0.128	-	0.028	0.028	0.027	93.6	0.027	93.6
42	500	5	0.171	0.129	0.301	0.028	0.111	0.027	92.6	0.027	93.2

^aIf n_kt is heterogeneous, Median n_kt [range] is reported, otherwise the constant n is reported.