TABLE 3.

Estimation of the average treatment effects with varying types of treatment effect heterogeneity across exposure time in 1000 simulated data sets with continuous outcomes. Each simulated data set represents a stepped-wedge CRT with E = 7 exposure-time periods, T = 8 steps, 14 clusters, and n = 100 individuals per cluster per time periods. The Monte Carlo error associated with 95% coverage for 1000 simulation iterations is 0.7%. 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
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) = 2, Δ = 2, σα = 0.141, σδ = 0
1	2.000	0.138	-	0.032	0.032	0.032	94.2	0.032	94.4
2	2.000	0.138	-	0.052	0.050	0.048	92.8	0.048	92.5
3	2.000	0.138	-	0.037	0.037	0.036	94.1	0.036	93.8
4	2.001	0.138	-	0.053	0.051	0.049	93.0	0.049	93.7
5	2.000	0.138	0.010	0.033	0.034	0.036	96.4	0.036	96.7
g(e) = 2 + δe with δe ~ 𝓝(0, 22), Δ = 2, σα = 0.141, σδ = 2
1	2.193	0.213	-	0.033	0.055	0.047	0.3	0.032	0.0
2	2.255	0.220	-	0.053	0.084	0.064	0.8	0.048	0.2
3	3.552	0.536	-	0.039	0.058	0.050	0.0	0.038	0.0
4	2.002	0.139	-	0.052	0.051	0.049	92.5	0.049	94.3
5	2.003	0.139	2.001	0.052	0.758	0.049	92.5	0.049	94.2
g(e) = (e − 1.840)/1.080, Δ = 2, σα = 0.141, σδ = 2
1	−1.236	0.992	-	0.034	0.041	0.043	0.0	0.033	0.0
2	2.000	0.139	-	0.051	0.050	0.048	93.5	0.048	92.7
3	−0.444	0.742	-	0.039	0.044	0.046	0.0	0.038	0.0
4	2.000	0.139	-	0.052	0.051	0.049	93.3	0.049	92.6
5	1.997	0.139	1.999	0.052	0.757	0.049	93.2	0.049	92.3
g(e) = −2.536I(e = 1) + 2.756I(e >1), Δ = 2, σα = 0.141, σδ = 2
1	−0.760	0.919	-	0.034	0.058	0.070	0.0	0.033	0.0
2	2.788	0.302	-	0.055	0.080	0.063	0.0	0.052	0.0
3	2.000	0.139	-	0.037	0.037	0.036	93.6	0.036	93.4
4	2.000	0.139	-	0.054	0.051	0.049	91.6	0.049	89.9
5	1.998	0.140	2.000	0.054	0.758	0.049	91.7	0.049	90.6