Comparing analytical strategies for balancing site-level characteristics in stepped-wedge cluster randomized trials: a simulation study

Ma, Clement; Lee, Alina; Courtney, Darren; Castle, David; Wang, Wei

doi:10.1186/s12874-023-02027-y

Table 2 Relative Root Mean Square Error (RRMSE) of the estimated treatment effects

From: Comparing analytical strategies for balancing site-level characteristics in stepped-wedge cluster randomized trials: a simulation study

ICC	Number of sites	Sample size at each step	Imbalance index	Percentiles	With learning effect			With constant effect
					Effect size			Effect size
					0.2	0.5	1.0	0.2	0.5	1.0
0.01^a	6	10	0.000	0^th	1.646	0.738	0.444	0.747	0.304	0.158
			0.239	33^rd	1.653	0.758	0.472	0.748	0.314	0.159
			0.478	67^th	1.733	0.848	0.540	0.782	0.327	0.163
			0.717	83^rd	1.824	1.015	0.699	0.799	0.341	0.167
			0.956	100^th	1.951	1.225	0.964	0.851	0.373	0.18
		20	0.000	0^th	1.295	0.610	0.376	0.557	0.227	0.115
			0.239	33^rd	1.322	0.632	0.396	0.56	0.229	0.114
			0.478	67^th	1.383	0.717	0.453	0.568	0.236	0.117
			0.717	83^rd	1.515	0.870	0.569	0.589	0.242	0.121
			0.956	100^th	1.630	1.121	0.813	0.627	0.253	0.123
	12	10	0.000	0^th	0.896	0.409	0.253	0.389	0.161	0.082
			0.148	33^rd	0.902	0.430	0.264	0.395	0.162	0.083
			0.296	67^th	0.956	0.488	0.310	0.396	0.164	0.083
			0.414	83^rd	0.993	0.542	0.361	0.414	0.168	0.085
			0.946	100^th	1.365	1.060	0.835	0.491	0.197	0.094
		20	0.000	0^th	0.711	0.336	0.215	0.291	0.118	0.060
			0.148	33^rd	0.721	0.348	0.227	0.292	0.119	0.060
			0.296	67^th	0.780	0.399	0.262	0.297	0.120	0.060
			0.414	83^rd	0.812	0.452	0.298	0.296	0.120	0.061
			0.946	100^th	1.232	0.968	0.669	0.339	0.131	0.064
0.10^b	6	10	0.000	0^th	2.238	0.955	0.548	0.855	0.341	0.173
			0.239	33^rd	2.223	0.968	0.569	0.849	0.348	0.173
			0.478	67^th	2.314	1.042	0.632	0.860	0.351	0.173
			0.717	83^rd	2.349	1.169	0.775	0.849	0.349	0.173
			0.956	100^th	2.453	1.324	0.997	0.859	0.356	0.179
		20	0.000	0^th	1.656	0.752	0.437	0.614	0.249	0.124
			0.239	33^rd	1.706	0.768	0.460	0.615	0.249	0.124
			0.478	67^th	1.736	0.819	0.513	0.610	0.249	0.124
			0.717	83^rd	1.823	0.964	0.621	0.606	0.248	0.126
			0.956	100^th	1.930	1.159	0.841	0.614	0.248	0.123
	12	10	0.000	0^th	1.134	0.497	0.292	0.440	0.178	0.089
			0.148	33^rd	1.145	0.515	0.300	0.443	0.178	0.089
			0.296	67^th	1.188	0.562	0.346	0.437	0.178	0.089
			0.414	83^rd	1.209	0.610	0.395	0.449	0.178	0.090
			0.946	100^th	1.505	1.072	0.852	0.440	0.183	0.093
		20	0.000	0^th	0.840	0.381	0.233	0.318	0.127	0.064
			0.148	33^rd	0.845	0.392	0.245	0.318	0.128	0.064
			0.296	67^th	0.892	0.436	0.280	0.318	0.128	0.064
			0.414	83^rd	0.926	0.490	0.316	0.317	0.127	0.064
			0.946	100^th	1.281	0.974	0.680	0.313	0.127	0.064

^aThe ICC for the treatment condition for the 6-site SWCRTs were 0.040, 0.174, and 0.448 for the three effect sizes, 0.20, 0.50, and 1.00, respectively. The ICC for the treatment condition in the 12-site SWCRTs were 0.038, 0.161, and 0.424 for the three effect sizes respectively
^bThe ICC for the treatment conditions for the 6-site SWCRT were 0.125, 0.237, and 0.477 for the three effect sizes respectively. The ICC for the treatment conditions for the 12-site SWCRTs were 0.122, 0.226, and 0.456 for the three effect sizes respectively

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