Power calculation for detecting interaction effect in cross-sectional stepped-wedge cluster randomized trials: an important tool for disparity research

Yang, Chen; Berkalieva, Asem; Mazumdar, Madhu; Kwon, Deukwoo

doi:10.1186/s12874-024-02162-0

Table 2 Required cluster sizes to achieve 80% predicted power to detect interaction effect sizes for a simple exchangeable correlation structure with the number of clusters = 8 and ICC = 0.1

From: Power calculation for detecting interaction effect in cross-sectional stepped-wedge cluster randomized trials: an important tool for disparity research

\({\theta }_{1}\)(OTE)	\({\theta }_{3}\)(HTE)	Method	Prevalence rate for binary individual covariate, X
			30%							50%
			Cluster size	\(\Delta\) SE	Naïve SE		Robust SE		\(\varphi\)	Cluster size	\(\Delta\) SE	Naïve SE		Robust SE		\(\varphi\)
			Cluster size	\(\Delta\) SE	\({\psi }_{0}\)	\({\varphi }_{0}\)	\({\psi }_{0}\)	\({\varphi }_{0}\)	\(\varphi\)	Cluster size	\(\Delta\) SE	\({\psi }_{0}\)	\({\varphi }_{0}\)	\({\psi }_{0}\)	\({\varphi }_{0}\)	\(\varphi\)
\({\text{log}}\left(1.35\right)\)	\({\text{log}}\left(1.5\right)\)	GEE	110	-0.005	0.046	0.789	0.136	0.825	0.801	98	-0.005	0.038	0.785	0.118	0.824	0.803
		Mean(GEE,GEE-KC)	120	-	0.054	0.820	0.119	0.859	0.801	108	-	0.042	0.829	0.129	0.859	0.804
		GEE-KC	130	0.007	0.053	0.864	0.109	0.897	0.801	116	0.007	0.052	0.867	0.119	0.879	0.804
		GEE-MD	160	0.019	0.040	0.918	0.109	0.916	0.815	138	0.019	0.048	0.923	0.121	0.916	0.805
	\({\text{log}}\left(2\right)\)	GEE	40	-0.015	0.059	0.819	0.121	0.852	0.827	34	0.001	0.061	0.797	0.122	0.833	0.810
		GEE-KC	50	0.004	0.049	0.883	0.107	0.906	0.847	40	0.020	0.044	0.856	0.130	0.896	0.809
		GEE-MD	60	0.025	0.055	0.950	0.113	0.951	0.851	48	0.042	0.048	0.891	0.144	0.929	0.813
\({\text{log}}\left(1.68\right)\)	\({\text{log}}\left(1.5\right)\)	GEE	110	-0.002	0.046	0.791	0.118	0.822	0.807	96	-0.009	0.054	0.799	0.129	0.841	0.804
		Mean(GEE,GEE-KC)	120	-	0.055	0.829	0.126	0.860	0.807	106	-	0.046	0.820	0.116	0.847	0.805
		GEE-KC	130	0.009	0.052	0.847	0.121	0.867	0.806	114	0.002	0.048	0.833	0.115	0.869	0.805
		GEE-MD	160	0.022	0.039	0.908	0.119	0.922	0.819	134	0.015	0.053	0.891	0.109	0.904	0.801
	\({\text{log}}\left(2\right)\)	GEE	40	-0.005	0.053	0.811	0.124	0.846	0.831	34	-0.002	0.046	0.773	0.110	0.821	0.818
		GEE-KC	50	0.013	0.041	0.889	0.116	0.905	0.850	40	0.017	0.036	0.857	0.112	0.890	0.816
		GEE-MD	60	0.034	0.063	0.929	0.128	0.949	0.854	46	0.039	0.050	0.907	0.147	0.927	0.804

Estimated required cluster size was determined to achieve at least 80% predicted power. Bias of the standard error \(\Delta\) SE, empirical Type I error \({\psi }_{0}\), simulated power \({\varphi }_{0}\) (GEE fitted using both naïve and robust SE, respectively), and predicted power \(\varphi\) were obtained from the GEE power calculator with ICC = 0.1 using three methods GEE, GEE-KC, and GEE-MD for various combinations of HTE \({\theta }_{3}\) and OTE \({\theta }_{1}\). For scenarios with \({\theta }_{3}={\text{log}}\left(1.5\right)\), we also report the average of cluster sizes obtained by GEE and GEE-KC as a fourth method. Under scenario of prevalence = 30%, the cluster sizes are taken as multiples of ten intentionally to generate integer number of observations for both X = 0 and X = 1 within each cluster. And for the same reason, only even numbers are taken into account under the scenario of prevalence = 50%
Boldfaced simulated power denotes simulated power falls outside of 95% confidence interval for predicted power

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ISSN: 1471-2288

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