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 3 Required cluster sizes to achieve 80% predicted power to detect interaction effect sizes for a nested exchangeable correlation structure with the number of clusters = 8, ICC = 0.1, and CAC = 0.8

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	120	-0.009	0.047	0.804	0.118	0.824	0.829	100	0.001	0.050	0.808	0.105	0.850	0.806
		Mean(GEE,GEE-KC)	130	-	0.047	0.833	0.124	0.866	0.827	110	-	0.047	0.850	0.092	0.862	0.806
		GEE-KC	140	0.010	0.054	0.862	0.115	0.881	0.824	118	0.008	0.048	0.851	0.110	0.888	0.805
		GEE-MD	160	0.020	0.045	0.912	0.106	0.916	0.809	140	0.016	0.038	0.909	0.116	0.909	0.804
	\({\text{log}}\left(2\right)\)	GEE	40	-0.014	0.037	0.821	0.093	0.847	0.825	34	-0.012	0.054	0.784	0.120	0.824	0.809
		GEE-KC	50	0.005	0.055	0.886	0.136	0.902	0.845	40	0.008	0.058	0.859	0.130	0.881	0.807
		GEE-MD	60	0.026	0.037	0.937	0.126	0.941	0.849	48	0.029	0.041	0.891	0.113	0.914	0.811
\({\text{log}}\left(1.68\right)\)	\({\text{log}}\left(1.5\right)\)	GEE	110	-0.000	0.050	0.777	0.125	0.825	0.804	96	-0.002	0.043	0.799	0.116	0.830	0.801
		Mean(GEE,GEE-KC)	120	-	0.054	0.814	0.118	0.866	0.804	106	-	0.044	0.792	0.125	0.838	0.801
		GEE-KC	130	0.005	0.036	0.842	0.115	0.874	0.803	114	0.004	0.047	0.831	0.118	0.864	0.801
		GEE-MD	160	0.025	0.050	0.922	0.127	0.938	0.815	136	0.021	0.043	0.905	0.128	0.899	0.802
	\({\text{log}}\left(2\right)\)	GEE	40	-0.007	0.044	0.819	0.124	0.862	0.830	34	-0.011	0.048	0.768	0.115	0.829	0.817
		GEE-KC	50	0.012	0.041	0.897	0.115	0.914	0.849	40	0.008	0.049	0.847	0.128	0.886	0.815
		GEE-MD	60	0.033	0.040	0.935	0.118	0.949	0.853	46	0.030	0.052	0.884	0.122	0.916	0.802

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 and CAC = 0.8 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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