Stepped wedge cluster randomized controlled trials: sample size and power determinations

Stepped wedge cluster randomized controlled trials (RCTs) are increasingly used in evaluating a causal-effect relationship between an intervention and an outcome. Sample size and power calculations are critical in designing a statistical study. Thus, the purpose of our study is to evaluate the power for both the continuous and binary responses in the context of the stepped wedge cluster design including three levels (such as hospital, physician, and individual levels). The data structure of stepped wedge cluster RCTs is hierarchical and correlated, and we used the mixed models approach to account for the correlation of observations within each level. This approach, comprised of linear mixed models (LMM) and generalized linear mixed models (GLMM), is particularly appropriate for data with more than one level. For the continuous responses, we used LMM and GLMM with the identity link function; for the binary responses, we used GLMM with the logit link function. To compute the power of the hypothesis test for no intervention effect versus an assumed intervention effect, simulation studies were conducted and the empirical estimate of the power was obtained by calculating the percentage of the estimated intervention effect falling in the rejection region of the test when the hypothesis of no intervention effect is false. From the results of the simulation studies, we found that the power increased as the intervention effect increased for both the continuous and binary responses, controlling for other parameters. As the overall sample size increased, a smaller minimum detectable difference with power at least 80% can be obtained. For the continuous responses only, the power increased as the within-individual correlation increased, controlling for other parameters. This increase of power with the correlation was prominent in the low intervention effect as compared to the high intervention effect. In this study, we proposed statistical models, demonstrated power calculations, and discussed important features of sample size and power for the stepped wedge cluster design. The findings provide essential information in determining the optimal sample size and also can assure adequate power for stepped wedge cluster RCTs, which will have significant impact on research in public health in the future.