Sample Size Determination for GEE Analyses of Stepped Wedge Cluster Randomized Trials

Abstract

In stepped wedge cluster randomized trials, intact clusters of individuals switch from control to intervention from a randomly assigned period onwards. Such trials are becoming increasingly popular in health services research. When a closed cohort is recruited from each cluster for longitudinal follow-up, proper sample size calculation should account for three distinct types of intraclass correlations: the within-period, the inter-period, and the within-individual correlations. Setting the latter two correlation parameters to be equal accommodates cross-sectional designs. We propose sample size procedures for continuous and binary responses within the framework of generalized estimating equations that employ a block exchangeable within-cluster correlation structure defined from the distinct correlation types. For continuous responses, we show that the intraclass correlations affect power only through two eigenvalues of the correlation matrix. We demonstrate that analytical power agrees well with simulated power for as few as eight clusters, when data are analyzed using bias-corrected estimating equations for the correlation parameters concurrently with a bias-corrected sandwich variance estimator.

Sample size requirements for detecting treatment effect heterogeneity in cluster randomized trials

“…Fourth, we have limited our attention to parallel CRTs, while other recent CRTs have considered the crossover 49 or stepped wedge designs. 35,50,51 It would be interesting to extend the existing sample size procedures developed for these unidirectional designs to similarly accommodate an interaction test. Finally, we have assumed equal cluster sizes to simplify the derivation of the sample size formula.…”

Power and sample size requirements for GEE analyses of cluster randomized crossover trials

“…However, for the within‐cluster association structure, an additional correlation parameter, α 2 , is required since repeated measurements are taken from the same individual . Consequently, the two‐period nested exchangeable correlation structure is extended to a two‐period block exchangeable correlation structure as in the work of Li et al The derivations provided in Section 3.1 and 3.2 can be repeated with the block exchangeable structure to obtain the revised sample size formulae. We provide additional technical details for such an extension in Web Appendix G. Our main finding is that the revised sample size formulae share the exact same structures with , and , with λ 2 and λ 3 replaced by the appropriate eigenvalues of the block exchangeable matrix.…”

Optimal designs in three‐level cluster randomized trials with a binary outcome

“…Given a value of K and n i , PD can be determined if the constraints hold: min( 1 , 2 , 3i ) > 0, where 1 = 1 − r, 2 = 1 + (K − 1)r − K , 3i = 1 + (K − 1)r + K(n i − 1) are the distinct eigenvalues of R iw (r, ρ). The proof was provided in Web Appendix A in the work of Li et al 26 Here, the constraints are equivalent to…”