A flexible sample size solution for longitudinal and crossover cluster randomized trials with continuous outcomes

Longitudinal cluster randomized trial (LCRT) and crossover cluster randomized trial (CCRT) are two variants of cluster randomized trials. In LCRTs, clusters of subjects are randomly assigned to different treatment groups and each subject has repeated measurements over the study period. In CCRTs, clusters of subjects are randomly assigned to different sequences. Within each sequence, clusters receive all treatments in a particular order. Both LCRTs and CCRTs lead to complicated correlation structures that involve longitudinal and intracluster correlations. Generalized linear mixed model (GLMM) and generalized estimating equation (GEE) approaches have been frequently employed in data analysis and sample size estimation. In this study we propose closed-form sample size and power formulas for LCRTs and CCRTs based on the GEE approach. These formulas are flexible to incorporate unbalanced randomization, different missing patterns, arbitrary correlation structures, and randomly varying cluster sizes, providing a practical yet robust sample size solution. Simulation studies show that the proposed methods achieve good performance with empirical powers and type I errors close to their nominal values.