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The cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel cluster randomized design, which often involves a limited number of clusters. In recent years, the cluster randomized crossover design has been increasingly used to evaluate the effectiveness of health care policy or programs, and the interest often lies in quantifying the population-averaged intervention effect. In this paper, we consider the two-treatment two-period crossover design, and develop sample size procedures for continuous and binary outcomes corresponding to a population-averaged model estimated by generalized estimating equations, accounting for both within-period and interperiod correlations. In particular, we show that the required sample size depends on the correlation parameters through an eigenvalue of the within-cluster correlation matrix for continuous outcomes and through two distinct eigenvalues of the correlation matrix for binary outcomes. We demonstrate that the empirical power corresponds well with the predicted power by the proposed formulae for as few as eight clusters, when outcomes are analyzed using the matrix-adjusted estimating equations for the correlation parameters concurrently with a suitable bias-corrected sandwich variance estimator.
Li et al. (Mon,) studied this question.