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Performance of methods for small-sample inference in generalized linear mixed models for stepped-wedge designs with unequal cluster sizes Xu, Liang


Stepped-wedge cluster randomized trials are characterized by the sequential transition of clusters from control to intervention. Most studies that explored the statistical properties of such trials relied on asymptotic theory and/or assumed equal cluster sizes. In practice, the sample size is often limited, and cluster sizes are subject to variation. The impact of unequal cluster sizes has been studied in the context of parallel-arm cluster randomized trials, but it is unclear whether these results are generalizable to the stepped-wedge trial. Also, statistical performance varies across different allocations when the cluster sizes are unbalanced. We conducted simulations for continuous and binary outcomes to evaluate the performance of various analytical approaches for cross-sectional stepped-wedge trials with limited sample size and unequal cluster sizes. We explored methods commonly used for parallel-arm cluster randomized trials including the Wald test, F-tests with degrees of freedom approximations (Hemming et al. and Satterthwaite), the Kenward-Roger approximation and the bootstrap. Type I error was generally inflated with the Wald test for the continuous outcome while the Kenward-Roger approximation was overly conservative for both binary and continuous outcomes. Bootstrapping and F-tests with degrees of freedom approximations generally helped reduce Type I error inflation. Bias in the treatment effect estimate and its standard error are minimal for continuous outcomes and moderate for binary outcomes with the Wald test. Those metrics are also somewhat correlated with the correlation of treatment and time and the imbalance of treatment. When adjusted for differences in Type I error, the tests were similarly powerful with minimal bias in treatment effect estimates. We provide general recommendations for choosing an analysis approach given the parameter values of the design.

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