Multiple Comparisons With Overdispersed Multinomial Data: Methods, Properties and Application

ABSTRACT Overdispersion, a common issue in clustered multinomial data, can lead to biased standard errors and compromised statistical inference if not adequately addressed. This study describes a comprehensive procedure for constructing multiple comparisons of interest and applying multiplicity adjustments in the analysis of clustered, potentially overdispersed multinomial data. We investigate four quasi‐likelihood estimators and the Dirichlet‐multinomial model to account for overdispersion. Through a simulation study, we evaluate the performance of these methods under various scenarios, focusing on family‐wise error rate, statistical power and coverage probability. Our findings indicate that the Afroz quasi‐likelihood estimator is recommended when strict error control is required, whereas the Dirichlet‐multinomial model is preferable when high statistical power is desired, albeit with a slightly increased tolerance for false positives. Additionally, we address the challenge of zero‐count categories within groups, demonstrating that incorporating pseudo‐observations can effectively mitigate associated estimation difficulties. Practical applications to real datasets from toxicology and flow cytometry underscore the robustness and practical utility of these methods.