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

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.