Count responses are becoming increasingly important in biostatistical analysis because of the development of new biomedical techniques such as next-generation sequencing and digital polymerase chain reaction. However, overdispersion is a common problem in modeling count responses the popular Poisson model. Although the Poisson model has been studied extensively for cross-sectional observations, addressing overdispersion for longitudinal data without parametric distributional assumptions remains challenging, especially with missing data. In this paper, we propose a method to detect overdispersion in repeated measures in a non-parametric manner by extending the Mann–Whitney–Wilcoxon rank sum test to longitudinal data. In addition, we also incorporate the inverse probability weighted method to address the data missingness. This approach demonstrated reliability under various scenarios, presented accurate estimations of parameters, and showed robustness with the presence of data missingness.
Zhang H*, He H, Lu N, Zhu L, Zhang B, Zhang Z, Tang L. A non-parametric model to address overdispersed count response in a longitudinal data setting with missingness. Statistical Methods in Medical Research 26(3):1461-1475, 2017.