A non-parametric model to address overdispersed count response in a longitudinal data setting with missingness

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; a commonly met problem in modeling them with the popular Poisson model is overdispersion. Although it 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. The proposed model is illustrated with both simulated and real study data.