Modeling Censored Count Data with the Censored Heterogeneous Negative Binomial Model

Censoring frequently affects the analysis of survival data. Censoring also affects count data. The Poisson and negative binomial (NB) models are two of the most commonly used models for count data analysis. The censored NB (CNB) model is a variant of the NB model that is appropriate for censored, overdispersed Poisson data. Another variant, the heterogeneous NB model (HNB), involves a generalization of the overdispersion scale parameter where observation-specific parameterization of the parameter is allowed. This research explored the merger of the CNB and HNB models to form the censored heterogeneous NB (CHNB) model. Censoring in the CHNB model is either dataset-defined or observation-specific, occurring on the left, right, or on the left and right simultaneously; also, the model can accommodate interval data. The research question was whether the CHNB model performs better than the HNB, CNB, and traditional NB models. A simulation study was undertaken to assess the performance of the CHNB model in comparison to the HNB, CNB, and NB models. The study incorporated varying sample sizes, censoring types, percentages of censored observations, and sets of parameters for the heterogeneity. Models were compared based on bias, coverage probability, and other criteria. Results show that the CHNB model performs very well for count data which includes left, right, and left and right censoring simultaneously, exceeding the performances of the HNB, CNB, and NB models. By modeling heterogeneity, the CHNB model improves the analysis of censored negative binomial data encountered in public health and other areas of research.