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Marginalized models are in great demand by most researchers in the lifesciences particularly in clinical trials, epidemiology, health-economics,surveys and many others since they allow generalization of inference to theentire population under study. For count data, standard procedures such as thePoisson regression and negative binomial model provide population averageinference for model parameters. However, occurrence of excess zero counts andlack of independence in empirical data have necessitated their extension toaccommodate these phenomena. These extensions, though useful, complicatesinterpretations of effects. For example, the zero-inflated Poisson modelaccounts for the presence of excess zeros but the parameter estimates do nothave a direct marginal inferential ability as its base model, the Poissonmodel. Marginalizations due to the presence of excess zeros are underdevelopedthough demand for such is interestingly high. The aim of this paper is todevelop a marginalized model for zero-inflated univariate count outcome in thepresence of overdispersion. Emphasis is placed on methodological development,efficient estimation of model parameters, implementation and application to twoempirical studies. A simulation study is performed to assess the performance ofthe model. Results from the analysis of two case studies indicated that therefined procedure performs significantly better than models which do notsimultaneously correct for overdispersion and presence of excess zero counts interms of likelihood comparisons and AIC values. The simulation studies alsosupported these findings. In addition, the proposed technique yielded smallbiases and mean square errors for model parameters. To ensure that the proposedmethod enjoys widespread use, it is implemented using the SAS NLMIXED procedurewith minimal coding efforts.

Statistical model for overdispersed count outcome with many zeros: an approach for direct marginal inference