The zero-inflated Poisson (ZIP) regression model is often employed in public health research to examine the relationships between exposures of interest and a count outcome exhibiting many zeros, in excess of the amount expected under sampling from a Poisson distribution. The regression coefficients of the ZIP model have latent class interpretations, which correspond to a susceptible subpopulation at risk for the condition, with counts generated from a Poisson distribution, and a non-susceptible subpopulation that provides the extra or excess zeros. The ZIP model parameters, however, are not well suited for inference targeted at overall exposure effects, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. We develop a marginalized ZIP model for independent responses to model the population mean count directly, allowing straightforward inference for overall exposure effects and easy accommodation of offsets representing individuals' risk times, as well as empirical robust variance estimation for overall log incidence density ratios. Through simulation studies, the performance of maximum likelihood estimation of the marginalized ZIP model is assessed and compared to existing post-hoc methods for the estimation of overall effects in the traditional ZIP model framework. The marginalized ZIP model is applied to a recent study of a motivational interview-based safer sex counseling intervention, designed to reduce unprotected sexual act counts. Also, we develop a marginalized ZIP model with random effects to allow for more complicated data structures. SAS macros are developed for the marginalized ZIP model for independent data to assist applied analysts in the direct modeling of the population mean in count data with excess zeros.
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