A marginalized zero-inflated Poisson regression model with overall exposure effects

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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 provide the extra or excess zeros. The ZIP model parameters, however, are not well suited for inference targeted at marginal means, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. We develop a marginalized ZIP model approach for independent responses to model the population mean count directly, allowing straightforward inference for overall exposure effects and 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 other methods of estimating overall exposure effects. The marginalized ZIP model is applied to a recent study of a motivational interviewing-based safer sex counseling intervention, designed to reduce unprotected sexual act counts.