A Marginalized Zero-inflated Poisson Regression Model with Random Effects

J R Stat Soc Ser C Appl Stat. 2015 Nov;64(5):815-830. doi: 10.1111/rssc.12104. Epub 2015 Apr 30.

Abstract

Public health research often concerns relationships between exposures and correlated count outcomes. When counts exhibit more zeros than expected under Poisson sampling, the zero-inflated Poisson (ZIP) model with random effects may be used. However, the latent class formulation of the ZIP model can make marginal inference on the sampled population challenging. This article presents a marginalized ZIP model with random effects to directly model the mean of the mixture distribution consisting of 'susceptible' individuals and excess zeroes, providing straightforward inference for overall exposure effects. Simulations evaluate finite sample properties, and the new methods are applied to a motivational interviewing-based safer sex intervention trial, designed to reduce the number of unprotected sexual acts.

Keywords: Marginalized Models; Repeated Measures; Unprotected Intercourse; Zero-inflation.