Medical and public health research often involve the analysis of repeated or longitudinal count data that exhibit excess zeros such as the number of yearly doctor visits by a group of individuals over a number of years. Zero-inflated Poisson (ZIP) regression models can be used to account for excess zeros in count data. We propose an extension of the ZIP model that is appropriate for longitudinal data. Our extension includes a non stationary, observation-driven time series model based correlation structure. We discuss estimation of the model parameters and the inefficiency of the estimators when the correlation structure is mis-specified. The model's application to the analysis of health care utilization data is also discussed.

Time-series count data with excessive zeros frequently occur in environmental, medical and biological studies. These data have been traditionally handled by conditional and marginal modeling approaches separately in the literature. The conditional modeling approaches are computationally much simpler, whereas marginal modeling approaches can link the overall mean with covariates directly. In this paper, we propose new models that can have conditional and marginal modeling interpretations for zero-inflated time-series counts using compound Poisson distributed random effects. We also develop a computationally efficient estimation method for our models using a quasi-likelihood approach. The proposed method is illustrated with an application to air pollution-related emergency room visits. We also evaluate the performance of our method through simulation studies.

Clustered multinomial data with random cluster sizes commonly appear in health, environmental and ecological studies. Traditional approaches for analyzing clustered multinomial data contemplate two assumptions. One of these assumptions is that cluster sizes are fixed, whereas the other demands cluster sizes to be positive. Randomness of the cluster sizes may be the determinant of the within-cluster correlation and between-cluster variation. We propose a baseline-category mixed model for clustered multinomial data with random cluster sizes based on Poisson mixed models. Our orthodox best linear unbiased predictor approach to this model depends only on the moment structure of unobserved distribution-free random effects. Our approach also consolidates the marginal and conditional modeling interpretations. Unlike the traditional methods, our approach can accommodate both random and zero cluster sizes. Two real-life multinomial data examples, crime data and food contamination data, are used to manifest our proposed methodology.