Too many zeros, too long a tail: Mixed-effects, mixed-distribution modeling as a powerful approach to analyze public health data

Count data are common in public health research and statistical modeling. Poisson-based regressions offer a powerful method to analyze count data that can be incorporated in multilevel or hierarchical analyses to help address violations of assumptions for Ordinary Least Squares regression models. The assumption of equidispersion in Poisson models is often not met in real data, typically due the presence of overdispersion. Negative binomial models may be used to more appropriately examine overdispersed data, yet researchers may still encounter difficulties in study modeling due to the presence of ‘excessive' zeros. While a variety of zero-inflated Poisson (ZIP) as well as zero-inflated negative binomial (ZINB) models exist to address the presence of excessive zeros and overdispersion, these models may not be the most appropriate for all public health data. Specifically, outcome data that are semi-continuous in nature – with large number of zeros and high degree of skew among non-zero values – may be most appropriately modeled via mixed-effects, mixed-distribution (MEMD) modeling. MEMD accounts for violations of distributional assumptions in Poisson-based regression models. Similar to ZIP and ZINB, MEMD simultaneously estimates models for both any occurrence of the outcome (logistic regression) as well as intensity among those with any occurrence (Poisson regression), along with their covariance. This study: 1) presents an overview of different modeling approaches for analyzing public health count data, 2) discusses distributional assumptions and their implications for choosing the most appropriate model, and 3) provides a practical example of MEMD modeling using real public health data.