Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution

Abstract

This article proposes a Bayesian regression model for nonlinear zero-inflated longitudinal count data that models the median count as an alternative to the mean count. The nonlinear model generalizes a recently introduced linear mixed-effects model based on the zero-inflated discrete Weibull (ZIDW) distribution. The ZIDW distribution is more robust to severe skewness in the data than conventional zero-inflated count distributions such as the zero-inflated negative binomial (ZINB) distribution. Moreover, the ZIDW distribution is attractive because of its convenience to model the median counts given its closed-form quantile function. The median is a more robust measure of central tendency than the mean when the data, for instance, zero-inflated counts, are right-skewed. In an application of the model we consider a biphasic mixed-effects model consisting of an intercept term and two slope terms. Conventionally, the ZIDW model separately specifies the predictors for the zero-inflation probability and the counting process's median count. In our application, the two latent class interpretations are not clinically plausible. Therefore, we propose a marginal ZIDW model that directly models the biphasic median counts marginally. We also consider the marginal ZINB model to make inferences about the nonlinear mean counts over time. Our simulation study shows that the models have good properties in terms of accuracy and confidence interval coverage.