Flexible modeling of longitudinal highly skewed outcomes

The analysis of data from epidemiologic and environmental studies presents challenges such as skewness of distribution, rounding and multiple measurements over time. To model trends over time based on repeated measurements, we propose a general latent model suitable for highly skewed data. The model assumes that the observed outcome is determined by an unobservable outcome that follows a Weibull distribution. To accommodate correlations among repeated responses over time, we introduce a general random effect from the power variance function (PVF) family of distributions, including the gamma distribution often employed in the literature. The resulting marginal likelihood has a closed form without resorting to numerical or approximation methods. We study estimation and hypothesis testing under these models, with different choices of random effect distributions. Simulation studies are conducted to evaluate their performance. Finally, we apply the proposed method to exposure data collected from the Michigan polybrominated biphenyl (MIPBB) study.