Bayesian Analysis for Longitudinal Semicontinuous Data

In many biomedical applications, researchers encounter semicontinuous data whereby data are either continuous or zero. When the data are collected over time the observations are correlated. Analysis of these kind of longitudinal semi-continuous data is challenging due to the presence of strong skewness in the data. In this paper, we develop a flexible class of zero-inflated models in a longitudinal setting. Improving on a likelihood-based approach (using Monte-Carlo EM) that was proposed by Albert and Shen (2005), we use a Bayesian approach to analyze longitudinal data from a acupuncture clinical trial in which we compare the effects of active acupuncture, sham acupuncture and standard medical care on chemotherapy-induced nausea in patients being treated for advanced stage breast cancer. A penalized spline model is introduced into the linear predictor of the model to explore the possibility of nonlinear treatment effect. The subject-specific effects involved in the model are assumed to follow a nonparametric Dirichlet process (DP) mixture. We also account ∗Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303-3083, USA; Email: [email protected] †Biometric Research Branch, Division of Cancer Treatment and Diagnosis, National Cancer Institute