Bayesian Inference in Censored Mixed-Effects Models Using Heavy-Tailed Distributions

• Activity Number: 21
• Type: Topic Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Victor Lachos*+ and Dipak K. Dey and Dipankar Bandyopadhyay
• Companies: University of Campinas and University of Connecticut and University of Minnesota
• Keywords: Censored data ; HIV viral load ; Gibbs Algorithms ; Influential observations ; Linear mixed models ; MCMC

Abstract

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear (and nonlinear) mixed-effects models (with modifications to accommodate censoring) are routinely used to analyze this type of data and are based on normality assumptions for the random terms. However, those analyses might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored nonlinear models replacing the Gaussian assumptions for the random terms with normal/independent (NI) distributions. The NI is an attractive class of symmetric heavy-tailed densities that includes the normal, Student's-t, slash, and the contaminated normal distributions as special cases. The marginal likelihood is tractable (using approximations for nonlinear models) and can be used to develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with two HIV studies on viral loads that were initially analyzed using normal mixed-effects models.