Hierarchical Bayes Models for the Progression of HIV Infection Using Longitudinal CD4 T-Cell Numbers

Abstract

Taking the absolute number of CD4 T-cells as a marker of disease progression for persons infected with the human immunodeficiency virus (HIV), we model longitudinal series of such counts for a sample of 327 subjects in the San Francisco Men's Health Study (Waves 1–8, excluding zidovudine cases). We conduct a fully Bayesian analysis of these data. We employ individual level nonlinear models incorporating such critical features as incomplete and unbalanced data, population covariates (age at study entry and an indicator of self-reported herpes simplex virus infection), unobserved random change points, heterogeneous variances, and errors in variables. We construct prior distributions using results of previously published work from several different sources and data from HIV-negative men in this study. We also develop an approach to Bayesian model choice and individual prediction. Our analysis provides marginal posterior distributions for all population parameters in our model for this cohort. Using an inverse prediction approach, we also develop the posterior distributions of time for CD4 T-cell number to reach a specified level.

Key Words:

• AIDS
• Gibbs sampler
• Growth curves
• Inverse prediction
• Random change points