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.
Bibliographical noteFunding Information:
* Nicholas Lange is Assistant Professor, Department of Community Health, Division of Biology and Medicine, Brown University, Providence, RI 02912. Bradley P. Carlin is Assistant Professor, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455. Alan E. Gelfand is Professor, Department of Statistics, University of Connecticut, Storrs, CT 06269. This research was supported in part by Faculty Grant 2-40508 from the Division of Biologyand Medicine, Brown University (NL) and by National Science Foundation Grants DMS 8805676 (BPC) and DMS 8918563 (AEG). The authors thank the San Francisco Men's Health Study, NIAID Contract A124643, for the use of their data and Victor DeGruttola, Rob Kass, Rachel Royce, and Adrian Smith for helpful comments. We also thank an associateeditor, two reviewers,and many colleagues for their insightful comments that greatly improved the article.
* Thomas A. Louis is Professor and Head, Division of Biostatistics, University of Minnesota School of Public Health, Minneapolis, MN 55455. Partial support was provided by National Institute of Allergy and Infectious Diseases Contract NO I-AI-Q5073 and National Cancer Institute Grant PO ICA50305.
- Gibbs sampler
- Growth curves
- Inverse prediction
- Random change points