Bayes estimates for immunological progression rates in HIV disease

We develop Bayesian methods for calculating shrinkage estimates of immunological progression rates (for example, CD4 count decline rates) in populations of HIV-infected patients. These methods make the assumption that decline of immunological markers may be modelled as approximately linear on some suitable chosen scale. They are applicable in situations where seroconversion times are unknown and follow-up of patients is variable, with some patients having only sparse measurements of immunological markers. Fitting of models is achieved by Gibbs sampling and CD4 count data from 603 members of the Edinburgh City Hospital Cohort with at least two CD4 determinations are analysed to provide an illustration. It is found that Bayesian shrinkage estimates for CD4 slopes on the square root scale are much more effective predictors of future CD4 counts than the least squares estimates, with respect to squared error loss. Of various shrinkage estimators considered, the most effective corresponds to the simplest model, which can also be fitted using SAS. A characterization of the pattern of CD4 loss in the Edinburgh cohort is obtained (mean rate of decline on root scale-1.61 per annum, standard deviation 1.03) and the effect of various covariates (sex, age, risk category and HLA antigen type) on immunological progression is considered. It is found that homosexual men in Edinburgh and patients with HLA haplotype A1B8DR3 experience significantly faster loss of CD4.