BAYES ESTIMATES FOR IMMUNOLOGICAL PROGRESSION RATES IN HIV DISEASE

We develop Bayesian methods for calculating shrinkage estimates of imm unological progression rates (for example, CD4 count decline rates) in populations of HIV-infected patients. These methods make the assumpti on that decline of immunological markers may be modelled as approximat ely linear on some suitable chosen scale. They are applicable in situa tions where seroconversion times are unknown and follow-up of patients is variable, with some patients having only sparse measurements of im munological markers. Fitting of models is achieved by Gibbs sampling a nd CD4 count data from 603 members of the Edinburgh City Hospital Coho rt with at least two CD4 determinations are analysed to provide an ill ustration. It is found that Bayesian shrinkage estimates for CD4 slope s on the square root scale are much more effective predictors of futur e CD4 counts than the least squares estimates, with respect to squared error loss. Of various shrinkage estimators considered, the most effe ctive corresponds to the simplest model, which can also be fitted usin g 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, a ge, risk category and HLA antigen type) on immunological progression i s considered. It is found that homosexual men in Edinburgh and patient s with HLA haplotype A1B8DR3 experience significantly faster loss of C D4. (C) 1997 by John Wiley & Sons, Ltd.