We explore the fitting of a class of hierarchical regression models to longitudinal CD4 lymphocyte count data from the Edinburgh City Hospital cohort. This mainly drug-using (IDU) cohort provides an excellent resource for the study of HIV disease progression for several reasons: seroconversions have been estimated for a large proportion of the cohort on the basis of stored sera retrospectively tested for HIV antibodies and knowledge of needle-sharing behaviour; immunological monitoring has been thorough since 1985 with blood taken at most clinic visits and regular attendance behaviour encouraged; immunological measurements are considered accurate from quality control comparisons between UK laboratories.

Thus we are able to consider a set of 164 seropositives who have well-estimated seroconversions and at least 10 CD4 counts each to the end of 1991; 102 of these subjects have at least 15 counts and 51 have at least 20 giving good longitudinal marker series. We also have checking data from 1992 which are not used in the initial modelling but which are used later to compare the models we fit.

Our basic model is a hierarchical regression model for the square root of CD4 count which we find to decay in a plausibly linear fashion. We fit the model using Markov chain Monte Carlo techniques, specifically the Gibbs sampler. This approach is easily implemented and takes in its stride the highly unbalanced time ‘design’ of the data which would cause great problems in conventional modelling. Our model could also be described as a random effects growth curve and bears similarities to recent work by Lange et al. (1992).