We fit a class of random effects linear growth curve models for the square root of CD4 count to serial marker data from 164 HIV-positive individuals with known (or accurately estimated) dates of seroconversion and at least 10 CD4 measurements each (median 16). We do so by adopting a Bayesian viewpoint and using the Markov chain Monte Carlo technique Gibbs sampling. In particular, we examine the effect of the antiretroviral treatment zidovudine on the square root of CD4 series for the 136 patients who took the drug. Treatment effects are modelled by positing recoveries in square root of CD4 level proportional to current immuno-competence and changes in slope proportional to current rate of square root of CD4 loss. Both fixed and random treatment effects are considered and models are criticized and compared using Bayesian predictive methodology and checking data which comprise 424 new observations. Results indicate re-elevation of square root of CD4 level is associated with treatment but the effect, though significant, is mostly of small magnitude and is possibly transient; models neglecting consideration of treatment fit the checking data almost as well. Best overall model estimates mean rate of square root of CD4 loss per annum to be 2.1 (standard error 0.12); mean seroconversion value of square root of CD4 is 28.4 (SE 0.65). The estimated variance of individual slopes is 1.9 (SE 0.28), there being considerable individual variation in rate of CD4 loss, and a recovery in level of 0.047 (SE 0.014) times current square root of CD4 level is estimated at treatment uptake.