Models for the incubation of AIDS and variations according to age and period

The objective of the methods proposed is to provide a parametric model for the incubation of AIDS and to use the chosen parameterization to test for the effect of age at seroconversion, and, after adjusting for markers of immunosuppression, to assess variations in periods corresponding to different levels of use of AIDS therapies at the population level. We compared the fit of Weibull, log-normal and three-parameter logistic models incorporating truncation in prevalent cohort and interval censored data. We showed the advantages by restricting the analysis to follow-up durations of greater than five years to improve estimation of the tail of the distribution for the prediction of long-term survivors. We applied the proposed methods to the combination of 1649 seroprevalent and 476 seroconverters with 1022 and 177 AIDS cases, respectively, who have been followed in the Multicenter AIDS Cohort Study (MACS) up to April 1995. Differences according to age at seroconversion are quantified in terms of relative percentiles and their associated 95 per cent confidence intervals were calculated using methods of multiple imputation. Using the proposed methods, we found that the log-normal model provides a fit as good as the three-parameter logistic; both are close to the non-parametric estimate and are significantly better than the fit of the Weibull model. We found that the older the age at seroconversion, the shorter the time to AIDS (relative percentile = 0.72 for age > or = 40 versus age < 25), and that the incubation of AIDS in calendar periods where treatment has been widely administered has been significantly longer among individuals with low CD4 cell counts.