A model-based approach to estimate the AIDS-free time distribution in homosexual men using longitudinal data

A model-based approach is developed to estimate the distribution of time from seroconversion to diagnosis with acquired immunodeficiency syndrome (AIDS) as a function of selected time-dependent covariates. The approach is applied to longitudinal data collected over 4 years of follow-up from 450 men seropositive for the human immunodeficiency virus (90 AIDS cases) and 62 seroconverters (nine AIDS cases) participating in the Chicago part of the Multicenter AIDS Cohort Study. Because of the periodic nature of monitoring, the seroconversion time is interval-censored for seroconverters and left-censored for seroprevalent cohort members; the end-point is right-censored for 413 individuals. Since serological monitoring is not continuous but only at regularly scheduled visit times, a model for the discrete hazard rate (DHR) is proposed that is a generalized linear model that relates the DHR to the covariate history through the complementary log-log link. Classification trees are used for preliminary screening of covariates to identify predictors of AIDS that should be incorporated into the DHR model. The missing seroconversion times for all men are imputed 100 times to obtain 100 completed datasets from which the parameters of the DHR are then estimated using the maximum-likelihood method. The final DHR model includes the following infection progression (marker) variables: CD4%, hemoglobin, p24 antigen, and CD4% x p24 antigen interaction. Using this DHR model, the discrete survival distribution of AIDS-free time is estimated for the given population. The jackknife procedure is used to assess the precision of the estimated survival distribution.