Modeling the Progression of HIV Infection

Abstract Statistical modeling of the progression of markers of HIV infection is complicated by three problems: (1) the times of infection are generally unknown; (2) the follow-up of infected patients is generally much shorter than the average time from infection to AIDS; and (3) the repeated measures of the markers are correlated. The marker we study in this article is T-helper cell count. As a consequence of these three problems, it is difficult to distinguish between different models for the decline in T-helper cell count over time for HIV-infected individuals. Some investigators have proposed that the decline is gradual until shortly before the onset of AIDS, yet available data do not reject models of a fairly constant decline over the entire latency period between HIV infection and onset of AIDS. The ability to discriminate between models can be enhanced by incorporating information about the distributions of the times of seroconversion (development of measurable antibodies) among HIV seropositive individuals and of markers among the seronegative. This can be achieved through the use of growth curve methods that treat time of infection as a random variable whose distribution is estimable, either from the data on progression itself or from external cohorts. Estimation of growth curve model parameters requires a generalization of existing methods for the maximization of mixture likelihoods to accommodate three different components of stochastic variation: (1) the random and unobservable times of infection, (2) individual random effects, and (3) measurement errors. We apply our proposed method to data on progression of T-helper cell count in 490 HIV-infected men from the Men's Health Study in San Francisco and use an externally available estimate of the infection time distribution for the entire city. We conclude from our analysis that models that assume a steady linear decline of T-helper cell count on the square root scale and accommodate the three sources of variation mentioned previously provide adequate fits to the study data. We also note that the linear decline does not apply near the time of seroconversion; this event seems to be accompanied by a sharp drop in T-helper cell count.