Estimating Patterns of CD4+ Lymphocyte Decline Using Data from a Prevalent Cohort of HIV Infected Individuals

In natural history studies of chronic disease, it is of interest to understand the evolution of key variables that measure aspects of disease progression. This is particularly true for immunological variables in persons infected with the Human Immunodeficiency Virus (HIV). The natural timescale for such studies is time since infection. However, most data available for analysis arise from prevalent cohorts, where the date of infection is unknown for most or all individuals. As a result, standard curve fitting algorithms are not immediately applicable. Here we propose two methods to circumvent this difficulty. The first uses repeated measurement data to provide information not only on the level of the variable of interest, but also on its rate of change, while the second uses an estimate of the expected time since infection. Both methods are based on the principal curves algorithm of Hastie and Stuetzle, and are applied to data from a prevalent cohort of HIV-infected homosexual men, giving estimates of the average pattern of CD4+ lymphocyte decline. These methods are applicable to natural history studies using data from prevalent cohorts where the time of disease origin is uncertain, provided certain ancillary information is available from external sources.

The Design and Analysis of Partner Studies of HIV Transmission

Common goals in epidemiologic studies of infectious diseases include identification of the infectious agent, description of the modes of transmission and characterization of factors that influence the probability of transmission from infected to uninfected individuals. In the case of AIDS, the agent has been identified as the Human Immunodeficiency Virus (HIV), and transmission is known to occur through a variety of contact mechanisms including unprotected sexual intercourse, transfusion of infected blood products and sharing of needles in intravenous drug use. Relatively little is known about the probability of IV transmission associated with the various modes of contact, or the role that other cofactors play in promoting or suppressing transmission. Here, transmission probability refers to the probability that the virus is transmitted to a susceptible individual following exposure consisting of a series of potentially infectious contacts. The infectivity of HIV for a given route of transmission is defined to be the per contact probability of infection. Knowledge of infectivity and its relationship to other factors is important in understanding the dynamics of the AIDS epidemic and in suggesting appropriate measures to control its spread. The primary source of empirical data about infectivity comes from sexual partners of infected individuals. Partner studies consist of a series of such partnerships, usually heterosexual and monogamous, each composed of an initially infected "index case" and a partner who may or may not be infected by the time of data collection. However, because the infection times of both partners may be unknown and the history of contacts uncertain, any quantitative characterization of infectivity is extremely difficult. Thus, most statistical analyses of partner study data involve the simplifying assumption that infectivity is a constant common to all partnerships. The major objectives of this work are to describe and discuss the design and analysis of partner studies, providing a general statistical framework for investigations of infectivity and risk factors for HIV transmission. The development is largely based on three papers: Jewell and Shiboski (1990), Kim and Lagakos (1990), and Shiboski and Jewell (1992).

The Impact of Uncertainty in the AIDS Incubation Period on Reconstructions of the HIV Epidemic

Backcalculation is the primary method used to reconstruct past human immunodeficiency virus (HIV) infection rates, to estimate current prevalence of HIV infection, and to project future incidence of acquired immunodeficiency syndrome (AIDS). The method is very sensitive to uncertainty about the incubation period. We estimate incubation distributions from three sets of cohort data and find that the estimates for the cohorts are substantially different. Backcalculations employing the different estimates produce equally good fits to reported AIDS counts but quite different estimates of cumulative infections. These results suggest that the incubation distribution is likely to differ for different populations and that the differences are large enough to have a big impact on the resulting estimates of HIV infection rates. This seriously limits the usefulness of backcalculation for populations (such as intravenous drug users, heterosexuals, and women) that lack precise information on incubation times.