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).

A unifying approach for haplotype analysis of quantitative traits in family-based association studies: Testing and estimating gene-environment interactions with complex exposure variables

We propose robust and e±cient tests and estimators for gene-environment/gene-drug interactions in family-based association studies. The methodology is designed for studies in which haplotypes, quantitative pheno- types and complex exposure/treatment variables are analyzed. Using causal inference methodology, we derive family-based association tests and estimators for the genetic main effects and the interactions. The tests and estimators are robust against population admixture and strati¯cation without requiring adjustment for confounding variables. We illustrate the practical relevance of our approach by an application to a COPD study. The data analysis suggests a gene-environment interaction between a SNP in the Serpine gene and smok- ing status/pack years of smoking that reduces the FEV1 volume by about 0.02 liter per pack year of smoking. Simulation studies show that the pro- posed methodology is su±ciently powered for realistic sample sizes and that it provides valid tests and effect size estimators in the presence of admixture and stratification.

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.