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.

Semiparametric Estimation in General Repeated Measures Problems

This paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal/clustered data, conditional logistic regression for matched case-control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile-kernel and backfitting estimation methods for these problems, derive their asymptotic distributions, and show that in likelihood problems the methods are semiparametric efficient. While generally not true, with our methods profiling and backfitting are asymptotically equivalent. We also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm. The proposed methods are evaluated using simulation studies and applied to the Kenya hemoglobin data.