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 among persons infected with the human immunodeficiency virus (HIV). The natural time scale for such studies is time since infection. Most data available for analysis, however, 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, and is based on the principal curves algorithm of Hastie and Stuetzle. The second uses an external estimate of the expected time since infection. Both methods use locally-weighted linear smoothers, 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 apply to natural history studies that use data from prevalent cohorts where the time of disease origin is uncertain, provided availability of certain information from external sources.