Estimation of time since exposure for a prevalent cohort

In natural history studies of human immunodeficiency virus type 1 (HIV-1) infection a substantial proportion of participants are seropositive at time of enrollment in the study. These participants form a prevalent subcohort. Estimation of the unknown times since exposure to HIV-1 in the prevalent subcohort is of primary importance for estimation of the incubation time of AIDS. The subset of the cohort that tested negative for antibody to HIV-1 at study entry and was observed to seroconvert forms the incident subcohort that provides longitudinal data on markers of maturity (that is, duration) of infection. We use parametric life table regression models incorporating truncation to describe the conditional distribution (imputing model) of the times since seroconversion given a vector of the markers of maturity. Using the fitted model and the values of the markers of maturity of infection provided by the seroprevalent subcohort at entry into the study, we can impute the unknown times since seroconversion for the prevalent subcohort. We implement multiple imputation based on a model-robust estimate of the covariance matrix of parameters of the imputing model to provide confidence intervals for the geometric mean of the time since seroconversion in the prevalent subcohort, and to compare maturity of infection of cohorts recruited in different cities. The accuracy of imputation is further validated by comparisons of imputation-based estimates of AIDS incubation distribution in the seroprevalent subcohort with more direct estimates obtained from the seroincident subcohort.