Nonparametric estimation of the incubation period of AIDS based on a prevalent cohort with unknown infection times.

Estimation of the incubation period distribution of human immunodeficiency virus based on prevalent cohorts of subjects, already infected at the time of recruitment, is complicated by the absence of information on the original times of infection. Here, we overcome this difficulty by using a prior distribution for the infection times, based on external data. Our estimate is nonparametric, but uses smoothness assumptions to avoid instability. The method is illustrated on two prevalent cohorts from San Francisco, separately and combined. The estimates produced agree with other published estimates of the incubation period distribution.