NONPARAMETRIC-ESTIMATION FOR A FORM OF DOUBLY CENSORED-DATA, WITH APPLICATION TO 2 PROBLEMS IN AIDS

In many epidemiologic studies of human immunodeficiency virus (HIV) di sease, interest focuses on the distribution of the length of the inter val of time between two events. Two such problems are considered here, estimation of the distribution of time or number of sexual contacts b etween infection of an individual (an index case) and transmission of HIV to their sexual partner, and estimation of the distribution of tim e between infectiousness as a blood donor and the development of detec table antibody. Data regarding these two problems are available from c ertain partner studies, and the HIV Lookback Study. In both cases the statistical development is complicated by the fact that the times of b oth events are interval censored, so that the length of time between t he events is never observed exactly. Nonparametric methods for estimat ion of the interval length distribution are developed by casting the p roblem in terms of nonparametric estimation of a mixing distribution; particular attention is paid to identifiability issues.