Nonparametric Estimation for a form of Doubly Censored Data, with Application to Two Problems in AIDS

Abstract

In many epidemiologic studies of human immunodeficiency virus (HIV) disease, interest focuses on the distribution of the length of the interval of time between two events. Two such problems are considered here, estimation of the distribution of time or number of sexual contacts between infection of an individual (an index case) and transmission of HIV to their sexual partner, and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody. Data regarding these two problems are available from certain partner studies, and the HIV Lookback Study. In both cases the statistical development is complicated by the fact that the times of both events are interval censored, so that the length of time between the events is never observed exactly. Nonparametric methods for estimation of the interval length distribution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution; particular attention is paid to identifiability issues.

Key Words:

• Acquired immune deficiency syndrome
• Double censoring
• Human immunodeficiency virus
• Mixture likelihoods
• Nonparametric estimation