NONPARAMETRIC-ESTIMATION AND DOUBLY-CENSORED DATA - GENERAL IDEAS ANDAPPLICATIONS TO 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. In many such cases, statistical estima tion of properties of this distribution is complicated by the fact tha t observation of the times of both events is subject to intervalcensor ing so that the length of time between the events is never observed ex actly. Following DeGruttola and Lagakos, we call such data doubly-cens ored. Jewell, Malani and Vittinghoff showed that, with certain assumpt ions and for a particular doubly-censored data structure, non-parametr ic maximum likelihood estimation of the interval length distribution i s equivalent to non-parametric estimation of a mixing distribution. He re, we extend these ideas to various other kinds of doubly-censored da ta. We consider application of the methods to various studies generate d by investigations into the natural history of HIV disease with parti cular attention given to estimation of the distribution of time betwee n infection of an individual (an index case) and transmission of HIV t o their sexual partner.