NONPARAMETRIC-ESTIMATION OF SURVIVAL DISTRIBUTIONS WITH CENSORED INITIATING TIME, AND CENSORED AND TRUNCATED TERMINATING TIME - APPLICATIONTO TRANSFUSION DATA FOR ACQUIRED-IMMUNE-DEFICIENCY-SYNDROME

The analysis of survival data with censored initiating time, and censo red and truncated terminating time arises in same recent epidemiologic al studies. The transfusion-related acquired immune deficiency syndrom e (AIDS) data of the Centers for Disease Control (CDC) are a typical e xample. The initiating time in this case is the time of infection by t he human immunodeficiency virus and is not observed for every patient either because of unrecorded transfusion times or multiple transfusion s. The terminating time here is the onset of AIDS and is truncated, th e result at being able to report within an observational period only a proportion of the infected cases which came down with AIDS in the tim e period. We consider nonparametric estimation of the survival as well as the initiating time distributions assuming that they are independe nt and non-informatively censored. We propose a simple algorithm to ob tain the maximum likelihood estimates for the discrete formulation of the problem and apply it to estimating the AIDS latency and infection distributions for four age groups of transfusion-related AIDS from the CDC surveillance database.