Local likelihood analysis of the latency distribution with interval censored intermediate events.

The distribution of time between an intermediate event and a terminal event is frequently of interest both in studying the behaviour of populations and in predicting outcomes for individuals. Current methods for estimating this latency distribution have either imposed assumptions on the hazard for the terminal event following the occurrence of the intermediate event or on the parametric form of the hazards. Here, local likelihood estimation is applied to the underlying hazard functions of a three-state process in which the time of the intermediate event may be interval censored and the time of the terminal event is either observed or right censored. Smooth non-parametric estimates of the latency distribution, along with bootstrap confidence intervals, are calculated, and tests for the comparison of two latency distributions are presented. The method is applied to two studies: a cohort of haemophiliacs who were infected with HIV by contaminated blood factor and followed for AIDS onset, and an AIDS clinical trial in which the intermediate event is the time to 50 per cent drop in CD4 count and the terminal event is AIDS or death. Simulations are presented to assess the performance of the estimation procedure. Copyright 2002 John Wiley & Sons, Ltd.