Estimation from truncated lifetime data with supplementary information on covariates and censoring times

In epidemiology, reliability and other areas one encounters situations where response times and covariates for individuals in a population are observed only if the response time does not exceed an associated censoring time. Methods for obtaining supplementary information about covariates and censoring times for nonresponding individuals are considered. Estimation procedures are developed for the resulting combination of truncated data and supplementary data. Theoretical and simulation results are given, and the methodology illustrated on some automobile failure data collected under a warranty plan.