Analysis of a nonsusceptible fraction with current status data

In studies involving subclinical events, times of events are often subject to interval censoring since their occurrence is only detected at inspection times. When individuals are event-free at an initial time and a single follow-up inspection is made, current status data are obtained. In many settings, however, the population comprised a susceptible and a nonsusceptible subpopulation, where only susceptible individuals will go on to experience the event. Then interest often lies primarily in identifying prognostic variables for susceptibility, and secondarily in the event time distribution among the susceptible individuals. We give a simple mixture model that facilitates estimation of the proportion of susceptible individuals, covariate effects on the odds of susceptibility, and the event time distribution under a current status observation scheme. Asymptotic relative efficiency of maximum likelihood estimators is considered based on the Fisher information for a variety of settings. EM algorithms are proposed for parametric, weakly parametric, and nonparametric estimation of the event time distribution. The methods are applied to motivating studies examining an immunological response to low molecular weight heparin in patients undergoing orthopedic surgery.