S ep 2 00 5 Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

This article considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We derive a new explicit formula for the MLE that has both computational and theoretical advantages. Using this formula and the mark specific cumulative hazard function of Huang & Louis (1998), we derive the almost sure limit of the MLE. We conclude that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks, and illustrate the behavior of the inconsistent and repaired MLE in several examples.