University of Washington - Department of Statistics
We study the nonparametric maximum likelihood estimator (MLE) for current status data with competing risks. These data arise naturally in cross-sectional survival studies with several failure causes, and generalizations arise in HIV vaccine clinical trials.
Until now, the asymptotic properties of the MLE have been largely unknown. We resolve this issue by proving consistency, the rate of convergence, and the limiting distribution of the MLE. The asymptotic properties are nonstandard, since the rate of convergence is n^1/3, and the limiting distribution involves the slopes of the convex minorants of a self-induced system of correlated Brownian motion processes plus parabolic drifts.
Other aspects that we consider include uniqueness properties of the MLE, graph theory, and the estimation of smooth functionals. Finally, we study an extension of the model in which the competing risks are continuous. We show that the MLE is generally inconsistent in this model, and we propose a simple method to repair this inconsistency.