Nonparametric estimation with left-truncated semicompeting risks data

Abstract

SUMMARY Nonparametric estimators for competing risks data can be applied to semicompeting risks data, a type of multi-state data where a terminating event may censor a non terminating event, after forcing the data into the competing risks format. Complications may arise with left truncation of the terminating event, where the competing risks analysis naively truncates the nonterminating event using the left-truncation time for the terminating event, which may lead to large efficiency losses. We propose nonparametric estimators which use all semicompeting risks information and do not require artificial truncation. The uniform consistency and weak convergence of the estimators are established and variance estimators are provided. Simulation studies and an analysis of a diabetes registry demonstrate large efficiency gains over the naive estimators.