Comparing the small sample performance of several variance estimators under competing risks

Abstract

We examine several variance estimators for cumulative incidence estimators that have been proposed over time, some of which are derived from asymptotic martingale or counting process theory, and some of which are developed from the moments of the multinomial distribution. There is little published work comparing these variance estimators, largely because the variance estimators are algebraically complex and difficult to interpret and all but one have yet to be programmed for a standard statistical package. Through simulation and application to real data, we compare the performance of six variance estimators in relation to each other and the bootstrap in order to confirm earlier reports of their performance and to provide future direction toward their application. We find that the multinomial-moment-based estimators have performance close to that of the bootstrap, and are quite accurate for estimating the variance, even in samples of 20 subjects. All but one of the martingale theory-based estimators tend to perform poorly in small samples, tending to either overestimate or underestimate the empirical variance in samples of fewer than 100 subjects.