A note on variance estimation of the Aalen-Johansen estimator of the cumulative incidence function in competing risks, with a view towards left-truncated data.
The Aalen-Johansen estimator is the standard nonparametric estimator of the cumulative incidence function in competing risks. Estimating its variance in small samples has attracted some interest recently, together with a critique of the usual martingale-based estimators. We show that the preferred estimator equals a Greenwood-type estimator that has been derived as a recursion formula using counting processes and martingales in a more general multistate framework. We also extend previous simulation studies on estimating the variance of the Aalen-Johansen estimator in small samples to left-truncated observation schemes, which may conveniently be handled within the counting processes framework. This investigation is motivated by a real data example on spontaneous abortion in pregnancies exposed to coumarin derivatives, where both competing risks and left-truncation have recently been shown to be crucial methodological issues (Meister and Schaefer (2008), Reproductive Toxicology 26, 31-35). Multistate-type software and data are available online to perform the analyses. The Greenwood-type estimator is recommended for use in practice.
Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstrasse 1, Freiburg, Germany.
Arthur
A
Allignol
Martin
M
Schumacher
Jan
J
Beyersmann
D000022:Abortion, Spontaneous / Q000139:chemically induced; D000704:Analysis of Variance; D003198:Computer Simulation; D003374:Coumarins / Q000009:adverse effects; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D053208:Kaplan-Meier Estimate; D008954:Models, Biological; D015233:Models, Statistical; D011247:Pregnancy; D012307:Risk Factors; D013269:Stochastic Processes
D003374:Coumarins; C030123:coumarin