Time-Dependent Predictive Accuracy in the Presence of Competing Risks
Version of Record online: 11 JAN 2010
© 2010, The International Biometric Society No claim to original US government works
Volume 66, Issue 4, pages 999–1011, December 2010
How to Cite
Saha, P. and Heagerty, P. J. (2010), Time-Dependent Predictive Accuracy in the Presence of Competing Risks. Biometrics, 66: 999–1011. doi: 10.1111/j.1541-0420.2009.01375.x
- Issue online: 11 JAN 2010
- Version of Record online: 11 JAN 2010
- Received October 2008. Revised September 2009. Accepted October 2009.
- Competing risks;
- Cox regression;
- Kaplan–Meier estimator;
- Kernel smoothing;
Summary Competing risks arise naturally in time-to-event studies. In this article, we propose time-dependent accuracy measures for a marker when we have censored survival times and competing risks. Time-dependent versions of sensitivity or true positive (TP) fraction naturally correspond to consideration of either cumulative (or prevalent) cases that accrue over a fixed time period, or alternatively to incident cases that are observed among event-free subjects at any select time. Time-dependent (dynamic) specificity (1–false positive (FP)) can be based on the marker distribution among event-free subjects. We extend these definitions to incorporate cause of failure for competing risks outcomes. The proposed estimation for cause-specific cumulative TP/dynamic FP is based on the nearest neighbor estimation of bivariate distribution function of the marker and the event time. On the other hand, incident TP/dynamic FP can be estimated using a possibly nonproportional hazards Cox model for the cause-specific hazards and riskset reweighting of the marker distribution. The proposed methods extend the time-dependent predictive accuracy measures of Heagerty, Lumley, and Pepe (2000, Biometrics 56, 337–344) and Heagerty and Zheng (2005, Biometrics 61, 92–105).