Time-Dependent Predictive Accuracy in the Presence of Competing Risks

• Published in: Biometrics Vol. 66; no. 4; pp. 999 - 1011
• Main Authors: Saha, P., Heagerty, P. J.
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.12.2010; Wiley-Blackwell; Blackwell Publishing Ltd
• Subjects: Accuracy; BIOMETRIC METHODOLOGY; Biometrics; biometry; Breast cancer; Censorship; Competing risks; Consistent estimators; Cox regression; Discrimination; Estimate reliability; Estimation bias; Estimation methods; Estimators; Kaplan-Meier estimator; Kernel smoothing; Kinetics; Methods; Modeling; Models, Statistical; Prediction; Predictive Value of Tests; Research methodology; Risk; Risk factors; Sensitivity; Specificity; Statistical analysis; Time; Time dependence; Time Factors
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2009.01375.x

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).