Time-dependent predictive accuracy in the presence of competing risks.
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).
Saha
P
P
Department of Biostatistics, University of Washington, Seattle, Washington 98195-7232, USA. psaha@u.washington.edu
Heagerty
P J
PJ
D007700:Kinetics; D008722:Methods; D015233:Models, Statistical; D011237:Predictive Value of Tests; D012306:Risk; D013997:Time Factors