Premium
A time‐dependent discrimination index for survival data
Author(s) -
Antolini Laura,
Boracchi Patrizia,
Biganzoli Elia
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2427
Subject(s) - interpretability , covariate , jackknife resampling , survival analysis , statistics , event (particle physics) , confidence interval , outcome (game theory) , spurious relationship , index (typography) , bootstrapping (finance) , accelerated failure time model , computer science , econometrics , mathematics , artificial intelligence , physics , mathematical economics , quantum mechanics , estimator , world wide web
Abstract To derive models suitable for outcome prediction, a crucial aspect is the availability of appropriate measures of predictive accuracy, which have to be usable for a general class of models. The Harrell's C discrimination index is an extension of the area under the ROC curve to the case of censored survival data, which owns a straightforward interpretability. For a model including covariates with time‐dependent effects and/or time‐dependent covariates, the original definition of C would require the prediction of individual failure times, which is not generally addressed in most clinical applications. Here we propose a time‐dependent discrimination index C td where the whole predicted survival function is utilized as outcome prediction, and the ability to discriminate among subjects having different outcome is summarized over time. C td is based on a novel definition of concordance: a subject who developed the event should have a less predicted probability of surviving beyond his/her survival time than any subject who survived longer. The predicted survival function of a subject who developed the event is compared to: (1) that of subjects who developed the event before his/her survival time, and (2) that of subjects who developed the event, or were censored, after his/her survival time. Subjects who were censored are involved in comparisons with subjects who developed the event before their observed times. The index reduces to the previous C in the presence of separation between survival curves on the whole follow‐up. A confidence interval for C td is derived using the jackknife method on correlated one‐sample U ‐statistics. The proposed index is used to evaluate the discrimination ability of a model, including covariates having time‐dependent effects, concerning time to relapse in breast cancer patients treated with adjuvant tamoxifen. The model was obtained from 596 patients entered prospectively at Istituto Nazionale per lo Studio e la Cura dei Tumori di Milano (INT). The model discrimination ability was validated on an independent testing data set of 175 patients provided by Centro Regionale Indicatori Biochimici di Tumore (CRIBT) in Venice. Copyright © 2005 John Wiley & Sons, Ltd.