The c-index is not proper for the evaluation of $t$-year predicted risks. (16th February 2018)

• Record Type: Journal Article
• Authors: Blanche, Paul; Kattan, Michael W; Gerds, Thomas A
• Is Part Of: Biostatistics. Volume 20:Number 2(2019)
• Page Start: 347
• Page End: 357
• Publication Date: 2018-02-16
• Subjects: Cox regression -- Concordance index -- Discrimination ability -- Model comparison -- Survival prediction; Medical statistics -- Periodicals; Biometry -- Periodicals; Health risk assessment -- Periodicals; Medicine -- Research -- Statistical methods -- Periodicals; 610.727
• DOI: 10.1093/biostatistics/kxy006
• Languages: English
• ISSNs: 1465-4644

Abstract

SUMMARY: We show that the widely used concordance index for time to event outcome is not proper when interest is in predicting a $t$ -year risk of an event, for example 10-year mortality. In the situation with a fixed prediction horizon, the concordance index can be higher for a misspecified model than for a correctly specified model. Impropriety happens because the concordance index assesses the order of the event times and not the order of the event status at the prediction horizon. The time-dependent area under the receiver operating characteristic curve does not have this problem and is proper in this context.