The c-index is not proper for the evaluation of t-year predicted risks

TY - JOUR

T1 - The c-index is not proper for the evaluation of t-year predicted risks

AU - Blanche, Paul

AU - Kattan, Michael W

AU - Gerds, Thomas A

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

U2 - 10.1093/biostatistics/kxy006

DO - 10.1093/biostatistics/kxy006

M3 - Journal article

C2 - 29462286

SN - 1465-4644

VL - 20

SP - 347

EP - 357

JO - Biostatistics

JF - Biostatistics

IS - 2

ER -