Resampling-based Confidence Intervals and Tests for the Concordance Index and the Win Ratio

This article analyzes various inference techniques for the $C$-index $p = 1/2 (P(T_1 > T_2) + P(T_1 \geq T_2))$ and the win ratio $w = p / (1-p)$ for possibly discretely distributed, independent survival times $T_1$ and $T_2$. While observation of $T_1$ and $T_2$ may be right-censored and are thus dealt with by the Kaplan-Meier estimator, observations larger than the end-of-study time are also reasonably accounted for. An appropiate handling of ties requires normalized versions of Kaplan-Meier and variance estimators. Asymptotically exact inference procedures based on standard normal quantiles are compared to their bootstrap- and permutation-based versions. A simulation study presents a robust superiority of permutation-based procedures over the non-resampling counterparts $-$ even for small, unequally sized samples, strong censoring and under different sample distributions.