The Concordance Index C and the Mann-Whitney Parameter Pr(X>Y) with Randomly Censored Data

Harrell's c-index or concordance C has been widely used as a measure of separation of two survival distributions. In the absence of censored data, the c-index estimates the Mann-Whitney parameter Pr(X>Y), which has been repeatedly utilized in various statistical contexts. In the presence of randomly censored data, the c-index no longer estimates Pr(X>Y); rather, a parameter that involves the underlying censoring distributions. This is in contrast to Efron's maximum likelihood estimator of the Mann-Whitney parameter, which is recommended in the setting of random censorship.