A consistent version of distance covariance for right-censored survival data and its application in hypothesis testing

Distance covariance is a powerful new dependence measure that was recently introduced by Szekely et al. and Szekely and Rizzo. In this work, the concept of distance covariance is extended to measuring dependence between a covariate vector and a right-censored survival endpoint by establishing an estimator based on an inverse-probability-of-censoring weighted U-statistic. The consistency of the novel estimator is derived. In a large simulation study, it is shown that induced distance covariance permutation tests show a good performance in detecting various complex associations. Applying the distance covariance permutation tests on a gene expression dataset from breast cancer patients outlines its potential for biostatistical practice.