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. (2007) and Szekely and Rizzo (2009). 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. This article is protected by copyright. All rights reserved.