Inverse Probability of Censoring Weighted U-statistics for Right-Censored Data with an Application to Testing Hypotheses

A right-censored version of a U-statistic with a kernel of degree m-1 is introduced by the principle of a mean preserving reweighting scheme which is also applicable when the dependence between failure times and the censoring variable is explainable through observable covariates. Its asymptotic normality and an expression of its standard error are obtained through a martingale argument. We study the performances of our U-statistic by simulation and compare them with theoretical results. A doubly robust version of this reweighted U-statistic is also introduced to gain efficiency under correct models while preserving consistency in the face of model mis-specifications. Using a Kendall's kernel, we obtain a test statistic for testing homogeneity of failure times for multiple failure causes in a multiple decrement model. The performance of the proposed test is studied through simulations. Its usefulness is also illustrated by applying it to a real data set on graft-versus-host-disease.