Adjustments of multi-sample [formula omitted]-statistics to right censored data and confounding covariates

Abstract

U-statistics that can be used for comparing distribution of outcomes in two groups are considered. Adjustments to the classical U-statistics are proposed for overcoming potential biases arising from right-censoring of the outcomes and presence of confounding covariates. These newly proposed U-statistics are appropriate when, in addition to right censored outcomes, some fixed covariates are observed and deemed as confounders in an observational study. The summands of U-statistics are re-weighted and normalized based on a combination of inverse probability of censoring weights and propensity score based weights. Censoring times may depend on the group membership, confounders or some potentially observed time-dependent covariates, which may result in censoring mechanisms of varying degrees of complexity. In total, four censoring mechanisms are considered for the two-group comparison. Simulation results are used to illustrate the impact of right-censoring and confounding covariates on the performance of the newly proposed U-statistics under different censoring mechanisms. It is also demonstrated that large sample inferences for the adjusted U-statistics are valid using jackknife variance estimator. Comparisons of more than two groups are also considered from certain ways of pairwise two-group comparisons. The procedure is applied to analyze two real data sets for comparing two or more groups of event times. R codes of our procedure are available under supplementary material.