Adjustments of Multi-Sample U-Statistics to Right Censored Data and Confounding Covariates

Somnath Datta, Department of Biostatistics, University of Florida, USA

We consider U-statistics that can be used for comparing distribution of outcomes in two groups. We propose adjustments to the classical U-statistics for mediating potential bias come from right-censoring of the outcomes and presence of confounding covariates. These newly proposed U-statistics are appropriate when, in addition to right censored outcome, some ﬁxed covariates are observed and associated with both group membership and the outcome 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 time may depend on the group membership or some 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 confounding covariates and right-censoring on the performance of the newly proposed U-statistics under diﬀerent censoring mechanisms. We also demonstrate 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 pairwise group comparisons.