Generalized pairwise comparisons for censored data: An overview

The method of generalized pairwise comparisons (GPC) is an extension of the well-known nonparametric Wilcoxon-Mann-Whitney test for comparing two groups of observations. Multiple generalizations of Wilcoxon-Mann-Whitney test and other GPC methods have been proposed over the years to handle censored data. These methods apply different approaches to handling loss of information due to censoring: ignoring noninformative pairwise comparisons due to censoring (Gehan, Harrell, and Buyse); imputation using estimates of the survival distribution (Efron, Péron, and Latta); or inverse probability of censoring weighting (IPCW, Datta and Dong). Based on the GPC statistic, a measure of treatment effect, the "net benefit," can be defined. It quantifies the difference between the probabilities that a randomly selected individual from one group is doing better than an individual from the other group. This paper aims at evaluating GPC methods for censored data, both in the context of hypothesis testing and estimation, and providing recommendations related to their choice in various situations. The methods that ignore uninformative pairs have comparable power to more complex and computationally demanding methods in situations of low censoring, and are slightly superior for high proportions (>40%) of censoring. If one is interested in estimation of the net benefit, Harrell's c index is an unbiased estimator if the proportional hazards assumption holds. Otherwise, the imputation (Efron or Peron) or IPCW (Datta, Dong) methods provide unbiased estimators in case of proportions of drop-out censoring up to 60%.