Rank transform statistics with censored data

A method for estimating the ranks of the underlying uncensored observations in a censored data set is proposed. The derived ranks are used to extend the use of the rank transform method to the censored matched pairs and the censored k-sample problems. The derived procedure for the censored matched pairs problem is new and consists of performing a paired-t test on the defined ranks. The procedure for the k-sample problem consists of performing a one-way ANOVA F-test on the derived ranks. This is essentially identical to a statistic proposed by Peto and Peto (1972). The asymptotic power of this procedure is derived and multiple comparison procedures based on it are proposed. The robustness of this test and multiple comparison procedures to departures from the assumption of equal censoring distributions is also established.