A conjecture of Prentice is established which states that for censored linear rank test, exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function. We show that under minimal conditions, asymptotically equivalent tests are obtained when either the Kaplan-Meier, Altshuler, or moment estimator of the survival function is used. Asymptotic normality is also established for a general random censorship model under the null hypothesis, and for contiguous alternatives. This is used to calculate efficacies, and when the censoring times are i.i.d., an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests.
"Asymptotic Properties of Censored Linear Rank Tests." Ann. Statist. 13 (1) 133 - 141, March, 1985. https://doi.org/10.1214/aos/1176346581