Optimal Weights for a Class of Rank Tests for Censored Bivariate Data

Summary The problem of testing equality of survival distributions on the basis of paired censored survival data has received considerable attention in literature. Some of the important statistics used for such purposes can be expressed as linear combinations of two statistics, one based on uncensored pairs and the other based on the censored pairs. Raychaudhuri and Rao (Nonparametric Statistics, 1996, 6, 1–11) investigated properties of two classes of such statistics and derived expressions for the optimal coefficients (weights) for the linear combination that will maximize efficacy within each class. As the optimal weights depend upon the form of the underlying survival and censoring distributions, statistics with optimal weights can only be used with estimated weights. This article presents a method of estimating optimal weights on the basis of an assumed model that specifies the distribution of the difference between the observed survival times conditional on the censoring pattern. The model, in addition to dispensing with the usual assumption that the survival and censoring variables are independent, also permits a graphical check of its lack of fit on the basis of observed data. The performance of statistics with the estimated weights is evaluated by using two simulation studies – one with data generated under the assumed model and the other assuming independence of the survival and censoring times. Simulation results show that the optimal statistics with estimated weights have good power properties in all cases considered, and that they compare well with other commonly used tests for paired censored survival data. An advantage of the tests with optimal weights is that, unlike their competitors, these tests have demonstrated performance characteristics in some cases where the assumption of independent censoring may not be justified.