Conditional Distribution-Free Tests for the Two-Sample Problem in the Presence of Right Censoring

Two-sample rank tests for survival data in the presence of arbitrary right censoring are considered. We distinguish between administrative censoring, arising because survival study participants do not enter as a cohort, and censoring due to "loss to follow-up." We show how conditionally distribution-free tests can be constructed in certain situations. Conditional versions of the generalized Wilcoxon and Mantel statistics are shown to be asymptotically normal in the conditional reference set, but with modified means and variances. Efficiency of these tests relative to asymptotically distribution-free competitors is unity, providing the censoring distributions are discrete, the same for both samples, and providing loss-to-follow-up (LFU) distributions are the same for the two samples. When these assumptions do not hold, efficiency can deteriorate considerably, being poorest, other things being equal, when the censoring distribution is continuous.