Rank Tests Based on Censored Data and Their Sequential Analogues

While the concept of "scoring" plays a fundamental role in the construction of two-sample rank statistics for complete data, this paper discusses how its dual - the concept of "payment" in a two-team game - leads to a general method of constructing two-sample rank tests from a given score function in the setting of censored data. A useful idea in this connection is the "payment transform" of a score function. Moreover, this payment concept provides a natural extension of the classical Mann-Whitney approach in nonparametric hypothesis testing to the case of general score functions and to the setting of censored data. More importantly, rank tests constructed using this payment concept have analytically tractable and computationally convenient sequential analogues, which are of particular interest in sequential analysis of censored survival data in comparative clinical trials with staggered entry.