A semiparametric extension of the Mann-Whitney test for randomly truncated data

In many applications, statistical data are frequently observed subject to a retrospective sampling criterion resulting in pure right-truncated data. In classical testing problems, the Mann-Whitney test is used for testing the equality of two distributions. A semiparametric extension of this test is developed for the case when truncation is present. We consider a model in which the truncation distribution is parameterized, while the lifetime distribution is left as a nonparametric component. The method is seen to be applicable to many patterns of truncation including left truncation, right truncation, and doubly truncated data for which no other nonparametric or semiparametric test is currently available. Applications of the semiparametric method are given. Simulation results indicate that for pure right-truncated data the semiparametric test is more powerful than a recent nonparametric test.