PERMUTATION TESTS USING ESTIMATED DISTRIBUTION-FUNCTIONS

In this article we develop permutation tests for estimated distributio n functions. The tests are formed by averaging a functional of estimat ed distribution functions that are calculated from independent samplin g units, where the units may be a single response, a set of repeated r esponses, or a censored response. We study primarily two functionals-t he difference in means functional and the Mann-Whitney functional, and two types of responses-repeated conditionally independent responses a nd censored responses. For repeated responses, the permutation test us ing the difference in means functional produces a permutation form of the corresponding mixed-effects test. A new permutation test is develo ped when we apply the Mann-Whitney functional to the repeated response s. This is a case in which the rank-transform method does not work. On the other hand, for right-censored or interval-censored data, we obta in permutation forms of standard rank tests using the Mann-Whitney fun ctional (or weighted forms of the functional), and the difference in m eans functional gives new tests. The latter tests generalize the permu tation t-test and the mean-based permutation tests to censored data. T hese permutation tests are valid for all sample sizes and do not need weights for stabilization like the weighted Kaplan-Meier statistics. W e perform the permutation tests on two examples, one with repeated mea sures and one with interval-censored responses.