Asymptotic Behavior of Linear Permutation Tests under General Alternatives, with Application to Test Selection and Study Design

原文摘要

Tests based on the permutation of observations are a common and attractive method of comparing two groups of outcomes, in part because they retain proper test size with minimal assumptions and can have high efficiency toward specific alternatives of interest. In addition, permutation tests may be used with discrete or categorical outcomes, for which linear rank tests are not designed. Permutation tests are now increasingly used to analyze discrete or continuous responses that themselves are functions of several statistics. Examples of such summary statistics include the area under the curve generated by repeated measures of a laboratory marker or an overall composite score from a quality of life study. Here even simple structures for the joint distribution of the component statistics can lead to complex differences between the distributions of summary statistics of the comparison groups. Despite their attractive features, surprisingly little is known about the behavior of linear permutation tests when the two groups differ even in simple ways. This lack of knowledge limits an assessment of the relative efficiency of different tests or the planning of the size of a study based on a permutation test. To address these issues, we derive the asymptotic distribution of permutation tests under a general contiguous alternative, and then investigate the implications for test selection and study design for several diverse areas of application. For discrete outcomes, areas of application include permutation tests for ordinal responses and for count data. For continuous outcomes, we explore several applications, including general results for location-scale families, a comparison of different data transformations, and a comparison to linear rank tests.

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