Efficiency comparisons of rank and permutation tests based on summary statistics computed from repeated measures data

A popular method of using repeated measures data to compare treatment group s in a clinical trial is to summarize each individual's outcomes with a sca lar summary statistic, and then to perform a two-group comparison of the re sulting statistics using a rank or permutation test. Many different types o f summary statistics are used in practice, including discrete and continuou s functions of the underlying repeated measures data. When the repeated mea sures processes of the comparison groups differ by a location shift at each time point, the asymptotic relative efficiency of (continuous) summary sta tistics that are linear functions of the repeated measures has been determi ned and used to compare tests in this class. However, little is known about the non-null behaviour of discrete summary statistics, about continuous su mmary statistics when the groups differ in more complex ways than location shifts or where the summary statistics are not linear functions of the repe ated measures. Indeed, even simple distributional structures on the repeate d measures variables can lead to complex differences between the distributi on of common summary statistics of the comparison groups. The presence of l eft censoring of the repeated measures, which can arise when these are labo ratory markers with lower limits of detection, further complicates the dist ribution of, and hence the ability to compare, summary statistics. This pap er uses recent theoretical results for the non-null behaviour of rank and p ermutation tests to examine the asymptotic relative efficiencies of several popular summary statistics, both discrete and continuous, under a variety of common settings. We assume a flexible linear growth curve model to descr ibe the repeated measures responses and focus on the types of settings that commonly arise in HIV/AIDS and other diseases. Copyright (C) 2001 John Wil ey & Sons, Ltd.