A better conclusion might be that there are situations in which permutation tests should be used, and other situations in which permutation tests should not be used. This approach opens the door to broader agreement, but begs the obvious question of when to use permutation tests. We consider this issue from a variety of perspectives, and conclude that permutation tests are ideal to study efficacy in a randomized clinical trial which compares, in a heterogeneous patient population, two or more treatments, each of which may be most effective in some patients, when the primary analysis does not adjust for covariates. We propose the p-value interval as a novel measure of the conservatism of a permutation test that can be defined independently of the significance level. This p- value interval can be used to ensure that the permutation test have both good global power and an acceptable degree of conservatism.
Some subjects miss observations, thus becoming incomplete blocks of observations.
Our approach is to estimate the trend by the linear regression method within each block and apply the one-sample Wilcoxon test to the estimated linear trends. The one-sample Wilcoxon test will be sensitive to the trend if it exists. The proposed test statistic is asymptotically normal and consistent. We can also estimate the overall magnitude of the linear trend and its confidence interval by a proper non-parametric method. By Monte Carlo studies, we compare the performance of the proposed test against extended Page and Jonckheere tests.