We consider multiple comparison test procedures among treatment effects in a randomized block design. We propose closed testing procedures based on signed rank statistics and Friedman test statistics for all pairwise comparisons of treatment effects. Although anyone has been failed to discuss a distribution-free method except Bonferroni procedures as a multiple comparison test, the proposed procedures are exactly distribution-free. Next we consider the randomized block design under simple ordered restrictions of treatment effects. We propose distribution-free closed testing procedures based on one-sided signed rank statistics and rank statistics of Chacko (1963) for all pairwise comparisons. Simulation studies are performed under the null hypothesis and some alternative hypotheses. In this studies, the proposed procedures show a good performance. We also illustrate an application to death rates by using proposed procedures.

Missing data is a common problem in longitudinal clinical trials, and mixed-effects models for repeated measures (MMRM) have been widely applied to circumvent the resulting bias effectively. However, many standard inference methods of MMRM lead to the inflation of type I error rates for the tests of regression coefficient parameters when the longitudinal dataset is small and incomplete. Permutation inference methods have been established as accurate inference methods under small sample settings. In this article, we propose two effective permutation-based inference methods for the analyses using MMRM. One is the permutation of the treatment assignment variable and the other is the permutation of weighted residuals estimated by the reduced model under null hypothesis. We conducted numerical evaluations via simulation studies under realistic situations to evaluate performances of the proposed methods. The two methods generally provided valid inference results and performed relatively well compared with the current standard methods, even for small and incomplete datasets. Applications to a postnatal depression clinical trial are also presented.

A central problem in medical research is how to make inferences about the causal effects of treatments or exposures. In this article, we review fundamental concepts for making such inferences in randomized clinical trials or observational studies. The statistical framework consists of potential outcomes, an assignment mechanism, and probability distributions. Randomization-based and model-based methods of statistical inference are illustrated with a series of extracorporeal membrane oxygenation (ECMO) clinical trials, which are thought-provoking in that each trial used different assignment mechanisms.