A Permutation Solution to Test for Treatment Effects in Alternation Design Single-Case Experiments

Research involving a clinical intervention is normally aimed at testing the treatment effects on a dependent variable, which is assumed to be a relevant indicator of health or quality-of-life status. In much clinical research large-n trials are in fact impractical because the availability of individuals within well-defined categories is limited in this application field. This makes it more and more important to concentrate on single-case experiments. The goal with these is to investigate the presence of a difference in the effect of the treatments considered in the study. In this setting, valid inference generally cannot be made using the parametric statistical procedures that are typically used for the analysis of clinical trials and other large-n designs. Hence, nonparametric tools can be a valid alternative to analyze this kind of data. We propose a permutation solution to assess treatment effects in single-case experiments within alternation designs. An extension to the case of more than two treatments is also presented. A simulation study shows that the approach is both reliable under the null hypothesis and powerful under the alternative, and that it improves the performance of a considered competitor. In the end, we present the results of a real case application.