A studentized permutation test for three-arm trials in the 'gold standard' design

The 'gold standard' design for three-arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group. This trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment, active control, and placebo. Parametric testing methods have been studied plentifully over the past years. However, these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes. In this article, we introduce a studentized permutation test for testing non-inferiority and superiority of the experimental treatment compared to the active control in three-arm trials in the `gold standard' design. The performance of the studentized permutation test for finite sample sizes is assessed in a Monte-Carlo simulation study under various parameter constellations. Emphasis is put on whether the studentized permutation test meets the target significance level. For comparison purposes, commonly used Wald-type tests are included in the simulation study. The simulation study shows that the presented studentized permutation test for assessing non-inferiority in three-arm trials in the 'gold standard' design outperforms its competitors for count data. The methods discussed in this paper are implemented in the R package ThreeArmedTrials which is available on the comprehensive R archive network (CRAN).