The assessment and planning of non-inferiority trials for retention of effect hypotheses - towards a general approach

The objective of this paper is to develop statistical methodology for planning and evaluating three-armed non-inferiority trials for general retention of effect hypotheses, where the endpoint of interest may follow any (regular) parametric distribution family. This generalizes and unifies specific results for binary, normally and exponentially distributed endpoints. We propose a Wald-type test procedure for the retention of effect hypothesis (RET), which assures that the test treatment maintains at least a proportion $\Delta$ of reference treatment effect compared to placebo. At this, we distinguish the cases where the variance of the test statistic is estimated unrestrictedly and restrictedly to the null hypothesis, to improve accuracy of the nominal level. We present a general valid sample size allocation rule to achieve optimal power and sample size formulas, which significantly improve existing ones. Moreover, we propose a general applicable rule of thumb for sample allocation and give conditions where this rule is theoretically justified. The presented methodologies are discussed in detail for binary and for Poisson distributed endpoints by means of two clinical trials in the treatment of depression and in the treatment of epilepsy, respectively. $R$-software for implementation of the proposed tests and for sample size planning accompanies this paper.