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Background. Non-inferiority (NI) trials are increasingly used to evaluate newtreatments expected to have secondary advantages over standard of care, butsimilar efficacy on the primary outcome. When designing a NI trial with abinary primary outcome, the choice of effect measure for the NI margin has animportant effect on sample size calculations; furthermore, if the control eventrisk observed is markedly different from that assumed, the trial can quicklylose power or the results become difficult to interpret. Methods. We propose anew way of designing NI trials to overcome the issues raised by unexpectedcontrol event risks by specifying a NI frontier, i.e. a curve defining the mostappropriate non-inferiority margin for each possible value of control eventrisk. We propose a fixed arcsine difference frontier, the power-stabilisingtransformation for binary outcomes. We propose and compare three ways ofdesigning a trial using this frontier. Results. Testing and reporting on thearcsine scale leads to results which are challenging to interpret clinically.Working on the arcsine scale generally requires a larger sample size comparedto the risk difference scale. Therefore, working on the risk difference scale,modifying the margin after observing the control event risk, might bepreferable, as it requires a smaller sample size. However, this approach tendsto slightly inflate type I error rate; a solution is to use a lowersignificance level for testing. When working on the risk ratio scale, the sameapproach leads to power levels above the nominal one, maintaining type I errorunder control. Conclusions. Our proposed methods of designing NI trials usingpower-stabilising frontiers make trial design more resilient to unexpectedvalues of the control event risk, at the only cost of requiring larger samplesizes when the goal is to report results on the risk difference scale.

Handling an uncertain control group event risk in non-inferiority trials: non-inferiority frontiers and the power-stabilising transformation