  Background. Non-inferiority (NI) trials are increasingly used to evaluate new
treatments expected to have secondary advantages over standard of care, but
similar efficacy on the primary outcome. When designing a NI trial with a
binary primary outcome, the choice of effect measure for the NI margin has an
important effect on sample size calculations; furthermore, if the control event
risk observed is markedly different from that assumed, the trial can quickly
lose power or the results become difficult to interpret. Methods. We propose a
new way of designing NI trials to overcome the issues raised by unexpected
control event risks by specifying a NI frontier, i.e. a curve defining the most
appropriate non-inferiority margin for each possible value of control event
risk. We propose a fixed arcsine difference frontier, the power-stabilising
transformation for binary outcomes. We propose and compare three ways of
designing a trial using this frontier. Results. Testing and reporting on the
arcsine scale leads to results which are challenging to interpret clinically.
Working on the arcsine scale generally requires a larger sample size compared
to the risk difference scale. Therefore, working on the risk difference scale,
modifying the margin after observing the control event risk, might be
preferable, as it requires a smaller sample size. However, this approach tends
to slightly inflate type I error rate; a solution is to use a lower
significance level for testing. When working on the risk ratio scale, the same
approach leads to power levels above the nominal one, maintaining type I error
under control. Conclusions. Our proposed methods of designing NI trials using
power-stabilising frontiers make trial design more resilient to unexpected
values of the control event risk, at the only cost of requiring larger sample
sizes when the goal is to report results on the risk difference scale.
