Linear frontier
EVENT
Another possibility is to allow for a linear decrease between control event risks of 9%, 5% and 1%, with two different slopes to achieve the desired non-inferiority margins of 8 and 5 percentage points. This is possibly more likely to reflect reasonable clinical opinion, but the function is still not differentiable at the points where the slope changes and initial explorations suggested that unsmooth frontiers could make type 1 error control difficult at the inflection points.