Fig. 3

Sample sizes using logistic regression and loss of power with an extra unexpected effective intervention. A and B show the expected sample size with a single expected effective intervention that increases clinical success from 50 to 70%, based on > 5000 simulations, using logistic regression for analysis and aiming for 90% power. Then, each panel shows a different scenario with an additional unexpected effective intervention with the same main effect size, and, for the combination, either: logit-scale additivity (the combination yielding 84.48276% clinical success) (C), strong synergy with 99% clinical success (D), or no additivity at all (E). In the final case, the unexpectedly effective intervention only has a 60% success rate, and no additivity (F). For each panel, the background gray line shows the sample size or true power of a factorial trial powered for the same situation with the same wrong assumptions (changes are mostly due to the multiplicity adjustment). For the distributive designs, each curve is for a different number of allocations per patient k (equal to its starting point minus 2), with one color hue per number of allocations