Fig. 5

True control arms and mitigation strategies for interactions. A shows sample sizes for a scenario with 2 effective interventions (70% success) with additive efficacy on the logit scale (84.48276% clinical success), 8 ineffective interventions (no change), and 4 allocations per patient, as a function of the size of the control arm (relative to total inclusions). B shows the same situation but with non-additive efficacy (70% success for the combination, same as each standalone intervention). C and D show the same two effective interventions (with and without additivity) but with 2 allocations among 20 candidates rather than 4 among 10. The analysis algorithms are: “Confound” for a pooled difference of means between treated and non-treated, accepting bias due to pooling but counting on a small proportion of effective interventions, “No interaction” for a simple logistic regression with the main effects, “Pre-specified” for a single interaction term between the two effective interventions, “Backward” for a backward elimination strategy starting from all interaction terms involving the analyzed intervention and keeping only those with a p-value below the threshold