Power Calculation in 2k Factorial Optimization Trials: An Interactive Web Application, with Investigation of Robustness for Binary Outcome Variables

For 2 k factorial optimization trials with continuous outcomes, the standard approach to power calculation for a given component main effect involves a two-arm approximation in which the potential contributions of other component main and/or interaction effects are ignored. We assess whether an analogous approximation can apply to trials with binary outcomes. We extend prior Monte Carlo simulation work to the binary outcome context, simulating 2 k factorial optimization trials that vary in their design elements (sample sizes, randomization strategies, ICCs, and so on). We compare the empirical (observed) power to the power under the two-arm approximation. For factorial optimization trials that target binary outcomes and use independent randomization, the two-arm approximation performs well. Under within-cluster randomization, the approximation performs well at lower ICC (< 10%); the risk of overestimating power grows as ICC increases. Under between-cluster randomization, we find larger discrepancies between observed and approximated power, particularly with larger ICC and smaller cluster counts; notably, standard power formulas are already known to overestimate statistical power under such conditions, even in standard two-arm trial contexts. Investigators sizing 2 k factorial optimization trials with binary outcomes (or continuous) generally do not need to explore every combination of potential main effects and interactions; the two-arm approximation is often sufficient. Our freely accessible interactive web application provides scaffolding for sizing 2 k factorial optimization trials that target either continuous or binary outcomes; for trials that meet certain clustering and ICC specifications, the application presents warnings.