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<p>For 2<sup><i>k</i></sup> 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<sup><i>k</i></sup> 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 (&lt; 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<sup><i>k</i></sup> 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<sup><i>k</i></sup> factorial optimization trials that target either continuous or binary outcomes; for trials that meet certain clustering and ICC specifications, the application presents warnings.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月10日

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  • Jillian C. Strayhorn,
  • Phuc Vu,
  • Ruoxiang Zheng,
  • Alex Dahlen

摘要

For 2k 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 2k 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 2k 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 2k factorial optimization trials that target either continuous or binary outcomes; for trials that meet certain clustering and ICC specifications, the application presents warnings.