2x2 Factorial Design in Randomized Controlled Trials with Binary Outcomes: A Practical Guide on Sample Size Efficiency

• Activity Number: 175
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Shuang Huang* and Chengcheng Hu
• Companies: The University of Arizona and The University of Arizona
• Keywords: factorial design ; randomized controlled trials ; binary outcome ; sample size ; asymptotic efficiency ; simulation

Abstract

Randomized controlled trials (RCTs) with a factorial design have the appealing advantage of detecting effects of multiple treatments without additional cost of sample size. However, this is only guaranteed when the outcome is normally distributed and there is no significant interaction between treatments. We analyzed asymptotic efficiency in a 2x2 factorial design with a binary outcome relative to a simple 2-arm RCT. Results were presented as the ratio (analytical form where possible) of sample size of the 2x2 factorial RCT to that of the simple 2-arm RCT under different analytical schemes (marginal or factorial) and statistical approaches (logistic regression, Pearson chi-squared test, Fisher's exact test) in conjunction with the presence of interaction effects. Together with simulation results, we showed that 2x2 factorial RCTs with binary outcomes does not always achieve the same efficiency as those with normally distributed outcomes. Clinical investigators can use these ratio formulae to quickly evaluate whether a 2x2 factorial design can truly yield benefits in sample size.