Sample Sizes Required to Detect Two-Way and Three-Way Interactions Involving Slope Differences in Mixed-Effects Linear Models

• Published in: Journal of biopharmaceutical statistics Vol. 20; no. 4; pp. 787 - 802
• Main Authors: Heo, Moonseong, Leon, Andrew C.
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis Group 01.07.2010; Taylor & Francis Ltd
• Subjects: Algorithms; Clinical trials; Clinical Trials as Topic - methods; Computer Simulation; Correlation analysis; Depressive Disorder, Major - therapy; Effect size; Estimating techniques; Humans; Likelihood Functions; Linear Models; Maximum likelihood method; Power function; Randomized Controlled Trials as Topic - methods; Sample Size; Sample size requirements; Samples; Simulation; Statistical analysis; Statistical methods; Statistics; Three-way interaction; Two-way interaction
• ISSN: 1054-3406; 1520-5711; 1520-5711
• DOI: 10.1080/10543401003618819

Based on maximum likelihood estimates obtained from mixed-effects linear models, closed-form power functions are derived to detect two-way and three-way interactions that involve longitudinal course of outcome over time in clinical trials. Sample size estimates are shown to decrease with increasing within-subject correlations. It is further shown that when clinical trial designs are balanced in group sizes, the sample size required to detect an effect size for a three-way interaction is exactly fourfold that required to detect the same effect size of a two-way interaction. Furthermore, this fourfold relationship virtually holds for unbalanced allocations of subjects if one factor is balanced in the three-way interaction model. Simulations are presented that verify the sample size estimates for two-way and three-way interactions.