title: Sample sizes required to detect two-way and three-way interactions involving slope differences in mixed-effects linear models.
abstract: 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.
authors.affiliation: Division of Biostatistics, Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, New York 10461, USA. moonseong.heo@einstein.yu.edu
authors.forename: Moonseong
authors.initials: M
authors.lastname: Heo
authors.forename: Andrew C
authors.initials: AC
authors.lastname: Leon
mesh_terms: D000465:Algorithms; D002986:Clinical Trials as Topic / Q000379:methods*; D003198:Computer Simulation; D003865:Major Depressive Disorder / Q000628:therapy; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D016032:Randomized Controlled Trials as Topic / Q000379:methods; D018401:Sample Size