Sample sizes required to detect two-way and three-way interactions involving slope differences in mixed-effects linear models

Moonseong Heo, Andrew C. Leon

Research output: Contribution to journalArticle

30 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)787-802
Number of pages16
JournalJournal of Biopharmaceutical Statistics
Issue number4
Publication statusPublished - Jul 1 2010



  • Clinical trials
  • Effect size
  • Power function
  • Sample size requirements
  • Three-way interaction
  • Two-way interaction

ASJC Scopus subject areas

  • Statistics and Probability
  • Pharmacology
  • Pharmacology (medical)

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