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

Area of Science:

• Biostatistics
• Clinical Trial Design
• Longitudinal Data Analysis

Background:

• Longitudinal studies in clinical trials require robust statistical methods to detect treatment effects over time.
• Understanding interactions involving the course of outcomes is crucial for interpreting trial results.
• Accurate sample size calculations are essential for the efficiency and validity of clinical trials.

Purpose of the Study:

• To derive closed-form power functions for detecting two-way and three-way interactions in longitudinal clinical trials.
• To investigate the impact of within-subject correlations on sample size requirements.
• To establish the relationship between sample sizes needed for two-way versus three-way interactions.

Main Methods:

• Utilizing maximum likelihood estimates from mixed-effects linear models.
• Developing closed-form power functions to estimate sample sizes.
• Conducting simulations to validate the derived sample size estimates.

Main Results:

• Sample size estimates decrease as within-subject correlations increase.
• For balanced designs, a three-way interaction requires four times the sample size of a two-way interaction.
• This fourfold relationship is approximately maintained in unbalanced designs when one factor is balanced.

Conclusions:

• The derived power functions provide a practical tool for sample size estimation in longitudinal clinical trials.
• Within-subject correlation is a key factor influencing the required sample size.
• The findings offer guidance on the relative sample size demands for detecting different orders of interactions over time.