Statistical power and optimal design for randomized controlled trials investigating mediation effects.

Area of Science:

• Statistical methodologies
• Biostatistics
• Psychological research methods

Background:

• Mediation analyses in randomized controlled trials (RCTs) are crucial for understanding intervention mechanisms and improving treatments.
• Designing RCTs for mediation requires careful consideration of sample size for statistical power and resource efficiency.

Purpose of the Study:

• To develop closed-form statistical power formulas for RCTs examining mediation effects.
• To create an optimal design framework for sample allocation in mediation studies, considering unequal sampling costs.

Main Methods:

• Derived closed-form statistical power formulas for Sobel and joint significance tests in mediation analyses.
• Developed an optimal design framework to determine sample allocations for maximizing power under budget constraints or minimizing resources for target power.
• Assessed the impact of covariates on mediation effect magnitude and statistical power.

Main Results:

• The proposed power formulas enable precise calculation of statistical power for mediation analyses in RCTs.
• The optimal design framework identifies sample allocations that yield greater statistical power and efficiency compared to equal allocation.
• Covariates can influence both the magnitude of mediation effects and the statistical power of the study.

Conclusions:

• The developed statistical power formulas and optimal design framework enhance the efficiency and power of RCTs investigating mediation.
• These methods provide valuable tools for researchers designing intervention studies, particularly when resources are limited or unequal.
• Implementation in the R package 'odr' increases the accessibility and practical application of these advanced statistical techniques.