Sample Size Calculation for Comparing Time-Averaged Responses in K-Group Repeated-Measurement Studies

Area of Science:

• Biostatistics
• Clinical Trial Design
• Longitudinal Data Analysis

Background:

• Repeated measurement studies frequently compare K (≥3) treatments.
• Designing such clinical trials requires robust sample size calculations.
• Existing methods often focus on two-treatment comparisons, leaving multi-treatment designs less explored.

Purpose of the Study:

• To extend existing sample size formulas for comparing K (≥3) treatments in repeated measurement studies.
• To develop a closed-form sample size formula for simultaneous multi-treatment comparisons.
• To provide a tool for efficient clinical trial design in scenarios with multiple interventions.

Main Methods:

• Derivation of a closed-form sample size formula based on the noncentral χ(2) test statistic.
• Extension of the generalized estimating equation (GEE) approach for sample size calculation.
• Conducting simulation studies to evaluate the formula's performance under diverse conditions.

Main Results:

• The proposed sample size formula is derived for K (≥3) treatment comparisons.
• Simulation studies demonstrate that the formula achieves empirical powers and type I errors close to nominal levels.
• The formula accounts for various correlation structures, missing data patterns, and observation probabilities.

Conclusions:

• The developed sample size formula is effective for planning clinical trials with multiple treatment arms.
• The formula offers a practical approach for sample size determination in repeated measurement studies.
• The methodology is validated through simulations and illustrated with a clinical trial example.