Study design for a three-arm equivalence clinical trial with binomially distributed outcomes

Area of Science:

• Clinical Trials
• Biostatistics
• Pharmaceutical Research

Background:

• Equivalence in clinical trials is often assessed using three-arm designs involving a test drug, reference drug, and placebo.
• A three-arm equivalence trial typically involves three hypothesis tests: two for superiority against placebo and one for equivalence between test and reference drugs.

Purpose of the Study:

• To propose a design for three-arm equivalence trials that minimizes the risk of a test drug being found equivalent to the reference but not superior to placebo.
• To develop statistical methods for testing equivalence based on the ratio of differences in proportions for binary outcomes.

Main Methods:

• Derived test statistics and power functions using maximum likelihood estimate (MLE) and restricted MLE.
• Developed a method to calculate the required sample size by solving the power function for desired power and significance level.
• Illustrated the proposed design with an example and analyzed sample size requirements under various conditions.

Main Results:

• The proposed method provides a statistically sound approach to designing three-arm equivalence trials.
• The derived power functions and sample size calculations are essential for planning efficient clinical studies.
• The study demonstrates how to effectively test for both equivalence and superiority in a single trial design.

Conclusions:

• The proposed hypothesis testing framework based on the ratio of differences in proportions is effective for three-arm equivalence trials with binary outcomes.
• This design helps mitigate the risk of false-positive equivalence findings where the test drug is not superior to placebo.
• The methodology facilitates accurate sample size determination, ensuring adequate statistical power for clinical trial evaluations.