A Bayesian non-inferiority test for two independent binomial proportions.

Area of Science:

• Biostatistics
• Clinical Trials
• Drug Development

Background:

• Non-inferiority tests are crucial in drug development for comparing treatment efficacy.
• Existing non-inferiority tests predominantly rely on the frequentist framework.
• Bayesian approaches to non-inferiority testing remain underexplored.

Purpose of the Study:

• To propose a novel Bayesian index, τ = P(π₁ > π₂ - Δ₀|X₁, X₂), for assessing non-inferiority between two independent binomial proportions.
• To introduce and evaluate two distinct methods for calculating the Bayesian index τ: a normal approximation and an exact posterior probability method.
• To demonstrate the practical application and utility of the proposed Bayesian index τ in real-world clinical trial scenarios.

Main Methods:

• The study defines a new Bayesian index τ based on the posterior probability of one treatment's parameter exceeding another's by a specified margin.
• Two computational approaches are detailed: an approximate method utilizing normal approximation and an exact method employing the posterior probability density function.
• The accuracy of the approximate method is validated against the exact method through comparative analysis.

Main Results:

• The proposed Bayesian index τ provides a probabilistic measure of non-inferiority.
• Both the approximate and exact methods yield comparable results for calculating τ, indicating the feasibility of the approximate approach.
• Empirical results from clinical trials confirm the practical utility and applicability of index τ in evaluating non-inferiority.

Conclusions:

• The novel Bayesian index τ offers a valuable alternative for non-inferiority testing within the Bayesian framework.
• The developed methods for calculating τ are computationally tractable and provide reliable estimates.
• Index τ demonstrates potential for enhancing the analysis of treatment efficacy in drug development and clinical research.