Novel Bayesian Methods for Non-Inferiority Tests Based on Relative Risk and Odds Ratio for Dichotomous Data

Abstract

In a non-inferiority trial, the experimental treatment is compared against an active control instead of placebo. The goal of this study is often to show that the experimental treatment is non-inferior to the control by some pre-specified margin. The standard approach for these problems, which relies on asymptotic normality, usually requires large sample size to achieve some desired power level. In this paper, we propose alternative approaches based on Bayes factor and posterior probability for testing non-inferiority in the context of two-sample dichotomous data. A novel aspect of the proposed Bayesian methods is that the cut-off value for Bayes factors and posterior probabilities are determined from the data that approximately controls the overall errors. Results based on simulated data indicate that both of the proposed Bayesian approaches provide significant improvement in terms of statistical power as well as the total error rate over the popularly used frequentist procedures. This in turn indicates that the required sample size to achieve certain power level could be substantially lowered by using the proposed Bayesian approaches. The two Bayesian methods however performs very similar in terms of statistical power and total error rates.

Key Words:

• Bayes factor
• Non-inferiority
• Odds ratio
• Posterior probability
• Relative risk