Unifying Frequentist and Bayesian Approaches in Noninferiority Testing

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Mark A. Gamalo*+ and Ram C. Tiwari
• Companies: U.S. Food and Drug Administration/CDER/OTS/OB and U.S. Food and Drug Administration/CDER/OTS/OB
• Keywords: Non-inferiority ; Bayesian ; Frequentist ; Generalized P-values

Abstract

Regulatory framework recommends that novel statistical methodology for analyzing trial results parallels the Frequentist strategy, e.g., the new method must protect type-I error and arrive at a similar conclusion. Keeping these in mind, we construct a Bayesian approach for non-inferiority trials with normal response. A non-informative prior is assumed for the mean response of the experimental treatment and Jeffrey's prior for its corresponding variance when it is unknown. The posteriors of the mean response and variance of the treatment in historical trials are then assumed as priors for its corresponding parameters in the current trial, where that treatment serves as the active control. From these priors a Bayesian decision criterion is derived to determine whether the experimental treatment is non-inferior to the active control. We will also present a generalized $p$-value approach for assessing noninferiority that gives exact tail probabilities and is especially useful when variances are not equal between treatments. This generalized $p$-value approach is has a similar Bayesian construction but is entirely Frequentist. We will compare characteristics of the three approaches with