Inference of Equivalence for the Ratio of Two Normal Means with Unspecified Variances

• Activity Number: 335
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Siyan Xu*+ and Steven Y. Hua and Ronald Menton and Kerry Barker and Sandeep Menon and Ralph D'Agostino Sr.
• Companies: and Pfizer and Novartis and Pfizer and Pfizer and Boston University
• Keywords: Equivalence ; Likelihood-ratio test ; Likelihood function ; Unspecified variances ; Bayesian model

Abstract

Equivalence trials aim to demonstrate that new and standard treatments are equivalent within pre-defined clinically relevant limits. In the presence of unspecified variances, methods such as likelihood-ratio test replace them by the sample estimates; Bayesian models, on the other hand, integrate these nuisance parameters out. These methods do not fully account for the impact of the variability of the parameter of interest on the inference of equivalence. We propose a likelihood approach that retains the unspecified variances in the model and partitions the likelihood function into two components: F-statistic function for variances and t-statistic function for the ratio of two means. By incorporating unspecified variances, the proposed method can identify numeric range of variances where equivalence is more likely to be achieved. By partitioning the likelihood function into two components, the proposed method provides more inference information than method that relies solely on one component. Using a published real example data, the proposed likelihood method is shown to be a better alternative than current analysis methods for equivalence infefrence.