BioMetrics.com

Kullback-Leibler Divergence for Evaluating Bioequivalence: II. Simulation and Retrospective Assessment of Performance of the Proposed FDA metric and the Kullback-Leibler Divergence in Individual Bioequivalence Assessment

Scott D Patterson, Vladimir Dragalin, Valerii Fedorov, and Byron Jones

Abstract. Methodology has been proposed for evaluating switchability of two formulations of a drug that encompasses bioequivalence aspects using Dragalin and Fedorov’s application of the Kullback-Leibler Divergence (KLD) and a metric developed by the Food and Drug Administration (FDA) as measures of discrepancy between the distributions of the two formulations using two sequence replicate, crossover designs.

Standards are proposed for implementation of the KLD as an alternative procedure for the evaluation of similarity between formulations using the same study design as that proposed in FDA guidance. Simulations are conducted to evaluate the performance of the KLD relative to the metric proposed in guidance by the Food and Drug Administration for the evaluation of individual bioequivalence.

Previously published retrospective analyses using the FDA proposed metric are contrasted with those based on the KLD, and thoughts regarding future evaluations are explored. This investigation is conducted to provide an exploratory look into the properties of the two metrics in order to support a future, rigorous comparison.

It is concluded that the KLD is a viable alternative to the FDA-proposed metric and that its mathematical properties make it a readily interpretable measure of the individual differences between formulations.

Optimal Design for Multiple Responses with Variance Depending on Unknown Parameters

Valerii Fedorov, Robert Gagnon, and Sergei Leonov

Abstract: We discuss optimal design for multiresponse models with a variance matrix that depends on unknown parameters. The approach relies on optimization of convex functions of the Fisher information matrix. We propose iterated estimators which are asymptotically equivalent to maximum likelihood estimators. Combining these estimators with convex design theory leads to optimal design methods which can be used in the local optimality setting. A model with experimental costs is introduced which is studied within the normalized design paradigm and can be applied, for example, to the analysis of clinical trials with multiple endpoints.