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.
Statistical Approaches to Establishing Vaccine Safety
Vladimir Dragalin, Valerii Fedorov and Brigitte Cheuvart
Abstract: In a vaccine safety trial, the primary interest is to demonstrate that the vaccine is sufficiently safe rejecting the null hypothesis that the relative risk of an adverse event attributable to the new vaccine is above a pre-specified value, greater than one. The exact probability of type I error of the likelihood scores test, with sample size determined by normal approximation, is evaluated by enumeration of the binomial outcomes in the rejection region and is found to exceed the nominal level. In the case of rare adverse events, the Poisson approximation is recommended as an alternative and the corresponding conditional and unconditional tests are developed. Sample size and power calculations are given for these tests. Optimal randomization strategies which (i) minimize the total number of adverse cases and (ii) minimize the expected number of subjects when vaccine is unsafe are also proposed. We illustrate the methods proposed using a hypothetical vaccine safety study.
