Bayesian modeling of pharmaceutical data addressing the average effect of bivariate parameters of interest in a bioequivalence framework

Bioavailability is the rate and extent to which the active ingredient or active moiety is absorbed from a drug product and becomes available at the site of action. For drug products that are not intended to be absorbed into the bloodstream, bioavailability may be assessed by measurements intended to reflect the rate and extent to which the active ingredient or active moiety becomes available at the site of action. Bioequivalence according to regulatory requirements is the absence of a significant difference in the rate and extent to which the active ingredient or active moiety in pharmaceutical equivalents or pharmaceutical alternatives becomes available at the site of drug action when administered at the same molar dose under similar conditions in an appropriately designed study. The study is basically a crossover comparison of absorption of two compounds to determine the maximum absorption (Cmax) and the area under the curve (AUC) of the two compounds and determining if their mean difference falls into a specified confidence region of bioequivalence. Typically, generic drug formulations are often prescribed for ‘brand name’ (i.e.standard) formulations and given by pharmacists in an effort to reduce the cost of prescription-drug therapy. In most regions, generic replacement is allowed and encouraged, provided that the generic formulation is deemed to be therapeutically equivalent to the standard formulation by the United States Food and Drug Administration (FDA). The FDA publishes a list of drug products and equivalents, which is entitled, Approved Drug Products with Therapeutic Equivalence Evaluations. This is commonly known as the Orange Book. The FDA’s designation of ‘therapeutic equivalence’ indicates that the generic formulation is (among other things) bioequivalent to the standard formulation and usually indicates that the FDA expects that the formulations are likely to have equivalent clinical effect and, in addition, have no difference in their potential for adverse effects. The 1984 Amendments to the Drug Price Competition and Patent Term Restoration Act require that manufacturers seeking approval of generic formulations submit to the FDA data demonstrating bioequivalence to the reference or standard drug product One of the primary considerations for bioequivalence is the drug’s amount and rate of drug absorption and eventually expulsion. The approach taken in this paper is to model this system of absorption via a Bayesian technique taking into account the overall mean treatment and crossover period effects as well as the sequence in which the compounds are given to an individual in a properly designed trial. For each of the parameters of interest we will determine if those values across the two compounds satisfy the boundaries of an acceptable posterior credible region. Typically the Cmax and the AUC are treated independently in the analysis. For most applications to date this has been considered the standard strategy. As an added consideration, we will examine the consequences of a possible correlation between the Cmax and the AUC. In a typical crossover design, subjects are randomly separated into two groups of equal numbers. In the time period 1 the reference formulation is given to group A and the test to group B. During the ‘washout period’ it is assumed that there is sufficient time duration to allow elimination of the drug administered in the first period. Then in the time period 2 the reference formulation is given to group B and the test to group A. The crossover design allows one to statistically account for “period or sequence effects”. We will examine all the variables of interest using prior input empirical results from previous work. The model being investigated is a multivariate model with prior structural considerations on the correlation parameter in an attempt to properly account for the posterior correlation of the parameters of interest, usually the posterior mean of the AUC and the Cmax. Advantages and limitations of our approach will be discussed.