Exact PK Equivalence for a bridging study Steven Novick, Harry Yang (MedImmune) and Xiang Zhang (NC State) NCB, October 2015

In submission Journal of Biopharmaceutical Statistics Written with human-subject bridging study in mind. Easily adapted to animal PK study comparison.

Reference Drug Test Drug Pharmacokinetics: the study of the time course of drug absorption, distribution, metabolism, and excretion.

Regulatory Requirement: In Vivo Bioequivalence Change rate and extent of absorption of drug product for which the manufacture has changed. – FDA 1995: Guidance for Industry Immediate Release Solid Oral Dosage Forms, Scale-Up and Postapproval Changes: […] In Vivo Bioequivalence Documentation A sponsor proposes manufacturing a generic version of an approved off-patent product. – FDA 2006: Guidance for Industry: Bioequivalence Guidance

Regulatory Requirement: In Vivo Bioequivalence […] Demonstrate equivalence […] between the generic medicinal product and a reference medicinal product. – EMEA 2010: Guideline on the Investigation of Bioequivalence

AUC C max T max Absorption rate=elimination rate T 1/2 Basic pharmacokinetic (PK) considerations Let the curve be: f( , t )

Bioequivalence definition EMEA 2010: The plasma drug concentration time curve is […] used to assess bioequivalence between two formulations. FDA 2006: AUC and CMAX [are considered] as the pivotal parameters for bioequivalence determination. Area under the curve (AUC): reflects the extent of exposure. The maximum plasma concentration or peak exposure (C Max ) Statistical evaluations of T max and T 1/2 are not required.

Mice, Rats, and Dogs, oh my I was often asked to compare PK profiles of mice, rats, and dogs on two different formulations of the same drug compound via AUC, C max, T max, and T 1/2. Crossover studies Show statistical equivalence Sometimes shows statistical superiority

Some thoughts Westlake 1988: Equivalence of the PK metrics does not necessarily imply equivalence in the concentration time profile. EMEA 2010: The plasma drug concentration time curve is […] used to assess bioequivalence between two formulations.

Comparing the mean PK profiles

==> Does not imply anything about T max or T 1/2. We show: closeness in PK profiles is a more stringent measure than both AUC and C Max.

Oral, first-order, single-compartment PK model K a = absorption rate constant K e = elimination rate constant  = (Dose)x(Fraction absorbed)/(Volume)

A quick counter-example

Ratio of PK profiles Bioequivalence declared through AUC, C Max, and T 1/2 Bioequivalence not declared through PK profile comparison

Hypothesis testing

A small simulation Examine characteristics of p( ,  ) vs. traditional bioequivalence testing. Two arms: Reference (R) and Test (T) – 20 subjects per arm – 11 time points: 0.5 – 16 hours Hierarchical model

Data Generation for Simulation

Priors

Mean Reference PK curve Showing time points Example of 20 subjects on Reference drug

Testing Traditional Test: Proposed Test:

KaKa KeKe Max Ratio Reference Test log 10 (1) = 0Equal Test log 10 (1.1)Equiv Test log 10 (1.1)Equiv Test log 10 (1.35)Borderline Test log 10 (1.35)Borderline Test log 10 (1.88)Not Equiv (  =300 for all cases) Six Scenarios

Bayesian model fitting 4 independent MCMC chains via JAGS 200K posterior samples (total) – Burn in = 10,000 – Thinning = 200 Effective sample sizes > 10,000 Simulation ran for four weeks!

Simulation Results

Alternative #1 Close…most of the time (q=70%) 100q%

Curves are close together for 100q% time

Simulation Results q = 80%, 90%, 95%, 100%

Alternative #2 Subset of time points

Alternative #3: Differences The difference of the two curves are close together; i.e., not on the log scale. ==>

Posterior probability that log-ratio of two PK curves are close together for all time points in a time range. Method provides better control over consumer’s risk from a compliance point of view. Discussed three related, alternative metrics.

Thank you! Questions?