Charles Bon 19 May 2015

Two-Way, Randomized Crossover Study Healthy, Normal Adults -48 to -12 Hour Check-in Overnight Diet and Activity Restrictions Single Dose (1/2 subj. get Test & 1/2 get Ref) 10-Hour Pre-Dose to 4-Hour Post-Dose Fast Samples collected over 3-4 half-lives Adequate washout (crossover design) Crossover to Alternate Product (usual)

 Drug Concentration Time Profile

Measured Drug Concentrations AUC t = Area Under the Curve 0-t Sum ( ½ * (C 1 + C 2 ) * (T 2 - T 1 ) ) Calculated to C t AUC inf = AUC t + C t / Ke Proportional to amount absorbed Can calculate only if we have Ke

Measured Drug Concentrations AUCt, AUC  - Extent of Absorption Cmax - Rate & Extent of Absorption Tmax - Rate of Absorption Terminal Rate of Elimination (Ke, ß, z ) Terminal Half-Life of Elimination (t½)

Test of Equality (not of use for BE) Standard ANOVA (  =0.05) H 0 : New = Standard H a : New  Standard H 0 : New / Standard = 1 H a : New / Standard  1

BE Requires a Test of Comparability Two, One-Sided T-tests (  =0.05) H 0 1 : New / Standard < LL H a 1 : New / Standard  LL H 0 2 : New / Standard > UL H a 2 : New / Standard  UL

Average BE -  ≤ (  T -  R ) ≤   = Ln(1.25) -  = -Ln(1.25) = Ln(0.80) 2, 1-sided t-test (  = 0.05)  2-sided 90% CI Same As: (  T -  R ) 2 ≤  2 One-Sided 95% UCB

Highly Variable Drugs Narrow Therapeutic Index Drugs In-Vitro Population BE

Guidance for Industry Statistical Approaches to Establishing Bioequivalence U.S. Department of Health and Human Services Food and Drug Administration Center for Drug Evaluation and Research (CDER) January 2001 BP

Analysis of Ln-Transformed AUC & Cmax  Mixed-Effects Linear Model  Each subject, j, provides µ Tj and µ Rj  µ Tj & µ Rj from Dist n (µ T ) & Dist n (µ R )  σ BT 2 and σ BR 2  Correlation, ρ, between µ Tj and µ Rj.  σ D 2 is related to these parameters

σ D 2 = variance of (µ Tj - µ Rj ) = ( σ BT - σ BR ) (1- ρ ) σ BT σ BR The total variances for each formulation are defined as the sum of the within- and between-subject components σ TT 2 = σ WT 2 + σ BT 2 σ RR 2 = σ WR 2 + σ BR 2 For analysis of crossover studies, the means are given additional structure by the inclusion of period and sequence effect terms.

A mixed-scaling approach was suggested for individual BE. Reference-scaled method if the estimate of σ WR > σ W0, constant-scaling otherwise, with σ W0 = 0.20 (σ WR 2 or σ W0 2 as denominator). The guidance recommends that  I = 0.05 The guidance recommends that sponsors applying the individual BE approach may use either reference- scaling or constant-scaling at either side of the changeover point.

First Problem (  T -  R ) 2 > Ln(1.25) Offset by (σ BT 2 - σ BR 2 ) Must Constrain (  T -  R )

Second Problem A subject-by-formulation interaction could occur when an individual is representative of subjects present in the general population in low numbers, for whom the relative BA of the two products is markedly different than for the majority of the population, and for whom the two products are not bioequivalent, even though they might be bioequivalent in the majority of the population. Must constrain σ D 2

Irreconcilable Problems  Industry Resisted 4-way Studies  FDA’s Influential Proponent Left FDA Kill the Concept

The Real Problem The equation for the statistic could be readily understood by non-statisticians

High Variability In a Drug 1.BCS Class III or IV (Low Solubility) 2.Formulation Effects (MR vs. IR) 3.Biological Variable (Oral Progesterone)

What Doesn’t Cause High Variability Analytics Var(A + B) = Var(A) + Var(B) Analytics = (0.18) 2 Biological = (0.35) 2 Var(A + B) = (0.39) 2 Analytics = (0.05) 2 Biological = (0.35) 2 Var(A + B) = (0.36) 2

Highly Variable Drugs Prior to 2008 (2009)  Don’t pursue product  Run huge two-way BE study  Run slightly less huge four-way  Replicate design/large study  Scaled Average BE (USA)

CV = 35%, T/R = 0.93 (1.075), Prob ≥ 0.80 ABE (2-way)N = 66 (132 SP sets) SABE (3-way)N = 30 (90 SP sets) SABE (4-way)N = 20 (80 SP sets)

Must Replicate Reference Product  Partial Replicate: TRR, RTR, RRT  Full Replicate: TRTR, RTRT CV WR determines BE method  ≥ 30% the SABE method is used  < 30% must use ABE method

Using ln (Test/Ref) = ln(Test) – ln(Ref) removes Subject Effect

References Guidance for Industry, “Statistical Approaches to Establishing Bioequivalence”, U.S. FDA, CDER, Jan Haidar SH, et. al. Bioequivalence approaches for highly variable drugs and drug products. Pharm Res 2008; 25: Haidar SH, et. al. Evaluation of a Scaling Approach for the Bioequivalence of highly variable drugs. Pharm AAPS J 2008; 10: Draft Guidance on Progesterone. U.S. FDA, CDER, Feb Draft Guidance on Warfarin Sodium. U.S. FDA, CDER, Dec Draft Guidance on Budesonide. U.S. FDA, CDER, Sep 2012.