Charles Bon 19 May 2015. Two-Way, Randomized Crossover Study 12-80 + Healthy, Normal Adults -48 to -12 Hour Check-in Overnight Diet and Activity Restrictions

REFERENCE SCALING IN BIOEQUIVALENCE STATISTICS:

THEORY AND IN PRACTICE

Charles Bon

19 May 2015

REFERENCE SCALING IN BE STATISTICS

Two-Way, Randomized Crossover Study

12-80+ Healthy, Normal Adults-48 to -12 Hour Check-inOvernight Diet and Activity RestrictionsSingle Dose (1/2 subj. get Test & 1/2 get Ref)10-Hour Pre-Dose to 4-Hour Post-Dose Fast15-25 Samples collected over 3-4 half-livesAdequate washout (crossover design)Crossover to Alternate Product (usual)

REFERENCE SCALING IN BE STATISTICS Drug Concentration Time Profile


Measured Drug Concentrations

AUCt = Area Under the Curve 0-t Sum ( ½ * (C1 + C2) * (T2 - T1) )Calculated to Ct

AUCinf = AUCt + Ct / KeProportional to amount absorbedCan 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)H0: New = Standard Ha: New Standard

H0: New / Standard = 1Ha: New / Standard 1


BE Requires a Test of Comparability

Two, One-Sided T-tests (=0.05)H01: New / Standard < LLHa1: New / Standard LL

H02: New / Standard > ULHa2: 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 2001BP

REFERENCE SCALING IN BE STATISTICSAPPENDIX A

E(T - R)2 E(R1 - R2)2


Analysis of Ln-Transformed AUC & Cmax

Mixed-Effects Linear Model Each subject, j, provides µTj and µRj

µTj & µRj from Distn(µT) & Distn(µR)

σBT2 and σBR

2

Correlation, ρ, between µTj and µRj.

σD2 is related to these parameters


σD2 = variance of (µTj - µRj)

= (σBT - σBR)2 + 2 (1-ρ)σBTσBR

The total variances for each formulation are defined as the sum of the

within- and between-subject components

σTT

2 = σWT

2 + σBT

2

σRR

2 = σWR

2 + σBR

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 σWR > σW0, constant-scaling otherwise, with σW0 = 0.20 (σWR

2 or σW0

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 (σBT2 - σBR

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 σD2


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

2008+

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

CVWR determines BE method ≥ 30% the SABE method is used < 30% must use ABE method



Three-way, Crossover Study: TRR, RTR, and RRT.Sequence, Period and Treatment fixed effects.Subjects nested within Sequence random effect.Multiplicative model.

ABE uses ANOVA with above terms.

SABE uses only Sequence in its ANOVA model for variables (T – R) and (R1 - R2)


What Happens to the Subject Effect?

Subj Effect Test Ref Test/Ref ln(Test/Ref)

0.01 0.9 1 0.9 -0.1054

0.1 9 10 0.9 -0.1054

1 90 100 0.9 -0.1054

10 900 1000 0.9 -0.1054

100 9000 10000 0.9 -0.1054

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


What happens to the Period Effect?

T – 0.5 (R1 + R2)

TRR: P1 - 0.5 ( P2 + P3)RTR: P2 - 0.5 (P1 + P3)RRT: P3 - 0.5 (P1 + P2 )

Sum:P1+P2+P3 – P1 -P2-P3Mean: 0 for period effect

Estimate of (T – R) is (T – 0.5 (R1 + R2)) / 3


R1 – R2

Var(R1 – R2) = Var(R) + Var(R) = 2Var(R)

Var(R + c) = Var(R)

TRR: S2 = Var(R + P2) + Var (R + P3) = 2Var(R) RTR: S2 = Var(R + P1) + Var (R + P3) = 2Var(R) RRT: S2 = Var(R + P1) + Var (R + P2) = 2Var(R)

MSE : Estimate of 2Var(R)

Estimate of 2WR = MSE/2


(µT-µR)2 - WR2 ≤ 0

95% UCB for (µT-µR)2- 2WR

critbound = (x+y)+( (boundx-x)2+(boundy-y)2 )½

BE concluded if:

• 95% UCB ≤ 0

• 0.80 ≤ T/R ≤ 1.25


Draft Guidance on Progesterone

Active ingredient: Progesterone Form/Route: Capsule/Oral

SAS Program Statements for Scaled Average BE Analysis of Replicated Crossover Studies


Draft Guidance on Progesterone

PROC MIXED for fully replicated (4-way)? PROC GLM for partially replicated (3-way)


SAS Program Statements for Average BE Analysis of Replicated Crossover Studies

PROC MIXED;CLASSES SEQ SUBJ PER TRT;MODEL Y = SEQ PER TRT/ DDFM=SATTERTH; RANDOM TRT/TYPE=FA0(2) SUB=SUBJ G; REPEATED/GRP=TRT SUB=SUBJ;ESTIMATE 'T vs. R' TRT 1 -1/CL ALPHA=0.1;


The Problems

Study not conducted as a single dosing group Analyze each group separately Group*Seq as only term in statistical model Analyze ilat with Goup*Seq / dlat separately

ABE – nonconvergence of Proc Mixed Use CSH, FA0(1) ?


Narrow Therapeutic Index Drugs

Draft Guidance on Warfarin Sodium

Active ingredient: Warfarin SodiumForm/Route: Tablet/Oral



4-period, 2-sequence replicated crossover study

1. Evaluate by ABE (90% CI)

2. Evaluate by SABE with = Ln(1.111)2/(0.10)2

3. 95% confidence: wt /wR ≤ 2.5



Problems

Swr2 can become very small in a given data set What is considered a NTI drug?


Draft Guidance on Budesonide

Active ingredient: Budesonide Form/Route: Suspension/Inhalation


References

Guidance for Industry, “Statistical Approaches to Establishing Bioequivalence”, U.S. FDA, CDER, Jan. 2001.

Haidar SH, et. al. Bioequivalence approaches for highly variable drugs and drug products. Pharm Res 2008; 25:237-241.

Haidar SH, et. al. Evaluation of a Scaling Approach for the Bioequivalence of highly variable drugs. Pharm AAPS J 2008; 10:450-454.

Draft Guidance on Progesterone. U.S. FDA, CDER, Feb 2011.

Draft Guidance on Warfarin Sodium. U.S. FDA, CDER, Dec 2012.

Draft Guidance on Budesonide. U.S. FDA, CDER, Sep 2012.


Thank You

Documents

Charles Bon 19 May 2015. Two-Way, Randomized Crossover Study 12-80 + Healthy, Normal Adults -48 to -12 Hour Check-in Overnight Diet and Activity Restrictions