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The Posterior Probability of Dissolution Equivalence

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The Posterior Probability of Dissolution Equivalence

David J LeBlond 1 , John J Peterson 2 and Stan Altan 3)

1 Exploratory Statistics, Abbott,[email protected]

2 Research Statistics Unit, GlaxoSmithKline Pharmaceuticals

3 Pharmaceutical R&D, Johnson & Johnson

Midwest Biopharmaceutical Statistical Workshop

Muncie, Indiana

May 25, 2011

- Objective
- Background
- Why dissolution?
- Equivalence defined
- Current practice

- Why a Bayesian approach?
- Posterior probability defined
- MCMC
- Examples
- Equivalence of 2 lots
- Equivalence of 2 processes (multiple lots)
- Model dependent comparisons

- Summary

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- Make this tool available to you so you can use it if you want to.
- Statistical Modeling
- Software (R, WinBUGS)
- Example Data & Code
- [email protected]

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- Surrogate measure of in-vivo dissolution
- In-vivo dissolution rate affects drug bio-availability
- Bio-availability may affect PK (blood levels)
- Blood levels may affect safety and efficacy
- Compendial requirement for most solid oral dosage forms
- Need to show “equivalence” for process/ method change or transfer to obtain a bio-waiver.
- Need to show “non-equivalence” to prove in-vitro method can detect formulation / process differences.

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100

% Dissolved

0

Time

- 1 tablet/ stirred vessel
- 1 run usually = 6 tablets
- solution sampled at fixed intervals

- samples assayed
- cumulative concentration
- expressed as % of dosage form Label Content (%LC)
- Are and “equivalent”?

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- Identify parameter space based on
- Difference in Dissolution at multiple time points
- Difference in profile model parameters
- Condensed univariate distance measure

- Establish similarity region
- Constraints on parameter space
- Based on “customer requirements”

- Obtain distance estimate from data
- Conforms to parameter space

- Equivalence: distance estimate is “sufficiently contained within” the similarity region.

?

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D2

0

D1

0

- parameter space: Dissolution differences, Di, at p time points.
- similarity region:
- distance estimate = (point estimate)
- Equivalence: (no measure of uncertainty)

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TOST (one dimensional)

5%

5%

8%

2%

Yes

No

“MOST” (multi-dimensional)

No

Maybe

Yes

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- Must choose similarity region shape.
- Must choose confidence region shape.
- The number of shapes increases with number of dimensions.
- Lack of conformance between similarity and confidence region shapes conservative test
- Conclusion depends on shape choices.

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- The confidence level is not the probability of equivalence.
- It is the probability of covering the “true” difference in repeated trials.
- What if you really want to know the probability of equivalence?
- risk based decision making (ICH Q9)

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distance estimate: Joint Posterior of

Distance measures

Measure of Equivalence

= Integrated density

= Posterior Probability of Equivalence

Obtained by counting from MCMC

Similarity region

(“customer requirement”)

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Probability Model

(Likelihood)

Dissolution Data

(Test and Reference)

Prior Information

(non-informative)

MCMC

Draws from the joint posterior distribution of distance parameters

(10-100 thousand)

Count the fraction of draws within the similarity region

Conclude equivalency if fraction exceeds some limit (e.g. 95%)

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6 tablets per lot

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% Dissolution vector, Y, for the ith tablet from the kth lot …

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and

Since

can be shown (see appendix) to have the distribution

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Define a rectangular similarity region, S, as

and require that

to conclude equivalence.

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500 of 10,000 draws plotted

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% Dissolution vector, y, for the ith tablet from the kth run …

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elements of Vtablet

elements of Vrun

Max = 40

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Define a rectangular similarity region, S, as

and require that

to conclude equivalence.

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1000 of ~2,000 draws plotted

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- Data from reference 12
- 3 lots: 1 reference and 2 post-change lots
- A minor change and a major change lot
- 12 tablets per Lot
- Pre-change and Test Lots have different time points

- Comparison requires a parametric dissolution profile model
- Similarity region defined on the model parameter space

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Probit:

Logistic:

Weibull:

Exponential:

( 1st order kinetics )

Quadratic:

…and some others (Higuchi, Gompertz, Hixson-Crowell,…)

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M measures content

T is time to 63.2% Dissol.

beta measures delay

0.5

2.0

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- The following seemed to reduce colinearity and improve convergence.
- Replace T with lna = -b lnT
- Replace b with lnb
- transform time (t) from minutes to hours

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% Dissolution, Y, for the ith tablet from the kth lot at the jth time (t) point…

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“…At present, some issues are unresolved such as

(i) how many standard deviations (2 or 3) should be

used for a similarity criterion,

(ii) what to do if the ellipse is

only marginally out of the similarity region …”

from Sathe, Tsong, Shah (1996) Pharm Res 13(12) 1799-1803

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Prob = 0

2SD Similarity Region

Prob = 0.949

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- Pros
- Based on simple counting exercise (MCMC)
- Probability estimate for risk assessment
- Exact conformity between the similarity region and the estimate (integrated posterior)
- Incorporation of prior information (or not) as appropriate
- True equivalence (not significance) test
- Rewards high data information content

- Cons
- Requires (usually) MCMC
- Coverage properties require calibration studies.
- Regulatory acceptance?

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- Berger RL (1982) Multiparameter hypothesis testing and acceptance sampling, Technometrics 24(4) 295-300
- Schuirmann DJ (1987) Comparions of two one-sided procedures and power approach of rassessing the equivalence of average bioavailability, Journal of Pharmokinetics and Biopharmaceutics 15:657-680.
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- Food and Drug Administration. Guidance for Industry: Immediate Release Solid Oral Dosage Forms. Scale-Up and Postapproval Changes (SUPAC-IR): Chemistry, Manufacturing and Controls, In Vitro Dissolution Testing and In Vivo BE. 1995
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- Gudrun F (2001) Clinical Data Management - Guidelines for the Registration of Pharmaceuticals -- Notes for Guidance, Points to Consider and Related Documents for Drug Approval with Biostatistical Methodology - Guidelines on Dissolution Profile Comparison, Drug Information Journal, Vol. 35(3), pp 865-874
- FDA (2001) Guidance for industry: statistical approaches to bioequivalence.
- Eaton ML, Muirhead RJ, Steeno GS (2003) Aspects of the dissolution profile testing problem, Biopharmaceutical Report 11(2) 2-7
- Senn S (2001) Statistical issues in bioequivalence, Statistics in Medicine 20: 2785-2799
- Paulo Costa*, Jose´ Manuel Sousa Lobo (2001) Modeling and comparison of dissolution profiles, European Journal of Pharmaceutical Sciences 13, 123–133
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