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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 .

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the posterior probability of dissolution equivalence

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

outline
Outline
  • 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

MBSW May 25, 2011

objective
Objective
  • Make this tool available to you so you can use it if you want to.

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importance of in vitro dissolution
Importance of in-vitro dissolution
  • 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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measurement of in vitro dissolution

100

% Dissolved

0

Time

Measurement of in-vitro dissolution
  • 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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equivalence defined
Equivalence defined
  • 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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example f2 similarity metric see reference 9

D2

0

D1

0

Example: f2 similarity metric(see reference 9)
  • parameter space: Dissolution differences, Di, at p time points.
  • similarity region:
  • distance estimate = (point estimate)
  • Equivalence: (no measure of uncertainty)

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the confidence set approach
The confidence set approach

TOST (one dimensional)

5%

5%

8%

2%

Yes

No

“MOST” (multi-dimensional)

No

Maybe

Yes

MBSW May 25, 2011

confidence set approach considerations
Confidence set approach considerations
  • 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.

MBSW May 25, 2011

confidence set approach considerations10
Confidence set approach considerations
  • 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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proposed bayesian approach
Proposed Bayesian Approach

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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bayesian equivalency in a nutshell
Bayesian equivalency in a nutshell

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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example 1 multivariate dissolution model
Example 1: Multivariate Dissolution Model

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

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example 1 non informative prior information17
Example 1: Non-informative Prior Information

and

Since

can be shown (see appendix) to have the distribution

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example 1 definition of equivalence
Example 1: Definition of Equivalence

Define a rectangular similarity region, S, as

and require that

to conclude equivalence.

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example 1 results
Example 1: Results

500 of 10,000 draws plotted

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example 2 hierarchical model
Example 2: Hierarchical Model

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

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example 2 non informative prior information
Example 2: Non-informative prior information

elements of Vtablet

elements of Vrun

Max = 40

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example 2 definition of equivalence same as example 1
Example 2:Definition of Equivalence(same as Example 1)

Define a rectangular similarity region, S, as

and require that

to conclude equivalence.

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example 2 results
Example 2: Results

1000 of ~2,000 draws plotted

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example 3 a model dependent comparison
Example 3: A model dependent comparison
  • 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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dissolution profile models
Dissolution profile models

Probit:

Logistic:

Weibull:

Exponential:

( 1st order kinetics )

Quadratic:

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

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weibull parameters
Weibull parameters

M measures content

T is time to 63.2% Dissol.

beta measures delay

0.5

2.0

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weibull parameterization in winbugs
Weibull parameterization in WinBUGS
  • 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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nonlinear mixed model in winbugs
Nonlinear mixed model in WinBUGS

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

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weibull example judging similarity by confidence set approach
Weibull Example: Judging similarity by confidence set approach

“…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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weibull example posterior probability of dissolution equivalence
Weibull Example: Posterior Probability of Dissolution Equivalence

Prob = 0

2SD Similarity Region

Prob = 0.949

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pros and cons of a bayesian approach
Pros and Cons of a Bayesian Approach
  • 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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references
References
  • Schuirmann DJ (1981) On hypothesis testing to determine of the mean of a normal distribution is contained in a known interval, Biometrics 37:617
  • 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.
  • Shah VP, Yamamoto LA Schirmann D, Elkins J and Skelly JP (1987) Analysis of in vitro dissolution of whole versus half controlled release theophilline tablets, Pharm Res 4: 416-419
  • 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
  • Tsong Y, Sathe P, an dShah VP (1996) Compariong 2 dissolution data sets fro similarity ASA Proceedings of the Biopharmaceutical Section 129-134
  • Berger RL and Hsu JC (1996) Bioequivalence trials, intersection-union tests and equivalence confidence sets, Statistical Science 11(4) 283-319
  • J.W.Moore and H.H.Flanner, Mathematical Comparison of curves with an emphasis on in vitro dissolution profiles. Pharm. Tech. 20(6), : 64-74, 1996
  • Moore JW and Flanner HH (1996) Mathematical comparison of dissolution profiles, Pharmaceutical Technology 24:46-54
  • Tsong Y, Hammerstrom T, Sathe P, and Shah VP (1996) Statistical assessment of mean differences between two dissolution data sets, Drug Information Journal 30: 1105-1112
  • Polli JE, Rekhi GS, and Shah V (1996) Methods to compare dissolution profiles, Drug Information Journal 30: 1113-1120.
  • Sathe PM, Tsong Y, Shah VP (1996) In vitro dissolution profile comparion: statistics and analysis, model dependent approach, Pharmaceutical research 13(12): 1799-1803.
  • Polli JE, Rekhi GS, an dShah VP (1996) Methods to compare dissoltuion profiles and a rationale for wide dissoltuion specifications for metroprolol tartrate tablets j pharm Sci 86:690-700
  • FDA (1997) Guidance for industry: extended release oral dosage forms: development, evaluation, and application of in vitro/ in vivo correlations
  • Food and Drug Administration. Guidance for Industry: Dissolution Testing of Immediate Release Solid Oral Dosage Forms, 1997
  • Food and Drug Administration. Guidance for Industry: SUPAC-MR: Modified Release Solid Oral Dosage Forms. 1997
  • Chow SD and Ki FYC (1997) Statistical comparison between dissoltuion profiles of drug products, Journal of Biopharmaceutical statistics, 7(30): 241-258
  • Tsong Y, Hammerstrom T, an Chen JJ (1997) Multipoint dissoltuion specification and acceptance sampling rule based on profile modeling an dprincipal component analysis, Journal of biopharmaceutical statistics 7(3) 423-439.
  • Liu JP, Ma MC, Chow SC (1997) Statistical evaluation of similarity factor f2 as a criterion for assessment of similarity etween dissoltuion profiles Drug Info J 31: 1255-1271
  • Ju HL and Liaw S (1997) On the assessment of similarity of drug dissolution profile – a simulation study Drug Info J 31 1273-1289

MBSW May 25, 2011

references35
References
  • Shah VP, Tsong Y, Sathe P, and Liu J-P (1998) In vitro dissolution profile comparisons – statistics and analysis of the similarity factor f2, Pharm. Res. 15: 889-896, 1998
  • FDA (2000) Guidance for Industry Waiver of In Vivo Bioavailability and Bioequivalence Studies for Immediate- Release Solid Oral Dosage Forms Based on Biopharmaceutics Classification System
  • FDA (2000) Guidance for industry: bioavailability and Bioequivalence studies for orally administered drug products – general considerations
  • Ma M-C, Wang BC, Liu J-P, and Tsong Y (2000) Assessment of similarity between dissolution profiles, Journal of Biopharmaceutical statistics 10(2) 229-249
  • Gohel MC and Panchal MK (2000) Comparison of in vitro dissolution profiles using a novel, model independent approach, Pharmaceutical technology, March, 2000, pp 92-102
  • 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
  • Chow S-C, Shao j, and Wang H (2003) In vitro bioequivalence testing, Statistics in Medicine 22:55-68
  • Saranadasa H (2001) Defining similarity of dissolution profiles through Hotelling’s T2 statistic, Pharmaceutical Technology Februrary 2001, pp 46-54
  • Tsong Y, Sathe PM, and Shah VP (2003) In vitro dissoltuion profile comparison, pp 456-462, in Encyclopedia of Biopharmaceutical statistics, Marcel Dekker
  • Yi Tsong, Meiyu Shen, Vinod P Shah 2004 Three-stage sequential statistical dissolution testing rules. J Biopharm Stat Vol. 14, Issue 3, Pages 757-79
  • Saranadasa H and Krishnamoorthy K (2005) A multivariate test for similarity of two dissolution profiles, Journal of Biopharmaceutical Statistics 15, 265-278
  • EMEA guidance
  • WHO guidance
  • J. Siepmann∗, F. Siepmann (2008) Mathematical modeling of drug delivery, International Journal of Pharmaceutics 364 (2008) 328–343
  • Selen Arzu; Cruañes Maria T; Müllertz Anette; Dickinson Paul A; Cook Jack A; Polli James E; Kesisoglou Filippos; Crison John; Johnson Kevin C; Muirhead Gordon T; Schofield Timothy; Tsong Yi (Profiled Author: Polli, James E.) 2010Meeting report: applied biopharmaceutics and quality by design for dissolution/release specification setting: product quality for patient benefit. Food and Drug Administration, Silver Spring, Maryland, USA The AAPS journal;12(3):465-72
  • Yong Zhang, Meirong Huo, Jianping Zhou, Aifeng Zou, Weize Li, Chengli Yao, and Shaofei Xie (2010) DDSolver: An Add-In Program for Modeling and Comparison of Drug Dissolution ProfilesThe AAPS Journal, Vol. 12, No. 3, 263-271

MBSW May 25, 2011

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