The Posterior Probability of Dissolution Equivalence David J

The Posterior Probability of Dissolution Equivalence David J Le. Blond 1 , John J Peterson 2 and Stan Altan 3) 1 Exploratory Statistics, Abbott, david. leblond@abbott. com 2 Research Statistics Unit, Glaxo. Smith. Kline Pharmaceuticals 3 Pharmaceutical R&D, Johnson & Johnson Midwest Biopharmaceutical Statistical Workshop Muncie, Indiana May 25, 2011 MBSW May 25, 2011

► Objective Outline ► 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 2

Objective ► Make this tool available to you so you can use it if you want to. § Statistical Modeling § Software (R, Win. BUGS) § Example Data & Code § david. leblond@abbott. com MBSW May 25, 2011 3

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. MBSW May 25, 2011 4

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”? % Dissolved 100 0 Time MBSW May 25, 2011 5

Equivalence defined ► Identify parameter space based on ► Establish similarity region ► Obtain distance estimate from data ► Equivalence: distance estimate is “sufficiently contained within” the similarity region. § Difference in Dissolution at multiple time points § Difference in profile model parameters § Condensed univariate distance measure § Constraints on parameter space § Based on “customer requirements” § Conforms to parameter space MBSW May 25, 2011 ? 6

Example: f 2 similarity metric (see reference 9) ► parameter space: Dissolution differences, Di, at p time points. ► similarity region: D 2 0 0 D 1 ► distance estimate = (point estimate) ► Equivalence: (no measure of uncertainty) MBSW May 25, 2011 7

The confidence set approach TOST (one dimensional) 5% 5% 8% Yes 2% No “MOST” (multi-dimensional) Yes No MBSW May 25, 2011 Maybe 8

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 9

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 Q 9) MBSW May 25, 2011 10

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”) MBSW May 25, 2011 11

Bayesian equivalency in a nutshell Prior Information (non-informative) Probability Model (Likelihood) Dissolution Data (Test and Reference) 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%) MBSW May 25, 2011 12

Example 1: Is the Reference lot equivalent to the Test lot? 6 tablets per lot MBSW May 25, 2011 13

Example 1: Multivariate Dissolution Model % Dissolution vector, Y, for the ith tablet from the kth lot … MBSW May 25, 2011 14

Example 1: Non-informative Prior Information MBSW May 25, 2011 15

Example 1: Non-informative Prior Information MBSW May 25, 2011 16

Example 1: Non-informative Prior Information Since and can be shown (see appendix) to have the distribution MBSW May 25, 2011 17

Example 1: Non-informative Prior Information MBSW May 25, 2011 18

Example 1: Definition of Equivalence Define a rectangular similarity region, S, as and require that to conclude equivalence. MBSW May 25, 2011 19

Example 1: Results 500 of 10, 000 draws plotted MBSW May 25, 2011 20

Example 2: Equivalence of 2 processes MBSW May 25, 2011 21

Example 2: Hierarchical Model % Dissolution vector, y, for the ith tablet from the kth run … MBSW May 25, 2011 22

Example 2: Non-informative prior information elements of Vtablet elements of Vrun Max = 40 MBSW May 25, 2011 23

Example 2: Definition of Equivalence (same as Example 1) Define a rectangular similarity region, S, as and require that to conclude equivalence. MBSW May 25, 2011 24

Example 2: Results 1000 of ~2, 000 draws plotted MBSW May 25, 2011 25

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 MBSW May 25, 2011 26

Dissolution profile models Probit: Logistic: Weibull: Exponential: ( 1 st order kinetics ) Quadratic: …and some others (Higuchi, Gompertz, Hixson-Crowell, …) MBSW May 25, 2011 27

Weibull parameters M measures content T is time to 63. 2% Dissol. beta measures delay 0. 5 2. 0 MBSW May 25, 2011 28

Weibull parameterization in Win. BUGS ► The following seemed to reduce colinearity and improve convergence. § Replace T with lna = -b ln. T § Replace b with lnb § transform time (t) from minutes to hours MBSW May 25, 2011 29

Nonlinear mixed model in Win. BUGS % Dissolution, Y, for the ith tablet from the kth lot at the jth time (t) point… MBSW May 25, 2011 30

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 MBSW May 25, 2011 31

Weibull Example: Posterior Probability of Dissolution Equivalence Prob = 0 2 SD Similarity Region Prob = 0. 949 MBSW May 25, 2011 32

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? MBSW May 25, 2011 33

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 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 (SUPACIR): Chemistry, Manufacturing and Controls, In Vitro Dissolution Testing and In Vivo BE. 1995 Tsong Y, Sathe P, an d. Shah 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 d. Shah 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): 241258 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 f 2 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 34

References 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. Shah VP, Tsong Y, Sathe P, and Liu J-P (1998) In vitro dissolution profile comparisons – statistics and analysis of the similarity factor f 2, 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 T 2 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. ) 2010 Meeting 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 Profiles. The AAPS Journal, Vol. 12, No. 3, 263 -271 MBSW May 25, 2011 35

Appendix Derivation of prior distribution of si shown on slide 17 MBSW May 25, 2011 36