Report

Current Statistical Issues in Dissolution Profile Comparisons Sutan Wu, Ph.D. FDA/CDER 5/20/2014 1 Outlines: • Background of Dissolution Profile Comparisons • Current Methods for Dissolution Profile Comparisons • Current Statistical Concerns • Simulation Cases • Discussions 2 Disclaimer: The presented work and views in this talk represents the presenter’s personal work and views, and do not reflect any views or policy with CDER/FDA. 3 Backgrounds: Dissolution profile comparison: why so important? Extensive applications throughout the product development process Comparison between batches of pre-change and post-change under certain post-change conditions e.g.: add a lower strength, formulation change, manufacturing site change Generic Drug Evaluations FDA Guidance: Dissolution, SUPAC-SS, SUPAC-IR, IVIV and etc. 4 Dissolution Data Recorded at multiple time points At least 12 tablets at each selected time point is recommended Profile curves are drugdependent e.g: Immediate release vs. extend release Response: cumulative percentage in dissolution 5 Current Methods for Dissolution Profile Comparisons Model-Independent Approaches Similarity factor 2 (FDA Dissolution Guidance): 1 n f 2 50 log{[1 t 1 ( Rt Tt ) 2 ]0.5 100} n Multivariate Confidence Region Procedure --- Mahalanobis Distance: = Σ = ( − )′ Σ Σ +Σ 2 −1 ( − ) , = 1 , … . ′ , = (1 , … . )′ Model-Dependent Approaches: Select the most appropriate model such as logit, Weibull to fit the dissolution data Compare the statistical distance among the model parameters 6 Methods Pros • Simple to compute • Clear Cut-off Point: 50 Mahalanobis Distance • Model-dependent Approach • • Only the mean dissolution profile to be considered; • At least 3 same time point measurements for the test and reference batch; Comments • Approximately over 95% applications • Bootstrapping f2 is used for data with large variability • Only one measurement should be considered after 85% dissolution of both products; • %CV <=20% at the earlier time points and <=10% at other time points. Both the mean profile and the batch variability to be considered together Simple stat formula • Same time point measurements for the test and reference batches; • A few applications • Cut-off point not proposed • Hard to have a common acceptable cut-off point Measurements at different time points • • Model selection Cut-off point not proposed • Some internal lab studies Similarity factor 2 • Cons 7 Some Review Lessions: 75 B o 60 o t s 45 t f r 2 a 30 p p i 15 n g 0 0 15 30 45 60 75 Similary Factor f2 • Large variability was observed in some applications and the conclusions based on similarity factor f2 were in doubt. • Bootstrapping f2 was applied to re-evaluate the applications. Different conclusions were observed. 8 Motivations: How to cooperate the variability consideration into dissolution profile comparison in a feasible and practical way? Bootstrapping f2: Lower bound of the non-parametric bootstrapping confidence interval (90%) for f2 index 50 could be the cut-off point Subsequent Concerns: The validity of bootstrapping f2? Mahalanobis-Distance (M-Distance): A classical multivariate analysis tool for describing the distance between two vectors and widely used for outlier detection Upper Bound of the 90% 2-sided confidence interval (Tsong et. al. 1996) Subsequent Concerns: The validity of M-Distance? The cut-off point? 9 Objectives: Thoroughly examine the performance of bootstrapping f2 and f2 index: can bootstrapping f2 save the situations that f2 is not applicable? Gain empirical knowledge of the values of M-distance: does Mdistance is a good substitute? What would be the “appropriate” cut-off point(s)? 10 Simulation Cases: Scenarios 1: similarity factor f2 “safe” cases For both batches 1) %CV at earlier time points (within 15 mins) <= 20% and %CV <= 10% at other time points; 2) Only one measurement after 85% dissolution Scenarios 2: large batch variability cases (f2 is not recommended generally) %CV > 20% (<= 15 mins) or/and %CV > 10% (> 15mins) Different mean dissolution profile but same variability for both batches Same mean dissolution profile but testing batch has large variability Scenarios 3: multiple measurements after 85% dissolution “Safe” Variability cases: Dissolution Guidance recommendations Large Variability cases 11 Basic Simulation Structures: Dissolution Mean Profile from Weibull Distribution: % = ∗ [1 − exp(−() )], : , : , : , : Reference Batch: MDT= 25, B=1, Dmax=85 Testing Batch: 90 End Step 80 MDT 13 37 2 70 B 0.55 1.45 0.05 Dmax 73 97 2 Dissolution (%) Start Batch Variability (%CV) for 12 tablets: Start End Step <=15 mins 5% 50% 2% >15 mins 5% 60 50 40 Ref Batch 30 Testing Batch 1 20 Testing Batch 2 10 0 0 10 20 30 40 50 60 70 Time in Mins 30% 2% 5000 iterations for Bootstrapping f2 Time (mins): 5, 10, 15, 20, 30, 45, 60 12 Scenarios 1 Cases: Reference Testing %CV at all time points = 5% %CV at all time points = 10% f2 43.60 Bootstrapping f2 43.30 M-Distance 31.07 f2 84.23 Bootstrapping f2 84.10 M-Distance 2.81 When similarity factor f2 is applicable per FDA guidance, bootstrapping f2 and f2 give the same similar/dissimilar conclusions; %CV (<=15mins) = 15%, %CV (> 15mins) = 12% f2 51.04 Bootstrapping f2 50.77 M-Distance 9.18 In examined cases, the values of bootstrapping f2 is close to f2 values, though slightly smaller; Values of M-Distance could vary a lot, but within expectations. 13 Demo of M-distance vs. Bootstrapping f2: Bootstrapping f2 value M-Distance vs. Bootstrapping f2 100 75 50 25 0 0 5 10 15 20 25 30 M-Distance Values of M-Distance vary a lot: for higher Bootstrapping f2, M-Distance can be lower than 5; • for board line cases (around 50), M-Distance can vary from 7 to 20. 14 Scenarios 2 Cases: • Different Mean Dissolution Profile, but same variability at all the time points: some board line cases show up Dmax=89, MDT=19, B=0.85 Dmax=89, MDT=19, B=0.75 %CV all time points 30% %CV all time points 30% f2 50.10 f2 51.3 Bootstrapping f2 49.46 Bootstrapping f2 50.54 M-Distance 5.34 M-Distance 5.03 Dmax=89, MDT=19, B=0.75 Some discrepancies were observed between Bootstrapping f2 and f2 index %CV all time points 10% f2 50.40 Bootstrapping f2 50.10 M-Distance 9.31 Bootstrapping f2 gives different conclusions for the same mean profile but different batch variability Values of M-Distance vary: stratified by batch variability? 15 Same Mean Dissolution Profile but large variability for testing batch 90 Testing Batch 80 70 Ref Batch 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 In examined cases Bootstrapping f2 is more sensitive to batch variability, but still gives the same conclusion with cut-off point as 50; This may suggest to use a “higher” value as the cut-off point at large batch variability cases; M-Distance varies: depends on the batch variability 16 Scenarios 3: More than 1 measurement over 85% 100 90 80 70 60 50 40 30 Testing Batch Ref Batch 20 10 0 0 10 20 30 40 50 60 70 In examined cases, Bootstrapping f2 gives more appealing value but still same conclusion with cut-off point as 50; This may suggest to use a different value as cut-off point for bootstrapping f2. 17 Findings: When similarity factor f2 is applicable per FDA Dissolution guidance, bootstrapping f2 and f2 give the same similar/dissimilar conclusions; In the examined cases, Bootstrapping f2 is more sensitive to batch variability or multiple >85% measurements; However, with 50 as the cut-off points, bootstrapping f2 still gives the same conclusion as similarity factor f2; Values of M-Distance varies a lot and appears that <=3 could be a similar case, and over 30 could be a different case. Conclusions: Based on current review experiences and examined cases, bootstrapping f2 is recommended when the similarity factor f2 is around 50 or large batch variability is observed; At the large batch variability cases, new cut-off points may be proposed. Testing batches would be penalized by larger batch variability. M-Distance is another alternative approach for dissolution profile comparisons. Its values also depends on the batch variability. The cut-off point is required for further deep examinations, particularly, M-Distance values at different batch variability and bootstrapping f2 around 50. 18 Problems encountered with M-distance: Convergence issue with Inverse of Σ , Proposal: To compute the increment M-Distance _ = 1 , 2 − 1 , … , −1 − _ = (1 , 2 − 1 , … , −1 − ) Σ_ = , Σ_ = ( ) The proposed increment M-Distance can help us solve the convergence problem caused by highly correlated data (cumulative measurements); The interpretation of increment M-Distance: the distance between the increment vectors from the testing and reference batches. 19 References: • FDA Guidance: Dissolution Testing of Immediate Release Solid Oral Dosage Forms, 1997 • FDA Guidance: SUPAC for Immediate Release Solid Oral Dosage Forms, 1995 • FDA Guidance: Extended Release Oral Dosage Forms: Development, Evaluation, and Application of In Vitro/In Vivo Correlation, 1997 • In Vitro Dissolution Profile Comparison, Tsong et. al, 2003 • Assessment of Similarity Between Dissolution Profiles, Ma et. al, 2000 • In Vitro Dissolution Profile Comparison – Statistics and Analysis of the Similarity Factor f2, V. Shah et. al, 1998 • Statistical Assessment of Mean Differences Between Dissolution Data Sets, Tsong et al, 1996 20 Acknowledgement: FDA Collaborators and Co-workers: • ONDQA: Dr. John Duan, Dr. Tien-Mien Chen • OGD: Dr. Pradeep M. Sathe • OB: Dr. Yi Tsong 21 22 Back Up 23 90% Confidence Region of M-Distance: T K y xtest xref S pooled 1 y xtest xref F P, 2 n p 1,.90 ,where 2 2n p 1 K n 2n 2n 2 P By Langrage Multiplier Method * y1 xtest xref 1 F P , 2 n p 1,.90 * y xtest xref 1 F P , 2 n p 1,.90 2 u max D M l min D M T 1 K S x x x x pooled test ref test ref T 1 K S xtest x ref xtest xref pooled T 1 * 1 * *T S * , y y S pooled pooled 1 2 y1 y2 T 1 * 1 * *T S * , y y S pooled pooled 1 2 y1 y2 24