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**Current Statistical Issues in Dissolution Profile Comparisons**

Sutan Wu, Ph.D. FDA/CDER 5/20/2014

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Outlines: Background of Dissolution Profile Comparisons Current Methods for Dissolution Profile Comparisons Current Statistical Concerns Simulation Cases Discussions

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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.

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**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.

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**Dissolution Data Recorded at multiple time points**

At least 12 tablets at each selected time point is recommended Profile curves are drug-dependent e.g: Immediate release vs. extend release Response: cumulative percentage in dissolution

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**Current Methods for Dissolution Profile Comparisons**

Model-Independent Approaches Similarity factor 𝑓 2 (FDA Dissolution Guidance): Multivariate Confidence Region Procedure --- Mahalanobis Distance: 𝐷 𝑀 = ( 𝑹 𝑡 − 𝑻 𝑡 )′ Σ 𝑝𝑜𝑜𝑙𝑒𝑑 −1 ( 𝑹 𝑡 − 𝑻 𝑡 ) Σ 𝑝𝑜𝑜𝑙𝑒𝑑 = Σ 𝑡𝑒𝑠𝑡 + Σ 𝑟𝑒𝑓 2 , 𝑹 𝑡 = 𝑅 1 ,…. 𝑅 𝑡 ′ , 𝑻 𝑡 =( 𝑇 1 , …. 𝑇 𝑡 )′ 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

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**Model-dependent Approach**

Methods Pros Cons Comments Similarity factor 𝑓 2 Simple to compute Clear Cut-off Point: 50 Only the mean dissolution profile to be considered; At least 3 same time point measurements for the test and reference batch; 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. Approximatelyover 95% applications Bootstrapping f2 is used for data with large variability Mahalanobis Distance 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; Cut-off point not proposed A few applications Hard to have a common acceptable cut-off point Model-dependent Approach Measurements at different time points Model selection Some internal lab studies

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Some Review Lessions: 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.

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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?

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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 M-distance is a good substitute? What would be the “appropriate” cut-off point(s)?

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**%CV > 20% (<= 15 mins) or/and %CV > 10% (> 15mins)**

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

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**𝐷𝑖𝑠𝑠 % =𝐷𝑚𝑎𝑥 ∗[1−exp (−( 𝑡 𝑀𝐷𝑇 ) 𝐵 )],**

Basic Simulation Structures: Dissolution Mean Profile from Weibull Distribution: Reference Batch: MDT= 25, B=1, Dmax=85 Testing Batch: 𝐷𝑖𝑠𝑠 % =𝐷𝑚𝑎𝑥 ∗[1−exp (−( 𝑡 𝑀𝐷𝑇 ) 𝐵 )], 𝐷𝑚𝑎𝑥:𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛, 𝑡:𝑡𝑖𝑚𝑒 𝑝𝑜𝑖𝑛𝑡, 𝑀𝐷𝑇:𝑚𝑒𝑎𝑛 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒, 𝐵:𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 Start End Step MDT 13 37 2 B 0.55 1.45 0.05 Dmax 73 97 Batch Variability (%CV) for 12 tablets: Start End Step <=15 mins 5% 50% 2% >15 mins 30% 5000 iterations for Bootstrapping f2 Time (mins): 5, 10, 15, 20, 30, 45, 60

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**Scenarios 1 Cases: Reference Testing %CV at all time points = 5%**

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; 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. %CV (<=15mins) = 15%, %CV (> 15mins) = 12% f2 51.04 Bootstrapping f2 50.77 M-Distance 9.18

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**Demo of M-distance vs. Bootstrapping f2:**

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.

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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 %CV all time points 30% Dmax=89, MDT=19, B=0.75 %CV all time points 30% f2 50.10 Bootstrapping f2 49.46 M-Distance 5.34 f2 51.3 Bootstrapping f2 50.54 M-Distance 5.03 Dmax=89, MDT=19, B=0.75 %CV all time points 10% Some discrepancies were observed between Bootstrapping f2 and f2 index Bootstrapping f2 gives different conclusions for the same mean profile but different batch variability Values of M-Distance vary: stratified by batch variability? f2 50.40 Bootstrapping f2 50.10 M-Distance 9.31

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**Same Mean Dissolution Profile but large variability for testing batch**

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

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**Scenarios 3: More than 1 measurement over 85%**

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.

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**Findings: Conclusions:**

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.

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**Problems encountered with M-distance:**

Convergence issue with Inverse of Σ 𝑝𝑜𝑜𝑙𝑒𝑑 , Proposal: To compute the increment M-Distance 𝑅 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡_𝑡 = 𝑅 1 , 𝑅 2 − 𝑅 1 , …, 𝑅 𝑡−1 − 𝑅 𝑡 𝑇 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡_𝑡 =( 𝑇 1 , 𝑇 2 − 𝑇 1 , …, 𝑇 𝑡−1 − 𝑇 𝑡 ) Σ 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡_𝑅 =𝐶𝑜𝑣 𝑅 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛 𝑡 𝑡 , Σ 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡_𝑇 =𝐶𝑜𝑣( 𝑇 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛 𝑡 𝑡 ) 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.

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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

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Acknowledgement: FDA Collaborators and Co-workers: ONDQA: Dr. John Duan, Dr. Tien-Mien Chen OGD: Dr. Pradeep M. Sathe OB: Dr. Yi Tsong

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Thank You!

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Back Up

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**90% Confidence Region of M-Distance:**

,where By Langrage Multiplier Method

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