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 5

Current Methods for Dissolution Profile Comparisons

 Model-Independent Approaches  Similarity factor 𝑓 2 (FDA Dissolution Guidance): 

f

2 

50



log{[ 1



1

n



n t

 1

(

R t



T t

)

2

]

 0 .

5 

100 }

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 6

Methods

Similarity factor 𝑓 2

Pros

• • Simple to compute Clear Cut-off Point: 50

Cons Comments

• Only the mean dissolution profile to be considered; • Approximately over 95% applications • 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; • Bootstrapping f2 is used for data with large variability • %CV <=20% at the earlier time points and <=10% at other time points.

Mahalanobis Distance Model-dependent Approach • • • Both the mean profile and the batch variability to be considered together Simple stat formula Measurements at different time points • • • • Same time point measurements for the test and reference batches; Cut-off point not proposed Model selection Cut-off point not proposed • A few applications • • Hard to have a common acceptable cut-off point Some internal lab studies 7

Some Review Lessions:

75

p i n g B o o t s t r a p f 2

60 45 30 15 0 0 15 30 45

Similary Factor f2

60 75 • 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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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: 𝑡 𝐷𝑖𝑠𝑠 % = 𝐷𝑚𝑎𝑥 ∗ [1 − exp(−( 𝑀𝐷𝑇 ) 𝐵 )],  𝐷𝑚𝑎𝑥: 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛, 𝑡: 𝑡𝑖𝑚𝑒 𝑝𝑜𝑖𝑛𝑡, 𝐵: 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 Reference Batch: MDT= 25, B=1, Dmax=85 𝑀𝐷𝑇: 𝑚𝑒𝑎𝑛 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒,  Testing Batch: MDT B Dmax

Start

13 0.55

73

End

37 1.45

97

Step

2 0.05

2  Batch Variability (%CV) for 12 tablets: <=15 mins >15 mins

Start

5% 5%

End

50% 30%

Step

2% 2% 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40

Time in Mins

 5000 iterations for Bootstrapping f2 Time (mins): 5, 10, 15, 20, 30, 45, 60 50 Ref Batch Testing Batch 1 Testing Batch 2 60 12 70

Scenarios 1 Cases:

%CV at all time points = 5%

Reference Testing

%CV at all time points = 10% f2

Bootstrapping f2 M-Distance

%CV (<=15mins) = 15%, %CV (> 15mins) = 12% 43.60

43.30

31.07

f2

Bootstrapping f2 M-Distance

51.04

50.77

9.18

f2

Bootstrapping f2 M-Distance

84.23

84.10

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. 13

Demo of M-distance vs. Bootstrapping f2:

M-Distance vs. Bootstrapping f2

100 75 50 25 0 0 5 10

M-Distance

15 20  Values of M-Distance vary a lot:  for higher Bootstrapping f2, M-Distance can be lower than 5; 25 • for board line cases (around 50), M-Distance can vary from 7 to 20. 30 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=0.75

Dmax=89, MDT=19, B=0.85

%CV all time points 30% %CV all time points 30% Dmax=89, MDT=19, B=0.75

%CV all time points 10%

f2 f2 Bootstrapping f2 M-Distance 50.10

49.46

5.34

Bootstrapping f2 M-Distance 50.40

50.10

9.31

f2 Bootstrapping f2 M-Distance 51.3

50.54

5.03

 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?

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Same Mean Dissolution Profile but large variability for testing batch 90 80 30 20 10 0 70 60 50 40 0 10 Testing Batch Ref Batch 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 50 40 30 20 90 80 70 60 10 0 0 10 20 30 40 Testing Batch Ref Batch 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.

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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.

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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 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 𝑡 , Σ 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡_𝑇 = 𝐶𝑜𝑣(𝑇 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 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 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

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Back Up 23

90% Confidence Region of M-Distance:

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