STATISTICAL CONSIDERATIONS

WHEN EVALUATING CONTENT

UNIFORMITY

NJPhAST Meeting: Jim Bergum (BMS) & Kim Vukovinsky (Pfizer)

September 22 2011

1

Outline2

Content Uniformity Test - History

Large N Tests

PhRMA Statistics Expert Team

Modified Large N

European Proposals

Content Uniformity and Dissolution Acceptance

Limits (CuDAL)

Batch Release - Key Attributes

Potency (Average Drug Substance/Dosage Unit)

Dissolution (% Drug Substance Released at

Specified Time)

Content Uniformity (CU)

USP The degree of

uniformity in the amount of the drug

substance among dosage units.

3

Typical Criteria for CU

Proportion of individual results within a specified

range (ex: 85-115) or ranges (ex: 75-115)

Relative Standard Deviation (RSD)/Coefficient of

Variation (CV)

Distance From Target

4

History:

Old USP Content Uniformity Test

All measurements of dosage units and criteria values are in percentage label claim (%LC).

At each stage, calculate the sample average, , and the sample standard deviation s.

StageNumber

TestedPass stage if:

S1 10

CV < 6.0%

Tablets: All Results between 85% - 115% Label Claim

Capsules: No more than 1 result outside 85%- 115%LC

No result outside 75% - 125% LC

S2 20

CV < 7.8%

Tablets: No more than one result outside 85% - 115%LC

No result outside 75% - 125%LC

Capsules: No more than two results outside 85% - 115% LC

No result outside 75% - 125% LC

X

5

International Conference on

Harmonization (ICH)6

United States(US), Europe (EU), and Japan (JP)

Harmonize CU

PhRMA Statistics Expert Team

Base on JP test

Adjust JP test to perform similar to USP Tablet test.

History:

Old Japanese Content Uniformity Test

All measurements of dosage units and criteria values are in percentage label claim (%LC).

At each stage calculate the sample average, , and the sample standard deviation s.

StageNumber

testedPass stage if:

S1 10 Acceptance Value (AV) = | - 100| + 2.2s 15.0

S2 20

i) | - 100| + 1.9s 15.0 using all 30 results (S1 + S2)

ii) No dosage unit is outside the maximum allowed range of

75% to 125% Label Claim.

X

X

X

Max s S1 :15/2.2 = 6.8

S2 :15/1.9 = 7.9

7

Harmonized Uniformity of Dosage Unit (UDU) Test

All measurements of dosage units and criteria values are in percentage label claim (%LC).

At each stage calculate the sample average and the sample standard deviation s.

Stage Number tested Pass stage if:

S1 10 AV = |M - | + 2.4s 15.0, where M is defined below.

S2 20i) |M - | + 2.0s 15.0 using all 30 results (S1 + S2)

ii) No dosage unit is outside the maximum allowed range of

0.75*M to 1.25*M.

M is defined as follows:

(i) If is less than 98.5%LC, then M = 98.5%LC.

(ii) If is between 98.5 and 101.5%LC, then M = .

(iii) If is greater than 101.5%LC, then M = 101.5%LC.

X

X

X

X

X

X

X

Indifference Zone

8

Operating Characteristic (OC) Curves:

UDU vs Japan vs Old USP

UDU

Old USP Tablet

Japan

Batch Mean = 96%LCBatch Mean=100%LC

9

UDU

Old USP Tab

Japan

Example: 10 Tablets Stage 110

84 86 88 90 92 94 96 98 00 02

7 9 2 22 4 0 2 3 3

Mean = 96.5

S = 5.2

RSD(%) = 5.4

Min = 84.7

Max = 102.3

Old USP: 1out (85-115) (Fail)

Old JP: AV = 3.5 + 2.2*5.2 = 15.0 (Pass)

UDU: AV = 2.0 + 2.4*5.2 = 14.6 (Pass)

S1 CU Data1 98.42 84.73 101.34 100.25 97.26 94.27 91.98 99.09 102.3

10 96.2

Hot Topics/Issues in Past 15 years11

Gaining Greater Process Understanding

Quality by Design

Design Space

Better Non-destructive measurement techniques (NDT), such as NIR

Facilitates fast and precise measures

Significantly increases real time information (Real Time Release)

Improves manufacturing process understanding, control and capability

Provides content uniformity results for a large number of dosage units

Realization that USP tests are not batch release tests

Stated in USP General Notices [Section 3.10. Applicability of Standards], the UDU procedure is not intended for inspecting uniformity of finished product for lot/batch release. Statements about whether the UDU test is met apply only to the units tested.

Applying the USP UDU test for lot/batch release does not demonstrate compliance with the Current Good Manufacturing Practices (cGMPs) 21CFR Section 211.

How Can Statistics Help?12

Develop Statistical Procedures to

Evaluate Results from Large Sample Sizes (Large N)

Assure that batches will meet USP tests ( )

What is the goal?

Determine Large N release criteria that provide similar performance to the UDU test.

Original: PhRMA CMC Statistics Expert Team (Sandell, D.; Vukovinsky, K; Diener, M.; Hofer, J.; Pazdan, J.; Timmermans, J. Development of a Content Uniformity Test Suitable for Large Sample Sizes. Drug Information Journal2006, 40, 337-344).

Modified: Bergum, Vukovinsky "A Proposed Content-Uniformity Test for Large Sample Sizes", Pharm. Tech., November 2010, p 72-79

Ph. Eur. PAT working Group (European Pharmacopoeia): Evaluation of Uniformity of Dosage Units using Large Sample Sizes, 2011

Determine limits that provide assurance that a future sample taken from a batch will pass the UDU test.

Content Uniformity & Dissolution Acceptance Limits: Bergum, J.S. and Hua Li, "Acceptance Limits for the New ICH USP 29 Content Uniformity Test," Pharmaceutical Technology, October 2007, pp. 90-100.

13

Large N: PhRMA SET

N 100 250 500 1000 5000

C 4 11 23 47 239

Collect N 100 Dosage Units

Express Result as % LC

# Tablets outside

(85,115) %LC C?

Reject

Batch

Pass

Batch

No

Yes

One tiered counting test

Count number of results (C)

outside 85% to 115% LC

Criteria: C 0.048*N

Cs for Selected Ns

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One tiered counting test

Count number of results (C)

outside 85% to 115% LC

Criteria: C 0.03*N

No result outside 75-125% LC?

Cs for Selected Ns

Large N Test: Modified PhRMA SET

N 100 250 500 1000 5000

C 3 7 15 30 150

Collect N Dosage Units

Express Result as % LC

# Tablets outside

(85,115) %LC C?

Reject

Batch

Pass

Batch

No

Yes

15

OC Curves PhRMA SET vs Modified

UDU

Modified (N= 100)

PhRMA SET (N=100)

Batch Mean = 100%

Batch Mean = 96%

UDU

Modified (N= 100)

PhRMA SET (N=100)

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Large N: Ph. Eur. PAT WG Proposal

Parametic

Assuming Normal Distribution

K=2.4 stage 1 (n=10) and K=2.0 stage 2 (n=30)

=> Confidence Level = 84% and Coverage = 91%

For given N, compute k so that CI=84% and Cov=91%

Pass if |M - | + k*s 15.0 and no more than X units are outside 0.75*M to 1.25*M where X = 0 for N < 500 and increases for larger N.

Nonparametric

Same as PhRMA SET criteria with an allowance of tablets outside Target +/- 25 if N > 500.

X

17

European Large N Proposal Batch Mean = 100%LC

UDU

EU Parametric (N= 100)

EU Parametric (N=300)

EU Nonparametric (N=100)

18

CuDAL Test: Background

Methodology Developed in Mid 80s

Application: Process Validation (Show process does what it purports to do)

Show Specific Quality Attributes will meet associated Testing Standards (eg: CU)

Content Uniformity (units have similar amount of drug)

Dissolution (units dissolve at required rate)

Request/Mission - Develop limits based on the process validation sample results that provide confidence that the testing standard samples will pass the testing standard.

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Content Uniformity and Dissolution Acceptance Limits

Example: UDU Acceptance Limit Table

Mean RSD(%)

97.0 3.79

98.0 4.03

99.0 4.26

100.0 4.47

101.0 4.17

102.0 3.87

103.0 3.57

Meeting Relative Standard Deviation (RSD) Limit assures, with 90% confidence,

that a future testing standard sample take from the batch has greater than a 95%

chance of passing the UDU test.

90% Confidence Interval, 95% Coverage, n=30

Sample Results:

Mean = 99.0

RSD (%) = 3.42

Acceptance Limit

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Justification

Provides high assurance that batch meets regulatory standard

Assurance increases with increased sample size.

Will always need a standard to define Acceptable.

Can be used for more than validation or product release (ex: evaluation of NIR methods for CU used in real time release).

Tied directly to regulatory requirements

Ensures compliance with 21 CFR 211.165(d) - Testing and Release for distribution

Can be used as a tool to meet the expectations set forth by FDA's Process

Validation Guidance

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Strategy Part 1

1. Select Testing Standard (Ex: UDU)

2. Assume probability distribution for individual observations (ex: Normal with parameters (Mu) & (Standard Deviation))

3. Assuming known distribution parameters, mathematically derive* the Lower Bound for each stage (Note: Each stage may have multiple criteria!) This is the hard part!

4. Lower bound for overall test is the maximum of the individual stage lower bounds

*Bergum, J.S. and Hua Li, "Acceptance Limits for the New ICH USP 29 Content

Uniformity Test," Pharmaceutical Technology, October 2007, pp. 90-100.

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General Calculation23

1.) Probability of Passing each stage

= P(Ci1 and Ci2 and Cim) 1- j=1 (1-P(Cij))

where:

P(Si) is the probability of passing stage i,

P(Cij) is the probability of passing the j-th criterion

of the m criteria within the i-th stage.

2.) Probability of Passing a k-stage test

max{P(S1), P(S2), , P(Sk)}

m

UDU Test

95% Lower Bound Contour24

95% Lower Bound

Ba

tch

Sta

nda

rd D

evia

tion

Batch Mean

Prob(Passing UDU)

Mean

Std

Dev

Simulate USP

(N=1,000,000)

90 or 110 2.59 95.960

95 or 105 4.57 96.022

100 6.11 95.996

Sampling: Population (Whole Batch)25

Sampling: N=10 (1 Result/Location)26

Sampling: N=20 (2 Results/Location)27

Two Sample/Criteria Types

Acceptance Limit Sample (Results Compared to Acceptance Limit Table Criteria)

Sampling Plan 1: One unit per location

Sampling Plan 2: n units per location (allows estimation of between/within location variability)

UDU Sample (Results Compared to Testing UDU Criteria)

Sampling Plan: Defined by the Testing Standard (Usually a random sample from the batch Sampling Plan 1)

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Strategy Part 2

5. Select Sampling Plan (1 or 2).

6. Construct confidence interval for the distribution parameters based on user defined confidence level.

7. Determine lower bound probabilities for each point in the confidence interval.

8. Determine maximum probability across all points in confidence interval.

9. Compare maximum probability to user defined coverage (Lower Bound).

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UDU Test

Lower Bound with Simultaneous Confidence Interval

Batch Mean

ULS = Upper CI for Batch SD

95% Lower Bound

Ba

tch

Sta

nda

rd D

evia

tion

30

( , S)

( Z*ULS/ n, ULS)

X

Confidence Interval

X

Construct Acceptance Limit Table

To Generate Table, user selects

Confidence Level (Usually 90 or 95%)

Coverage Lower Bound - Desired Probability of future

Testing Standard Samples passing Testing Standard

(usually 95%).

Sampling Plan/Sample Size

Target (Usually 100)

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Content Uniformity and Dissolution Acceptance Limits

Example: UDU Acceptance Limit Table

Mean RSD(%)

97.0 3.79

98.0 4.03

99.0 4.26

100.0 4.47

101.0 4.17

102.0 3.87

103.0 3.57

Meeting Relative Standard Deviation (RSD) Limit assures, with 90% confidence,

that a future testing standard sample take from the batch has greater than a 95%

chance of passing the UDU test.

90% Confidence Interval, 95% Coverage, n=30

32

Sample Size Effect on RSD Limit

Sampling Plan 1

Sample

Mean(%LC)

RSD(%) Limit

10 30 60

95.0 2.35 3.30 3.71

98.0 2.88 4.03 4.53

100.0 3.21 4.47 5.00

102.0 2.77 3.87 4.36

105.0 2.13 2.99 3.36

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Evaluating Acceptance Limit Table

- Determining Adequate Sample Size

Pick sample size such that the probability of passing the acceptance limit table is:

High for a Good Batch (Acceptable Batch Mean and Std Dev)

Low for a Bad Batch (Unacceptable Batch Mean and Std Dev)

For given sample size, find probability of passing acceptance limit table by integrating over tabled values.

34

Example: Sampling Plan 1

P(Passing 90/95 Acceptance Limit Table)

Batch

Mean

Batch

RSD

Sample Size

10 30 60

100.02 99.0 100.0 100.0

3 59.7 99.9 100.0

98.02 96.0 100.0 100.0

3 46.2 98.8 100.0

96.02 84.5 100.0 100.0

3 26.0 84.9 99.7

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All Together Now (N=200)

USP

Modified Large N

Euro

Nonparametric

Parametric

CuDAL

90% CI/95% Cov

95% CI/95% Cov

36

Example: Sampling Plan 2 (15 X 4)37

Result Summary statistics

Location 1 2 3 4 Mean Variance Std Dev

1 97.08 99.72 98.37 97.5 98.17 1.36 1.17

2 99.72 100.32 101.01 100.29 100.34 0.28 0.53

3 99.9 98.27 98.88 97.96 98.75 0.73 0.86

4 98.78 98.17 98.94 97.78 98.42 0.29 0.54

5 96.32 96.61 99.66 97.2 97.45 2.31 1.52

6 100.97 102.17 99.06 98.8 100.25 2.57 1.60

7 97.02 97.35 98.65 99.98 98.25 1.83 1.35

8 99.39 98.81 98.63 98.06 98.72 0.30 0.55

9 99.59 97.8 97.67 98.95 98.50 0.86 0.93

10 97.97 98.54 100.26 98.74 98.88 0.96 0.98

11 96.09 98.61 97.49 97.5 97.42 1.07 1.03

12 98.87 97.81 97.28 98.8 98.19 0.60 0.78

13 101.1 102.6 100.48 98.62 100.70 2.71 1.65

14 100.8 100.34 98.49 100.93 100.14 1.27 1.13

15 99.7 100.09 100.14 99.2 99.78 0.19 0.44

Example: Sampling Plan 2 38

Example: Sampling Plan 239

Descriptive Statistics

Mean 98.93

SE (within-location Std Dev) 1.07

Standard deviation of location means 1.06

Standard Deviation of Location Means

0.9 1.0 1.1 1.2

SE LL UL LL UL LL UL LL UL

0.9 88.1 111.9 88.5 111.5 88.9 111.1 89.3 110.7

1.0 88.2 111.8 88.6 111.4 89.0 111.0 89.4 110.6

1.1 88.4 111.6 88.7 111.3 89.1 110.9 89.5 110.5

1.2 88.5 111.5 88.9 111.1 89.2 110.8 89.6 110.4

1.3 88.7 111.3 89.0 111.0 89.4 110.6 89.7 110.3

Sampling Plan 2:

Sample Size Evaluation40

Prob(Passing Acceptance Limit Table)

Batch

Mean

Variance Component (SD) Sampling Plan (Loc x #/Loc)

Between Location*(Example = 0.91)

Within Location(Example = 1.1) 15x4 15x2 10x2

100

1 1 100.0 100.0 100.0

2 100.0 100.0 96.6

2 1 100.0 100.0 99.7

2 99.6 98.2 81.7

97

1 1 100.0 100.0 100.0

2 98.6 97.9 82.3

2 1 100.0 99.9 94.8

2 90.4 81.9 53.3

* = ((SD Location Means)2 - SE2/n)

CuDAL: Current Status

General Methodology: ASTM E11 Standard E2709

Original (Done)

Lower Bound

Confidence Intervals

Acceptance Limit Table

Revision (In 2nd Ballot)

Add Sampling Plan 2

Content Uniformity: ASTM E55 Standard (3rd Ballot)

Lower Bound Calculations Specific to UDU Test

Future Other Tests?

41

Overview42

Analytical

Formulation

API

Q

b

D

Design Space

NOR

Statistical

Process Control

Continued Process Verificaton

Control Charts

Relate Response to Inputs

Submission

Post ApprovalProcess Design

Process Qualification

CuDAL

Large N

Testing/Monitoring

Reduced

Testing and/or

Criteria?

CuDAL

Large N

Summary/Take Home Messages43

UDU is a compromise between Old USP and Japan CU test

Modified large N

Easy to use.

Equivalent or more conservative than UDU for N < 250.

Sampling

Plans

1: One result per location

2: More than one result per location Allows more complete evaluation of between and within location variability

Batch size doesnt matter when batch size is much larger than sample size.

CuDAL

Can be used for any sample size.

Easy to use.

Provides assurance that batch will pass UDU test if tested.

Need Strategy for reducing testing as process knowledge increases (Ex: CuDAL => Modified Large N)