DEMONSTRATING CAPABILITY TO COMPLY WITH A TEST PROCEDURE: THE CONTENT UNIFORMITY AND DISSOLUTION ACCEPTANCE LIMITS (CUDAL) APPROACH

Jim Bergum September 12, 2011

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Key Responses For Batch Release

Potency (Average Drug Substance/Dosage Unit) Dissolution (% Drug Substance Released at

Specified Time) Content Uniformity

USP <905> The degree of uniformity in the amount of the drug substance among dosage units.

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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 |M - | + 2.4s ≤ 15.0, where M is defined below.

S2 20 i) |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.

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XIndifference Zone

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X X

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CuDAL Test: Background

Methodology Developed in Mid 80’s 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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Acceptance Limit Table Example for UDU Test

Mean (%LC) RSD(%)97.0 3.7998.0 4.0399.0 4.26

100.0 4.47101.0 4.17102.0 3.87103.0 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

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Acceptance Limit Sample Results:

Mean = 99.0RSD (%) = 3.76

Acceptance Limit

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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Final Statistical Statement

If acceptance limit sample passed limits, then with a pre-specified confidence level, the probability that a testing standard sample will pass the testing standard is greater than a pre-specified coverage value.

Example: With 90% confidence, a future testing standard sample take from the batch has greater than a 95% chance of passing the testing standard.

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Strategy – Part 1

1. Select Testing Standard (Ex: UDU)

2. Assume probability distribution for individual observations (ex: Normal with parameters µ (Mu) & σ (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 ContentUniformity Test," Pharmaceutical Technology, October 2007, pp. 90-100.

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UDU Test - 95% Lower Bound Contour9

Batc

h St

anda

rd D

evia

tion

Batch Mean

Prob(Passing UDU)

MeanStd Dev

Simulate USP (N=1,000,000)

90, 110 2.59 95.96095, 105 4.57 96.022

100 6.11 95.996

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

Batc

h St

anda

rd D

evia

tion

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( , S)•

( ± Z*ULS/√n, ULS)

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Confidence Interval

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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 Possible values specific to the Testing Standard (ex: Q

for Dissolution, Target for Content Uniformity)

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Acceptance Limit Table(Sampling Plan 1, 90% CI, 95% Coverage, n=30)

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

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Sample Size Effect on RSD LimitSampling Plan 1

SampleMean(%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.

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Example: Sampling Plan 1P(Passing Acceptance Limit Table)

Batch Mean

Batch RSD

Sample Size

10 30 60

100.02 99.0 100.0 100.03 59.7 99.9 100.0

98.02 96.0 100.0 100.03 46.2 98.8 100.0

96.02 84.5 100.0 100.03 26.0 84.9 99.7

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Sampling Plan 1Operating Characteristic Curve (OC)

USPLarge NCuDAL

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Batch Mean = 100%LC

USPCuDAL N = 10CuDAL N= 100CuDAL N= 300

Sampling Plan 1Operating Characteristic (OC) Curve

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Batch Mean = 96%LC

USPCuDAL N = 10CuDAL N= 100CuDAL N= 300

Example: Sampling Plan 2 (15 X 4)20

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 21

Example: Sampling Plan 222

Descriptive StatisticsMean 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 Evaluation

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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)

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?

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