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
14
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)
16
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.
19
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
20
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)
28
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).
29
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)
31
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
33
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)