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Perspective on Use of Statistical Tools

in Pharmaceutical Manufacturing

Karthik Iyer (CQE, CSSBB)

Senior Policy Advisor

CDER/OC/OMPQMarch 9th, 2012

AOAC Conference

* This presentation reflects the views of the author and should not

be construed to represent FDAs views or policies.

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Agenda

Enforcement Action Examples

CGMP References

ASTM Standards

Conclusions

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Recent warning letters and other compliance issues

Examples involving

Incorrect application of sampling plans

Equipment changes and process

capability

Container closure - determining baseline

defect rates

Recall exampleapplication of ASTM

E2709

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1. Warning Lettersampling plans

Firm using sampling plans incorrectly Pooled X vials, used only 1 reportable value, but used

n=X in sampling plan.

.based your lot or batch acceptance/rejectioncriteria on a single reportable value averaged from apooled sample.

For .., you are collecting 3 pooled samples (each pool= 10 vials). This equates to a lot disposition action on3 reportable values with corresponding AQL of X%and LQ of X% respectively. This is not equivalent toan X or X plan as claimed in your SOP.

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1. Warning Lettersampling plans

Response to 483 indicated firm did not know

how to use and interpret sampling plans

correctly. Firm did not understand concepts of

Acceptable Quality Level (AQL) and Limiting

Quality (LQ) and Operating Characteristic

Curve (OC) of a specific sampling plan.

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2. Warning Letterequipment comparability and process

capability

Four (4) tablet products, various strengths

Initial process qualification used a single-sided tablet

press. During routine production, however, theseproducts were also being manufactured using a

double-sided tablet press.

Compression using the double sided press was not

qualified.

Firms response to the FDA 483 attempted to show

statistical equivalence between the single and double

sides presses.

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capability

The firms written response referenced the Cpk values for processesusing a double-sided tablet press and the single-sided tablet press.

FDA evaluation of the FDA 483 response

The Cpk value alone was not an appropriate metric to demonstratestatistical equivalence. Cpk analysis requires a normal underlyingdistribution and a demonstrated state of statistical process control. Thefirm did not address these issues in their response.

Statistical equivalence between the two presses could have beenshown by using either parametric or non-parametric (based ondistribution analysis) approaches and comparing means and variances.Neither of these approaches was employed. Firm did not use theproper analysis to support their conclusion that no significant differencesexisted between the two compression processes.

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capability

Issues

Data did not support proper statistical

conclusions. Firm did not understand underlying

assumptions required to conduct Process

Capability calculations.

Firm did not conduct proper statistical

analysis to demonstrate equivalence between

two operations.

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3. Warning Lettercontainer closure quality and

baseline defect rates

ProductLVP in a dual chamber bag Numerous complaints of leaks, bursts, and premature activation

during 2 year period.

Root cause - variability in the film thickness that influenced thesealing of the bags. Bags have two seals and their strength (orweakness) relative to each other led to different failure modes.

Critical defects compromising sterility and stability.

Poor history for the supplier of this container closure

system. Incoming acceptance activities, as well as in-process

and finished product release activities, were foundinadequate.

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3. Warning Lettercontainer closure quality and

baseline defect rates

Issues In responding to the 483, the firm equated customer

complaints to true manufacturing defect rate. They did

not understand that market incident data may nottrack with the quality of the product prior to release.

The proposed sampling plans to identify these knownpotential defects were not based on appropriatestatistics.

Firm did not understand sampling plan used for lotrelease.

Firm could not justify using a riskier sampling plan(higher probability of accepting bad product).

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Application of ASTM E2709 - Standard Practice for Demonstrating Capability

to Comply with an Acceptance Procedure.

Tablets, Q value: 70%

Background: Firm was having recall issues due to dissolution failures on

stability. Dissolution data was analyzed using ASTM 2709. Sample data

below shown for 2 lots (Each row is a different lot). If evaluated correctly,

these lots would have been flagged as high risk for failure.

Unit

1

Unit

2

Unit

3

Unit

4

Unit

5

Unit

6

Unit

7

Unit

8

Unit

9

Unit

10

Unit

11

Unit

12 Mean SD RSD

USP -

PASS

or

FAIL

ASTM E2709

Probability @

95%

confidence

96% 72% 82% 74% 102% 70% 97% 63% 71% 78% 74% 60% 78% 14% 17% Pass 0.14%

77% 73% 90% 95% 92% 59% 73% 94% 60% 72% 62% 85% 78% 13% 17% Pass 0.14%

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CGMP References

211.110(a) & (b)

211.165(d)

211.180(e)

Preamble for 21 CFR 210, 211

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Key elements in these requirements

Control procedures

Monitor the output

Performance Variability in the characteristics of in-process

material and the drug product

.derived fromprevious acceptable processaverage and process variability estimates

(where possible)

.determined by...suitable statistical

procedures(where appropriate)

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Statistics

Can sample tablets at any stage of process and analyze for: Weight.

Content Uniformity.

Dissolution.

Other critical quality attributes and or parameters of interest.

Can make decisions at any stage of process with respect to: Ability for a lot to pass USP UDU and or Dissolution tests in the future.

(ASTM E2709)

Confidence in sampling. (ASTM E2334 & ASTM E122)

Capability and Performance analysis. (ASTM E2281) Statistical Process Control Charts. (Monitor Variation, ASTM E2587)

Following tools illustrate making inferences about untested units ona particular attribute, variable and or parameter with respect tosample size and an associated confidence.

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Voluntary Consensus Standards:

US Government Agencies OMB Circular A119

Federal Participation in the Development and Use ofVoluntary Consensus Standards and in Conformity

Assessment Activities (Rev. Feb 10, 1998) directs agencies to use voluntary consensus

standards in lieu of government-unique standardsexcept where inconsistent with law or otherwiseimpractical

intended to reduce to a minimum the reliance byagencies on government-unique standards.

http://www.whitehouse.gov/omb/circulars/a119/a119.html
http://www.whitehouse.gov/omb/circulars/a119/a119.htmlhttp://www.whitehouse.gov/omb/circulars/a119/a119.html

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Sample Size Effect on RSD Limit @ 95%Confidence / 95%Probability

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

85.1 87.5 90 92.5 95 97.5 100 102.5 105 107.5 110 112.5 114.9

Sample Mean

RS

n=10

n=20

n=30

n=100

n=500

n=1000

Sample Size Effect on RSD Limit @ 99% Confidence / 95% Probability

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

85.1 87.5 90 92.5 95 97.5 100 102.5 105 107.5 110 112.5 114.9

Sample Mean

RSD

n=10

n=20

n=30

n=100

n=500

n=1000

ASTM E2709Standard Practice for Demonstrating

Capability to Comply with an Acceptance

Procedure

One tool to analyze

Uniformity of Dosage

Units

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ASTM E2709 ExplanationStandard Practice for Demonstrating Capability

to Comply with an Acceptance Procedure

Slide shows the relationship between sample size andtolerance for variability. As sample size increases, so doesthe tolerance for variability.

The analysis was performed using ASTM E2709-10. The

RSD limits on the y-axis represent the maximum variability alot can possess to ensure with 95 or 99% confidence thatthere is at least a 95 or 99% probability a lot will comply withthe USP Uniformity of Dosage Units test based upon a givensample size, confidence level, and sample mean.

For example: If you sampled 30 units and had a samplemean of 95%, then the maximum RSD value for those 30units would be ~3.0% to be 95% confident that there is atleast a 95% probability a future sample from the lot wouldpass the USP UDU test.

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ASTM E2334Setting an Upper Confidence Bound For a Fraction or

Number of Non-Conforming items, or a Rate of Occurrence

for Non-conformities, Using Attribute Data, When There is a

Zero Response in the Sample

Confidence vs Sample Size

0

10

20

30

40

50

60

70

80

90

100

6 10 12 24 30 100 150 300 500 1000

Sample Size

Confidence

Pd=1%

Pd=0.5%

Pd=0.065%

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ASTM E2334 ExplanationSetting an Upper Confidence Bound For a Fraction or




Slide shows the relationship between Confidence andSample Size. As sample size increases, so doesconfidence demonstrated.

The analysis was performed using ASTM E2334-09.Keeping the maximum percent defective constant (1,0.5, and 0.065%) a line was generated to show howsample size effects the confidence demonstrated inhaving no more than the maximum percent defective. A

zero response was assumed (that is zero defects in thesample) and a binomial distribution was used. For example: If you desire a percent defective of no more than

0.5% and sample 30 units, then you are only ~15% confidentthat your lot has no more than 0.5% defects.

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ASTM E2334Setting an Upper Confidence Bound For a Fraction or




Sample Size vs Percentage of Non Conformities

0

5

10

15

20

25

30

35

40

10 20 30 50 500 1000

Sample Size

Percen

tageNonConforming

99%

Confidence

95%

Confidence

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ASTM E2334 ExplanationSetting an Upper Confidence Bound For a Fraction or

Number of Non-Conforming items, or a Rate of Occurrencefor Non-conformities, Using Attribute Data, When There is a


Slide shows the relationship between the upperconfidence bound on percent defects and sample size.

As sample size increases the upper confidence bound

on percent defects decreases. The analysis was performed using ASTM E2334-09.

Keeping the confidence level constant (95 and 99%) aline was generated to show how sample size effects theupper confidence bound percent defects. A zero

response was assumed (that is zero defects in thesample) and a binomial distribution was used. For example: If you want to be 99% confident that there is no

more than 1% defective units in your lot, then you must sample~460 units with a zero response.

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ASTM E122Standard Practice for

Calculating Sample Size to Estimate, With Specified

Precision, the Average for a Characteristic of a Lot or

Process

Estimate Precision vs Sample Size

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

10 20 30 50 500 1000

Sample Size

P

recision

Range

=1.0

=3.0

=5.0

=6.0

=10.0

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ASTM E122 explanationStandard Practice for

Calculating Sample Size to Estimate, With SpecifiedPrecision, the Average for a Characteristic of a Lot or

Process

Slide shows the relationship between sample

size and precision. As sample size increases,

so does your estimate precision. The analysis was done using ASTM E122-09.

Lines were generated using different sample

sizes to show the effect it has on your estimate

precision. For example: If you sampled 30 units and your sigma

value was 6, then your sample average is ~ +/-3.5%

of your true population average.

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Process and Measurement Capability Indices

Confidence in Manufacturing Capability

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

6 10 12 20 24 30 50 100 250 500 1000

Sample Size

ManufacturingCapability

95% Confidence

99% Confidence

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ASTM E2281 ExplanationStandard Practice for


Slide shows the relationship between a reportedProcess Capability Index (Cpk(3.14)) andsample size. As sample size increases, so does

the reported Cpk. When reporting a Cpk, a lower 95 or 99%

confidence bound should always be the valuereported. As this value accounts for the samplesize in which the C

pkwas estimated.

For example: If you sampled 30 units and estimateda Cpkof 3.14, then the value reported should be ~2.5(that is I am 99% confident that the Cpkfor myprocess is at least 2.5). The analysis was done using

ASTM E2281-08.

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Confidence in Manufacturing Performance

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

6 10 12 20 24 30 50 100 250 500 1000

Sample Size

Manufa

cturingPerformanc

e

95% Confidence

99% Confidence

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ASTM E2281 ExplanationStandard Practice for


Slide shows the relationship between a reportedProcess Performance Index (Ppk(2.79)) andsample size. As sample size increases, so does

the reported Ppk. When reporting a Ppk, a lower 95 or 99%

confidence bound should always be the valuereported. As this value accounts for the samplesize in which the P

pkwas estimated.

For example: If you sampled 30 units and estimateda Ppkof 2.79, then the value reported should be ~2.2(that is I am 99% confident that the Ppkfor my processis at least 2.2). The analysis was done using ASTME2281-08.

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SPC (Statistical Process Control) Charts are acollection of very effective statistical-graphicaltools which can be used to:

Understand and diagnose your data.

Track performance to identify problems, or shifts inperformance (good or bad).

Control or adjust the process to maintain desired

performance. Can be applied for data based on Incoming, In-

process, or Lot release samples.

ASTM E2587Standard Practice for Use of Control Charts inStatistical Process Control

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9181716151413121111

103

102

101

100

Sample

Sample

Mean __

X=101.868

UCL=103.048

LCL=100.689

9181716151413121111

4.5

3.0

1.5

0.0

Sample

SampleRange

_R=2.046

UCL=4.326

LCL=0

1

66

5

1

55

5

5

52

2

Voice of the ProcessIs the process in a state of control?

ASTM E2587Standard Practice for Use of Control Charts in Statistical Process ControlVariable X-bar-R chart

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ASTM E2587Standard Practice for Use of Control Charts in Statistical Process Control

Chart is used to detect special causes ofvariation during manufacturing.

Control is determined against standard 8rules established by Dr. Walter Shewhart.

Preceding chart is called X-bar-Range withSubgroup size of 5 tablets (each point isan average of 5 individual results).

Control limits reveal true variability of theprocess.

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ASTM E2587Standard Practice for Use of Control Charts in Statistical Process ControlAttribute nP chart

28252219161310741

12

10

8

6

4

2

0

Sample

SampleCount

__NP=4.9

UCL=11.38

LCL=0

Pass/Fail test for incoming tablet bottles (nP chart)

The tablet bottle is either pass or fail (Binary response)

Sample 100 bottles per incoming lot

Here we assume the failure rate is 5 bottles/100 bottlesNeed to know historical defect rate from supplier

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Conclusions

What have we covered?

Enforcement action examples and CGMP references.

Use of statistics to quantify relationship betweenconfidence associated with attribute, variable and or

parameter of interest with respect to the sample size

collected.

To make inferences on untested units.

Can be applied to In-coming, In-process, or Finished

samples.

Can be used for real time manufacturing and or

annual/periodic product reviews.

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Conclusions

Other Statistical Tools

Sampling plans

Do they describe Consumers Risk?

How are true defect rates calculated to use a particular

sampling plan?

Confidence, Prediction, and Tolerance Intervals

Is the correct statistical tool being applied for the

right analysis?

Do the tools help answer questions about

product quality and process performance?

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Conclusions

The specific statistical tools and analysisdepends on what variables, attributes,parameters are being used to monitor process

performance and product quality. The preceding example is just one set of

statistical methods available to monitor processperformance and product quality.

Statistics is a tool to elicit information to confirmthat a specific manufacturing process isproducing quality product.

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Acknowledgements

Alex ViehmannCDER/OPS

Grace McNallyCDER/OC

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