statistical approach to ppq

7/21/2019 Statistical Approach to PPQ

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Tara Scherder

Managing Director, Arlenda, Inc

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Statistical Approaches for PPQ

Options and Outcomes


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Reference: 2011 FDA Guidance Document: Process Validation

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During the process qualification (PQ) stage of

process validation, the process design is evaluatedto determine if it is capable of reproduciblecommercial manufacture

A successful PPQ will confirm the process design

and demonstrate that the commercialmanufacturing process performs as expected

.State a clear conclusion as to whether the dataindicates the process met the conditions

established in the protocol and whether theprocess is considered to be in a state of control


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Our Session Today

Choice of Statistical Method Understand Conclusions and Details

(assumptions, requirements)

Combine Statistics and Process Knowledge Part of Continuum of Process Understanding

Two examples1. Content Uniformity

2. Packaging Quality Measurements

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Methods

Exploratory Methods Variance Components Monte Carlo Simulation ASTM E2709 and E2810 Control Charts & Capability Tolerance Intervals Bayesian Prediction Interval ANOVA ANSI Acceptance Sampling for Variables &Attributes

Percent Non-Conformance

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Example: Content Uniformity

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Four samples drawn at each of15 locations across the batch,three batches


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Graphical methods

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151413121110987654321

110

105

100

95

Location

CU

A

B

C

Batch

Multi-Vari Chart for CU by Batch - Location

each batch has 4 samples at each of 15 locations

CU Sampling Plan 2

151413121110987654321

110

105

100

95

90

Location

CU

CU Sampling Plan 2each batch has 4 samples at each of 15 locations


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Variance Components

Parameter

Batch A Batch B Batch C

PointEstimate

% of total(%LC)

PointEstimate

% of

total

(%LC)

PointEstimate

% of total(%LC)

Between-location

SD2.57 80.9 1.00 8.1 3.39 90.2

Within-location

SD1.25 19.1 3.39 91.9 1.12 9.8

Total 2.86 100 3.54 100 3.57 100

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ParameterPoint

Estimate% Total

Overall Mean 100.1

Between-batch

SD 1.25 12.2Between-

location[Batch]

SD

2.52 50.2

Within-location

SD2.18 37.6

Total 3.56 100


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Monte Carlo Simulation

Probability of passing a method/procedurebased on user provided inputs

Provides a way of evaluating amethod/procedure or process usingcomputer generated data in place ofcollecting actual data

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Monte Carlo SimulationPercentage of Batches Passing UDU Test

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BatchPoint Estimate

Confidence

Limit

S1 S1 & S2 S1 S1 & S2

A 100 100 99.5 99.8

B 99.7 100 87.4 98.4

C 100 100 98.6 99.1

Parameter

Batch A Batch B Batch C

Point

Estimate

% of total

(%LC)

Point

Estimate

% of total

(%LC)

Point

Estimate

% of total

(%LC)

Between-location

SD2.57 80.9 1.00 8.1 3.39 90.2

Within-location

SD1.25 19.1 3.39 91.9 1.12 9.8

Total 2.86 100 3.54 100 3.57 100

Point Estimate

S1 S1 and S2

100.

0100.0

Parameter Point Estimate % Total

Overall Mean 100.1

Between-batch SD 1.25 12.2

Between-

location[Batch] SD2.52 50.2

Within-location SD 2.18 37.6

Total 3.56 100


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ASTM E2709/E2810: General Strategy

1. Determine Sampling Plan Sample Size (# Locations & # per location)

Use Prior Knowledge

OC curves, examination of acceptance limit tables

2. Construct/Choose Acceptance Limit Table Select Confidence Level (Usually 90 or 95%)

Select Coverage (usually 95%): Desired Probability ofSamples passing Testing Standard (eg USP UDU)

3. Collect Data & Compute Summary Statistics4. Compare to appropriate Acceptance Limit Table


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Acceptance Limit Table Examplefor USP UDU Test

Result

Location 1 2 3 4

1 97.08 99.72 98.37 97.50

2 99.72 100.32 101.01 100.29

3 99.90 98.27 98.88 97.96

4 98.78 98.17 98.94 97.78

5 96.32 96.61 99.66 97.20

6 100.97 102.17 99.06 98.80

7 97.02 97.35 98.65 99.98

8 99.39 98.81 98.63 98.06

9 99.59 97.80 97.67 98.95

10 97.97 98.54 100.26 98.74

11 96.09 98.61 97.49 97.50

12 98.87 97.81 97.28 98.80

13 101.10 102.60 100.48 98.62

14 100.80 100.34 98.49 100.93

15 99.70

100.09

100.14

99.20


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Acceptance Limit Table Examplefor USP UDU Test

Descriptive Statistics

Overall Mean 98.93

SE (within-location Std Dev) 1.07

Standard deviation of Location

Means1.06

90%CI/95%Cov 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


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Predicting Probability of PassingASTM 2810

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Across BatchesOverall Mean(%LC) 100.1

Variance Components (Std Dev)

Between Batch (%LC) 1.25*(p=0.02)

Between Location (%LC) 2.52*(p


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Control Charts: Two Subgroup Charts

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454137332925211713951

110

105

100

95

Sample

SampleMean

__X=99.91UC L=101.59

LCL=98.22

A B C

454137332925211713951

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12

8

4

0

Sample

SampleRange

_R=2.32

UCL=5.29

LCL=0

A B C

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1

8

5

1

1

1

1

51

111

1

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Xbar-R Chart of CU by Batch

454137332925211713951

110

100

90

SubgroupMean

_X=99.91

UCL=107.46

LCL=92.35

A B C

454137332925211713951

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5

0MRofSubgroupMean

__MR=2.84

UCL=9.28

LCL=0

A B C

454137332925211713951

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8

0

Sample

SampleRange

_R=2.32

UCL=5.29

LCL=0

A B C

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1

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I-MR-R/S (Between/Within) Chart of CU by Batch


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Tolerance Interval*

Assures with a pre-specified confidence level, that there is

at least a pre-specified probability (called coverage) thatthe individual results will fall within the interval endpoints

k depends on distribution, coverage and confidence

PTS-TI

95% confidence that the percentage of tablets outside the range of(85%, 115%) label claim (LC) is less than 12.5%

PTI-TOST

95% confidence and 87.5% coverage of the 85% to 115% LC limitingthe percentages of tablets below 85% and above 115% LC are bothless than 6.25% of the batch

*computationally complex for multi location sampling plan

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Bayesian Prediction Interval

Bayesian solution provides true prediction of failure offuture batches

Incorporates uncertainty in parameter estimation

Can incorporate between batch, between location, and

within location variance components

Statistical statement : X% probability that 95% ofbatches will pass UDU, or fall within some assayrange

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Fit model Perform simulations to obtain posterior distribution of

parameters Obtain predictive distribution of CU Assess

probability that .025 and .975 percentiles will be outside specification


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ANOVA

Fixed locations or batches: detectsignificant variation in group means

Random locations: detect significantvariation amonggroups

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ANOVA

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Batch and Location

Treated as Fixed Effects

ParameterPoint

Estimate% Total

Overall Mean 100.1

Between-batch

SD1.25 12.2

Between-

location[Batch]

SD

2.52 50.2

Within-location

SD2.18 37.6

Total 3.56 100

Batch and Location Treated

as Random Effects


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Example: Package Fill Volume

Packaging run time = 170 minutes

Fill rate = 180 bottles/minute

Total bottles filled = 30,600

Filler has 6 nozzle heads

Specifications: LSL = 99.5; USL = 100.5 ml

AQL (acceptance quality level) = 0.1%

Shift in mean after 26,000 bottles from 100.2-100.35 and Std Dev from 0.08 to 0.09 ml

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ANSI Z1.9

For Lot size = 30,600; AQL = 0.1%; Tightened, Level IIInspection, Variability Unknown, sample size of 100 isrequired.

One simulation , estimate of % non-conforming (ncf)was 0.052 (table B-5 of standard); maximum allowable% ncf is 0.218

Decision: ACCEPT the BATCH

Actual % ncf was 0.14%, which is higher than the AQLof 0.1%.

Based on the OC curve, if 100 samples are drawn from alot of this size with 0.14% ncf, the lot will be accepted75 % of the time. That is, a bottle with a defect willrandomly be found in the sample only 25 % of the time

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Control Charts & Capability

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Example: Critical DefectANSI Z1.4 Attribute Acceptance

50,000 bottles; AQL=0.065%; ANSI Z1.4 Tightened,Inspection level II (no specification for RejectableQuality Level, or Lot Tolerance Percent Defective)

Using Tables from standard, the required sample size is1250, and the lot will be accepted if 1 or lessnonconforming bottles are found.

Beta error is high; for instance, there is a 19% chance ofaccepting a lot that has 0.246 % nonconforming.

Consumer risk not controlled.

No statistical statement can be made regarding qualityof lot

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Example: Major DefectANSI Z1.4 Attribute Acceptance

50,000 bottles; AQL=1%; ANSI Z1.4 Tightened, Inspectionlevel II

Using Tables from standard, the required sample size is 500;lot will be accepted if 8 or less nonconforming bottles arefound

Can identify other sampling plans using software that might bemore efficient.

23543210

1.0

0.8

0.6

0.4

0.2

0.0

Lot Percent Defective

ProbabilityofAcceptance

n sample s ize

c acceptance number

275 4

500 8

n c

Operating Characteristic (OC) Curve


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Example: Critical DefectProportion Non-conforming

For any pass/fail sampling results, a statisticalstatement regarding the quality of the lot can bemade. For instance, a confidence statement can bemade regarding the bounds for the percent nonconforming

Example: assume no failures are found in a sample of1250. This allows the following statistical statement:

With 95.0% confidence, the population

nonconformance rate will be no morethan 0.0050 (~0.5%)(1)

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(1) Agresti/Coull interval from Lawrence D. Brown, T. Tony Cai and Anirban DasGupta, Interval

Estimation for aBinomial Proportion, Statistical Science, 2001, Vol. 16, No. 2, 101133


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James Bergum

Richard Montes

Helen Strickland Jennifer Walsh

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Contributors


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statistical approach to ppq

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