Transcript Release Limit Calculations Current Practice

DISCUSSANT COMMENTS
RELEASE LIMIT CALCULATIONS AND
STABILITY STUDIES
1
Stan Altan
ASSESSING RELEASE LIMITS AND
MANUFACTURING RISK FROM A
BAYESIAN PERSPECTIVE
2
Areti Manola
[email protected]
MANUFACTURING RISK ESTIMATION
Calculate the probabilities of future lots falling into each of
the 4 possible outcomes in relation to pass and fail at Release
and end of shelf life .
P(YSL<SpecSL|Y0≥RL)
P(YSL>SpecSL|Y0 ≥ RL)
P(YSL<SpecSL|Y0<RL)
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P(YSL>SpecSL|Y0<RL)
MANUFACTURING RISK ESTIMATION

Given Release Limits and Specifications
manufacturing risk can be described through a 2x2
table given below:
End of Shelf Life

Release
Pass (%) Fail (%) Total (%)
Pass (%)
C11
C12
R1
Fail (%)
C21
C22
R2
Total (%)
C1
C2
100
C12/R1=
P(YSL<SpecSL|Y0≥RL)
cost to the
company
Probabilities associated with the above 2x2 table can
be estimated through a Bayesian posterior predictive
distribution approach
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COMMENTS
Bill Porter has enumerated sources of variability,
the complexities of accounting for all of them, the
proposed Bayesian modeling goes a long way to
accommodating those in forming an ‘Error Budget’
 Pass,Fail is not synonymous with ‘Acceptable, Not
Acceptable’ or ‘Good, Bad’
 Prediction is a very risky proposition


how well characterized is the process
stable long term average and variability
 ‘erratic’ process


partially mitigated by non-informative priors, so
sensitivity analyses need to be carried out as part of the
analysis
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MULTIPLE STORAGE CONDITIONS:
ACCUMULATING UNCERTAINTY
Brad Evans
Pfizer
MBSW, May 23, 2012
Cumulative Degradation over Maximum Storage Time
Spec Limit = problem? (what about allowance for uncertainty?)
DP 2
Each study estimates the
Degradation rate for that condition.
Net degradation within a condition
= Rate * Time
DS3
DS 2
DS 1
DP 1
To predict the mean we can use the
slopes and intercepts from each study
Stability studies may be of different
lengths than the storage conditions
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TOTAL DEGRADATION
What is the net impact? Net uncertainty?
 Which attributes are the most limiting?
 Which storage temperature / time combination is the
most limiting?
 What times periods could/should be changed?
 Tradeoff of storage cost and degradation
 Statistics can play a strategic role here

COMMENTS

Bill Porter points out that the prediction should
focus on what is being delivered to the consumer



error propagation mainly driven by model parameter
uncertainty, DS to DP manufacture
Add analytical error at end
Piece wise regression model with appropriate
random components seems reasonable
amenable to a Bayesian approach to calculate limits at
the consumer stage
 heterogeneity between DS and DP


Choice of temperature conditions

Arrhenius relationship to suggest informative priors
and provide estimates of intermediate temperature rates
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IMPACT OF STABILITY ON SETTING
AND MEETING SPECIFICATIONS
IN AN UNCERTAIN WORLD
William R. Porter
MSBW 2012
MEASUREMENT VARIATION
 Measurement
by :






uncertainty can be affected
Within operators within equipment within
labs within days (repeatability).
(intermediate
Between operators.
precision)
Between equipment.
Between days.
Between labs (interlaboratory precision).
Between dosage forms/strengths (sample
preparation, excipient interactions).
}

Interactions with other components of measurement
uncertainty.
Copyright 2012 W. R. Porter
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BUT WAIT! THERE’S MORE!
WHAT ABOUT SUPPLY CHAIN CONTROL?

Control of storage conditions during manufacture
and distribution (e.g., maintaining cold
conditions for temperature sensitive products)
has been a major recent concern.

Proper design of stress degradation experiments
during product development and monitoring of
conditions during distribution can address these
issues.
Copyright 2012 W. R. Porter
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UNADDRESSED SUPPLY CHAIN ISSUES
 What
about mail-order pharmacies?
Regulatory expectations are that the supply
chain ends when the patient takes the drug,
and not before then. Medications are
dispensed with storage instructions.
 The U.S. Post office specifically states that
control of temperature is NOT provided, and
that the shipper is responsible for protection
against temperature extremes.

 What
about military deployments, where
troops are issued 180 day supplies of
medications?
Copyright 2012 W. R. Porter
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ERROR BUDGET

Given a set of final specifications, these must be
narrowed by amounts sufficient to account for:
Measurement uncertainty (guard banding).
 Stability-related changes in quality metrics,
especially within and between batch uncertainty at
end-of-shelf-life.


Whatever remains are the narrow limits that
define the release specifications.
Copyright 2012 W. R. Porter
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95% Confidence Limits for Mean
35
35
5
-5
μ
-15
-25
Governs design
for random effects
(uncertainty)
30
Standard Deviation Units
15
-35
15
Governs design
for fixed effects
(bias)
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Standard Deviation Units
95% Confidence Limits for Standard
Deviation
25
Copyright 2012 W. R.
Porter
DEGREES OF FREEDOM
20
15
σ
10
5
0
0
5
10
15
20
25
30
35
40
45
50
Sample Size
For n = 3, C.L is 220% larger than for n =
∞
For n = 4, C.L is 62% larger than for n =
∞
0
5
10
15
20
25
30
35
40
45
50
Sample Size
For n = 7, C.L is 220% larger than for n = ∞
For n = 14, C.L is 62% larger than for n = ∞
SAMPLE SIZES FOR VARIANCE ESTIMATES
1.8
95% confidence
90% confidence
80% confidence
1.2
1.4
1.6
After n=30, the
improvement in precision
for estimating the variance
diminishes rapidly
1.0
Ratio of Sample Variance to True Variance
2.0
2
2
P{ sample
/  true
 r | N  n}  p  confidencelevel
20
40
60
80
Sample Size
100
120
140
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0.5 0.6
0.2 0.3
0.4
within 20% of true STD
0.1
2
2
P{  sample
/  true
 0.2 | N  n}
0.0
Probability
0.7 0.8
0.9
1.0
Ratio of Sample STD to True STD
0
20
40
60
Sample Size n
80
100
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BUT REALLY, WHO CARES?
1.
In a QbD world, we should aim to produce consistent product
with minimum variance..
2.
If we can reduce process variation, reduce product
degradation variation and reduce measurement uncertainty
to low enough levels through QbD, then setting release limits
becomes moot.
 Does
increased scientific knowledge under QbD
necessarily lead to “reduced process variation,
reduced product degradation variation and
reduced measurement uncertainty...” ?

Statistical methods will play a major role in
characterizing the sources of variability and
projected process behavior to manage risk
Copyright 2012 W. R. Porter
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