Multiple Storage Conditions:
Accumulating Uncertainty
Brad Evans
Pfizer
MBSW, May 23, 2012
Question
• How to model Stability across:
– DS storage, multiple temperatures/times
– DP storage, multiple temperatures/times
• We run studies at each temperature, in
parallel (to save the time)
• However, final commercial product goes
through each temperature in serial
fashion (and may not hit max time)
Outline
• Biologics, but concepts apply to small molecules
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• Proteins
• Vaccines
Stability of Biologics
DS and DP Stability data (ICH, other)
Modeling, assumptions, data in, output
Usage scenarios
Questions, future work
Stability of Biologics
– Storage:
• In process holds: ambient, refrigerated
• Bulk Drug Substance
– In-process
– Frozen
• Cryo-Vessels
• Glass vials (lyophilized powder typically, some PFS)
– Temperatures:
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25C, 40C – accelerated conditions
-40C “typical” DS frozen storage.
DP (liquid or lye powder) typically 2-8C (5C here)
-70C and -20C also used at times
Storage cost$
• -40°C walk in that can hold up to 40 x
300L cryovessels: ~ $1.33 million
• CU5000 + Freeze/Thaw 100 : $700,000+
• CU5000 + cryomixer: almost $500,000
• Modular freezer that can hold 9 x 300L
cryovessels is over $500,000
• Cost: Controls, engineering, scale, freeze
profiles
Control Unit and Cryovessel
Freeze / Thaw unit
Exposure / Stability data
• Data collected at different steps
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In Process Holds (DS/API)
Storage/Packaging/Labeling
Formal ICH Stability lots
Excipient Robustness Studies
Shipping studies
Long Term Storage (DP)
Patient Exposure vs Data
• At patient usage, the product has been
exposed to multiple temperatures for
varying amounts of time
• Modeling should reflect this
• Could go to conditional modeling if data
were available (out of scope)
• Stability testing in parallel
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
Design
• Patients:
– samples exposed to maximum storage at each
intended temperature Analytical
– Remaining samples  “next” storage for
maximum time  Analytical (ie serial study)
– Would only need data from ‘last’ condition
• Internal Studies:
– Ideal study would take too long
– Data collected in “parallel”
– Need data from all conditions
Stability Data
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ICH Batches: 0,1,3,6,9,12,18,24 (typical)
Ad hoc studies
Excipient Robustness studies
In process studies
Shipping studies
Assays of interest
– Size Exclusion
– Monomer / Purity
– etc
Degradation Rates from Stability Studies of
different lengths, at different Temperatures
Three rates for Drug Substance
0
9
Two rates for Drug Product
18
27
36
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
12
24
36
48
Combining across Temperatures
• Follow ICH guidance?
– at every storage
– use worst case
– which batches / lots /studies to combine
• Reasonable model at each storage?
– Not an ICH stability analysis
– Slope may not be stable initially
• Common Slope / Intercept at each storage?
– Follows the center of the process
– Gives an idea if storage times might work
• Assumptions
Modeling
– Slopes within storage condition
independent of starting values
– Linear fit regardless of length of storage
• “Daisy Chain” the predictions together
– data at end of “this” storage lines up with
data at the start of “next” storage
– This is what **would** happen if the study
were conducted serially
– rate of change estimated within each
temperature condition
Flow
• Data in:
– Stability Exposure Data (actual, multi
temperature)
– Production Exposure Data – many scenarios
possible (what if scenarios?)
– Multiple Assay(s)?
• Output (per assay)
– Predictions within each storage
– Predictions ACROSS multiple storage
Scenarios
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What is limiting assay?
What storage “burns” the spec window?
Should a storage time be shortened?
Could a storage time be lengthened?
Would a different assay be limiting under a
different scenario?
– What is the cost to go to colder storage
relative to degradation slope:
– 5C (slope, cost) vs -20C (slope, cost)
– Limiting assay may change
Stacking across storage
– Time scale is easy
– New Time = sum (all times so far)
– May not be the same for actual vs. production
– Response is a little trickier:
– Initial storage: need Intercept (Tzero) and slope
– Subsequent: need only the slope, ie rate
– New Response = Tzero + Sum(duration x slope)
– Depends on actual or production
– Actual – the analytical going into the model
– Production – the storage times you want to consider
Statistical Details
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Prediction at “exposure” is sum of predictions:
Each piece has an associated variance
df error add across the regression models
RMSE could be a pooled RMSE
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
more efficient estimation
assumes variance does not depend on the mean
model selection would be more complicated
rationale: “same” assay, “same” compound
all storage
( increase
in Yhat during max time )  Conf Limits
Statistical Details
Similar calculations for each group (SAS loop through groups)
var
Varp
Pred
se
sep
t
=
=
=
=
=
=
rmse1**2 * (
1/n1 + (x - xbar1)**2/ss_x1);
rmse1**2 * (1 + 1/n1 + (x - xbar1)**2/ss_x1);
int1 + slope1 * x;
sqrt(var);
sqrt(varp);
tinv(1-&alphalevel/2,df1);
accumulate across storage, eventually leading to:
upperCLM = pred + t * se;
lowerCLM = pred - t * se;
upperCLP = pred + t * sep;
lowerCLP = pred - t * sep;
Variances add but t-mult drop with increasing
degrees of freedom, so width grows at less than
sqrt(# groups)
Comment
• I do NOT see this as a spline or change point
regression
• To do this, we would need to conduct the serial study
• All samples exposed to ONE and only one condition
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Initial sample: Tzero or baseline, ie intercept
First storage: Tzero + degradation in that condition
Second:
Tzero + degradation in that condition
Etc
• Total degradation to the product:
– Tzero + Degradation in Storage 1 + Degradation Storage 2 +
Caveats
• Worst batch may change over time
• All Stability data used even if production is less
»RMSE from full stability design
»Prediction variance based on full design, ie all time points
• Model fit should be checked
• Nonlinearity may occur
• One batch / one result may be very influential
Input
Time
Storage
Assay
Spec
DS/DP
??
0
-40C
Purity
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1
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3
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6
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0
25C
Acidic
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0
25C
Basic
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Output
Output for CS/CI
Common Slope
Common Intercept
Separate Slopes,
Separate Intercepts (worst case)
Recap / Questions
• Modeling reflects exposure seen in
consumer product
• Uses any data available
• Can consider different scenarios
– ICH, CS/CI, alpha levels
– Varying time within each temperature
• Internal decision making tool