1. Analysis of Stability Data with Equivalence Testing for Comparing New and Historical Processes Under Various Treatment Conditions
Ben Ahlstrom, Rick Burdick, Laura Pack, Leslie Sidor
Amgen Colorado, Quality Engineering
May 19, 2009
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2. Agenda Purpose of comparability for stability data
Problems with the p-value approach
Equivalence approach and acceptance criteria methods
Example

3. Example Data 2 package types (Bottle, Blister)
Packaging Data
(Chow, Statistical Design and Analysis of Stability Studies, p. 116, Table 5.6)
2 package types (Bottle, Blister)
10 lots (5 for each package type)
6 time points (0 to 18 months)

4. Comparability Analysis for Stability Data
Purpose
Compare the rates of degradation
P-value Analysis Steps
Fit the regression lines (process*time interaction)
Calculate p-value for process*time
Compare p-value to =0.05
Draw conclusion about comparability
pass (comparable) if p-value > 0.05
fail (not-comparable if p-value < 0.05)
I.E.: Evaluate the slopes of the treatment conditions

5. P-value Analysis to Evaluate Comparability for Stability Data
Bottle vs. Blister:
Are the processes comparable?
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6. P-value Approach Hypotheses If p-value < 0.05, reject H0
H0: slopes are comparable
HA: slopes are not comparable
If p-value < 0.05, reject H0
If p-value >0.05, fail to reject H0
Does not imply they are comparable, but rather that there isn’t enough evidence to say the slopes are different
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7. P-value Analysis to Evaluate Comparability for Stability Data
Packaging: Bottle vs. Blister
Do we pass or fail the p-value test?
Pass: p=0.8453
We compare the slopes using p-values
(Pass if p-value > 0.05 and Fail if p-value < 0.05)

8. Problems with P-value Approach
Reporting a P-value only tells us something about statistical significance.
A statistically significant difference in slopes does not necessarily have any practical importance relative to patient safety or efficacy.
P-values are non-informative because they do not quantify the difference in slopes in a manner that allows scientific interpretation of practical importance.
A p-value approach provides a disincentive to collect more data and learn more about a process.
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9. Equivalence Testing Method
Fit the model with all historical and new process data (includes different storage conditions, orientations, SKU’s, container types)
Compute the difference in slopes for the desired comparison
Bottle vs. Blister
Compute the 95% one-sided confidence limits around the difference observed over the time frame of interest
If the confidence limits are enclosed by the equivalence acceptance criteria, conclude that the historical and new processes are comparable
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10. Statistical Model
Parameters i and βi are the overall regression parameters for the ith process
Random variables aj allow the intercepts to vary for each lot
is the time value for process i, lot j, and time k.
Model can be extended to more levels

11. Statistical Equivalence Acceptance Criteria (EAC)
Goal Post is the space of expected historical performance
Football = 95% one-sided CLs around difference between slopes over time frame of interest
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12. Methods to Calculate Equivalence Acceptance Criteria (EAC)
Equivalence Acceptance Criteria (EAC) provide a definition of practical importance
The scientific client has the responsibility to determine a definition of practical importance (based on science, safety, specification, reg. commit., etc.)
Statistical methods can help establish a starting point for these decisions
Three statistical methods include:
Method 1: Common cause variability
Method 2: Excursion from Product Specification
Method 3: Historic Variability of Slope Estimates
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13. 3 Statistical Approaches for Defining EAC
Method 1
Method 2
Method 3
EAC based on common cause variability of the historic process
EAC based on product specification
EAC based on historic variability of slope estimates
-EAC is expressed as average change in response per month
-Requires a specification
-Requires at least 3 different lots in historic data set
-EAC is expressed as change response per month

14. Comparability in Profile Data
Reference condition
Difference between intercepts t = 0 A
B-A
Total difference between conditions at time T (intercept and slope)
Difference in response averages attributed to the difference in slopes B – A = δ B
Quality attribute
New condition T
Time (months)
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15. EAC Method 1: Common Cause Variability
Criteria is based on historical performance at various conditions
Lot to Lot variability
Measurement variability
Multiplier aligned with other statistical limits used to separate random noise from a true signal
Goal Post is the space of expected historical performance
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16. EAC Method 1: Common Cause Variability
T = Expiry = 18 months
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17. Percent Label Claim, P-value approach vs. Equivalence Test
Slope Bottle
Slope Blister
0.8453 NA
Slope difference over 18 months
Goal Post +/
Result
PASS
Key Point
Slope estimates are the same for both approaches
Equivalence graph
0.2722
Difference in Slopes
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18. EAC Method 2: Product Specification
Maximum allowable difference in slopes where new and historic have < p% excursion rate at expiry
Typically p=0.01, 0.025, 0.05
Use historic data
Relates comparability to specification
Typically p=.01, .025, .05
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19. EAC Method 2: Product Specification
Spec (LSL) K
bHist
bNew
E (Expiry)
Mean of historical
at expiry
Response
Time (months)
Pth lower
percentile
centered at
historic mean
where P is
probability
of excursion
centered
at new mean
Acceptable difference in slopes is q = K/E.
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20. EAC Method 2: Product Specification
K is unknown, so replace term in brackets with lower one-sided (1-P)*100% individual confidence bound based on historical (prediction bound)
Assume Lower Spec Limit (LSL) = 95
Expiry = 18 months
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21. EAC Method 3: Historic Slope Variability
Use historical data for calculation
Historical dataset provides nH independent estimates of the common slope β
EAC based on 99.5th percentile of distribution of difference in slopes from same lot.
If observed slope difference is consistent with this variability, equivalence is demonstrated.
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22. EAC Method 3: Historic Slope Variability^ ^ ^
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23. EAC Method 3: Historic Slope Variability
θ3 is the 99.5th percentile of the distribution of
2.576 is the 99.5th percentile of the standard normal distribution
U is a 95% upper bound on the standard error for an estimate of β based on a single lot

24. Comparison of Equivalence Acceptance Criteria
Hard for a client to know what a difference in slopes of, say, 0.1 % looks like in a table
Once client sees graph, they can get a feel for what a difference in slope means
Can visualize what the possible range of regression lines could be to still claim equivalence

25. Comparison of Equivalence Acceptance Criteria
Based only on historical data
Graph is created before data for the new process is collected
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26. Results by Method
HA: Show δ is less than some amount deemed practically important
Equivalence is demonstrated by computing two one-sided tests (TOST)
If the 95% lower one-sided confidence bound on δ is greater than -θ and the 95% upper one-sided confidence bound is less than θ, then equivalence is demonstrated

27. P-value Approach vs. Equivalence Approach
Ho: slopes are comparable
HA: slopes are not comparable
P-value
Equivalence Approach
Ho: slopes are not comparable
HA: slopes are comparable
Equivalence acceptance criteria set a priori
Based on interval estimates of slope difference using mixed regression model with random lots
Statistical convention is to have research objective in HA
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28. Move to Equivalence Testing for Comparability
Summary
P-value approach to comparability has numerous issues
High p-values do NOT prove equivalence
High p-values only indicate that there is NOT enough evidence to conclude slopes are different
At times, leads to ad hoc analysis requests when p-value is small
P-values sensitive to sample size
Goal posts allow you to state equivalence
Industry is moving in the direction of equivalence tests
Can be extended to accelerated studies
Move to Equivalence Testing for Comparability
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29. References
Limenati, G. B., Ringo, M. C., Ye, F., Bergquist, M. L., and McSorley, E. O. (2005). Beyond the t-test: Statistical equivalence testing. Analytical Chemistry, June 2005, pages 1A-6A.
Chambers, D. , Kelly, G., Limentani, G., Lister, A., Lung, K. R., and Warner, E. (2005) Analytical method equivalency: An acceptable analytical practice. Pharmaceutical Technology, Sept 2005, pages
Richter, S. , and Richter, C. (2002). A method for determining equivalence in industrial applications. Quality Engineering, 14(3), pages
Park, D. J. and Burdick, R. K. (2004). Confidence Intervals on Total Variance in a Regression Model with an Unbalanced Onefold Nested Error Structure, Communications in Statistics, Theory and Methods, 33, No. 11, pages

30. Back up slides

31. Back up slides EAC Method 2 Equal Difference Assumption:
This assumption may not always hold
The p-value for the interaction between time, process, and temperature tests this assumption

32. Comparison of Equivalence Acceptance Criteria
Plot regression line for historical process
At time=0 the value is
Calculate
Plot 2 additional lines
Value at time=0 is
Values at time=T are
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