1. Discussion on four presentations on Study design and statistical modeling for accelerated stability testing
Regular long term stability – shelf life is determined by long term degradation stored under one temperature/humidity condition or with one switched condition
Typically modeling degradation using linear regression model
Occasionally using non-linear model
Shelf life determined by intersection of confidence band with specification limits
Prediction no more than 50% of the observation time

2. Accelerated stability testing –shelf life prediction based on short storage condition under various combinations of storage conditions such as temperature and humidity.
Provides more information about impact of the storage condition.
Shelf life prediction no more than 10 times of experimental length
Non-linear regression with logistic or Arrhenius model with log transformed data
Determine the confidence band?

3. FDA statisticians reviewed submissions with accelerated stability testing
Analytical similarity of biosimilar product
Pediatric product development
Post marketing change of a product
To determine the storage strategy in early development stage

4. Some design recommendations for ASAP studies (Tim Kramer)
Some design recommendations for ASAP studies (Tim Kramer)
Methodology for evaluating designs
“Optimum” designs for 3, 4 and 5 environments
Comparison with standard 5-run design
Some extensions
Restricting designs to a subset of parameter space
Errors in humidity and temperature in chambers
Nonlinear degradation
What times and temperatures should be used to optimally determine shelf life (at 25°C/60% RH)?
Although degradation rate parameters are of interest, the main goal is to get a valid estimate of the shelf-life.

5. Design assumptions
Degradation rate fits humidity-corrected Arrhenius equation
Degradation increases linearly with time
Brief consideration of time0.5 or time2 dependency
True shelf life is either 2, 4 or 8 years
Activation energy is either 17.2, 25.7 or 34.3 kcal/mol
Humidity coefficient (bRH) is 0.00, 0.04 or 0.08
Specification limit is either 0.5%, 1.0% or 2.0%
Pre-exponential factor adjusted to achieve shelf life
Measurement uncertainty is either 6 or 10% of degradation with minimum of 0.02%

6. Activation Energy (kcals/mol)
Temperature °C
17.2
25.7
34.3 25
1.0 40
4.0
8.0
16.0 50
9.5
28.7
88.2 60
21.1
95.3
438.2 70
45.0
295.6
1983.4 80
92.0
859.4
8242.5

7. Activation Energy (kcals/mol)
Temperature °C
17.2
25.7
34.3 25
1461.0 40
363.6
182.9
91.2 50
154.6
50.9
16.6 60
69.2
15.3
3.3 70
32.4
4.9
0.7 80
15.9
1.7
0.2

8. Designs to optimally determine shelf life incorporate environments with appreciable degradation
Low temperatures may lead to “no information” results
4-run designs generally incorporate anchoring of one temperature/humidity combination with 2 points and varying temperature and humidity with other two points

9. Raised interesting questions Constant degradation rate
John Strong: Experiences and challenges with isoconversional kinetic stability modeling of packaged amorphous solid dispersions
Using isoconversional kinetic approach and Moisture-Adjusted Arrhenius Equation to study degradation due to glass transaction temperature of pakaging.
The object is to design an experiment such that at each temperature & humidity condition, we know how long it takes to achieve some fractional degradation (i.e. 0.2%), typically the specification limit.
Then we can ignore “how” the impurity got to the level of failure for determination of kinetic parameters to be used in further modeling.
Raised interesting questions
Constant degradation rate
Small sample parameter estimation
Physical change of dosage form

10. Argue for isoconversion approach for accelerated stability study
Ken Waterman: A scientific and statistical analysis of accelerated aging for pharmaceuticals: Accuracy and precision of fitting methods
Argue for isoconversion approach for accelerated stability study
Discuss the uncertainty in predictions
Isoconversion methods
Arrhenius
Distributions (MC vs. extrema isoconversion)
Linear vs. non-linear
Conclusions

11. Conclusion:
Modeling drug product shelf-life from accelerated data more accurate using isoconversion
Isoconversion more accurate using points bracketing specification limit than using all points
With isoconversion, regression interval (not confidence interval) includes error of fit, but difficult to calculate with varying SD
Extrema method reasonably approximates RI for interpolation; more conservative for extrapolation
Linear fitting of Arrhenius equation preferred

12. ken.waterman@freethinktech.com 2014
Notes on King, Kung, Fung “Statistical prediction of drug stability based on non-linear parameter estimation” J. Pharm. Sci. 1984;73:
Used rates based on each time point independently
Changing rate constants not projected accurately for shelf-life
Gives greater precision by treating each point as equivalent, even when far from isoconversion (32 points at 4 T’s gives better error bars than just 4 isoconversion values: more precise, but more likely to be wrong)
Non-linear fitting to Arrhenius
Weights higher T more heavily (and where they had most degradation)
Made more sense with constant errors used for loss of potency
Non-linear fitting in general bigger, less symmetric error bars, more likely to be in error if mechanism shift with T
Used mean and SD for linear fitting, even when not normally distributed (i.e., not statistically valid method)
Do not recommend general use of KKF method (fine for ideal behavior, loss of potency)

13. Juan Chen: Comparison of shelf life estimates generated by ASAPPrimeTM with the King, Kung and Fung approach
The ASAPprimeTM computerized system is a commercial computer program that analyzes data from accelerated stability studies using a 2-week, product-specific protocol accommodating both temperature and humidity effects through a modified Arrhenius model.
The program makes a number of claims:
Reliable estimates for temperature and relative humidity effects on degradation rates,
Accurate and precise shelf-life estimation,
Enable rational control strategies to assure product stability.
These claims require careful statistical considerations of the modeling strategies proposed by the system. We evaluate these claims in relation to widely accepted statistical considerations.

14. Conclusion
Uncertainty measure for shelf life at accelerated conditions is derived from an “error propagation” calculation using either replicate error or a user defined quantity.
Statistical rationale for uncertainty limits is not clear.
Does not lead to a statistical confidence statement.
Monte Carlo simulation of isoconversion times to predict RT shelf life:
Underlying distribution of isoconversion times at accelerated conditions is not documented.
The precision of ASAP reported Arrhenius model parameter estimates cannot be validated statistically.
Model parameters estimates are influenced by choice of specification limits and user specified SD.
R2 reported for overall model fitting is unclear and lacks documentation.