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
1
• 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?
2
• 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
3
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.
4
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%
5
Activation Energy (kcals/mol)
Temperature
°C
17.2
25.7
34.3
1.0
1.0
1.0
50
60
4.0
9.5
21.1
8.0
28.7
95.3
16.0
88.2
438.2
70
80
45.0
92.0
295.6
859.4
1983.4
8242.5
25
40
6
Activation Energy (kcals/mol)
Temperature
°C
17.2
25.7
34.3
25
40
50
60
70
80
1461.0
363.6
154.6
69.2
32.4
15.9
1461.0
182.9
50.9
15.3
4.9
1.7
1461.0
91.2
16.6
3.3
0.7
0.2
7
• 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
8
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
9
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
10
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
11
Notes on King, Kung, Fung “Statistical prediction of drug stability
based on non-linear parameter estimation” J. Pharm. Sci.
1984;73:657-662
•
•
•
•
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)
ken.waterman@freethinktech.com
2014
12
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, productspecific protocol accommodating both temperature and humidity effects
through a modified Arrhenius model.
The program makes a number of claims:
1. Reliable estimates for temperature and relative humidity effects on
degradation rates,
2. Accurate and precise shelf-life estimation,
3. 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.
13
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.