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Assessing Shelf Life Using Real-Time and Accelerated Stability Tests


Biopharmaceutical products in storage change as they age, but they are considered to be stable as long as their characteristics
remain within the manufacturer's specifications. The number of days that the product remains stable at the recommended storage
conditions is referred to as the shelf life. The experimental protocols commonly used for data collection that serve as the
basis for estimation of shelf life are called stability tests.
Shelf life is commonly estimated using two types of stability testing: real-time stability tests and accelerated stability
tests. In real-time stability testing, a product is stored at recommended storage conditions and monitored until it fails
the specification. In accelerated stability tests, a product is stored at elevated stress conditions (such as temperature,
humidity, and pH). Degradation at the recommended storage conditions can be predicted using known relationships between the
acceleration factor and the degradation rate.
Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Chart_thumb
Figure 1. A simulated set of stability results also showing the estimated degradation and 95% confidence limits.
Temperature is the most common acceleration factor used for chemicals,
pharmaceuticals, and biological products because its relationship with
the degradation rate is characterized by the Arrhenius equation.
Several methods of predicting shelf life based on accelerated stability
testing are described in the article. Humidity and pH also have
acceleration effects but, because they are complex, they will not be
discussed in detail here. Also, details on statistical modeling and
estimation are outside the scope of the article, but we provide
references to computer routines.
Regulations and History
The assessment of shelf life has evolved from examining the data and
making an educated guess, through plotting, to the application of
rigorous physical-chemical laws and statistical techniques. Regulators
now insist that adequate stability testing be conducted to provide
evidence of the performance of a drug or a biopharmaceutical product at
different environmental conditions and to establish the recommended
storage conditions and shelf life.1-3 Recently, Tsong reviewed the latest approaches to statistical modeling of stability tests,4 and ICH has published some guidelines for advanced testing design and data analysis.5,6
Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Chart_thumb
Table 1. Estimates of the degradation model and Table 2. Estimates of degradation rates, days of stability and 95% confidence
limits.
Modeling has become easier due to availability of standard statistical software that can perform the calculations. However,
an understanding of the general principles of stability testing is necessary to apply these programs correctly and obtain
appropriate results. Thus, the purpose of this paper is to provide an outline of the basic approaches to stability testing,
as well as to create a foundation for advanced statistical modeling and shelf life prediction.
Stability and Degradation Since degradation is usually defined in terms of loss of activity or performance, a product is considered to be degrading
when any characteristic of interest (for example potency or performance) decreases. Degradation usually follows a specific
pattern depending on the kinetics of the chemical reaction. The degradation pattern can follow zero-, first-, and second-order
reaction mechanisms.6
In zero-order reactions, degradation is independent of the
concentration of remaining intact molecules; in first-order reactions,
degradation is proportional to that concentration.6,7
Zero- and first-order reactions involve only one kind of molecule, and
can be described with linear or exponential relationships. Second- and
higher-order reactions involve multiple interactions of two or more
kinds of molecules and are characteristic of most biological materials
that consist of large and complex molecular structures. Although it is
common to approximate these reactions with an exponential relationship,
sometimes their degradation pattern needs to be modeled more precisely,
and no shortcuts will suffice.
The degradation rate
depends on the activation energy for the chemical reaction and is
product specific. We don't always have to deal with higher-order
equations; in many cases, the observed responses of different orders of
reactions are indistinguishable for products that degrade slowly. The degradation rate depends on the conditions where the chemical reaction takes place. Products degrade faster when subjected
to acceleration factors such as temperature, humidity, pH, and radiation. Modeling of the degradation pattern and estimation
of the degradation rate are important for assessing shelf life. Experimental protocols used for data collection are called
stability tests. In practice, evaluators use both real-time stability tests and accelerated stability tests. The real-time
stability test is preferable to regulators. However, since it can take up to two years to complete, the accelerated tests
are often used as temporary measures to expedite drug introduction.
Real-Time Stability Tests In real-time stability tests, a product is stored at recommended storage conditions and monitored for a period of time (ttest). Product will degrade below its specification, at some time, denoted ts, and we must also assure that ts is less than or equal to ttest. The estimated value of ts can be obtained by modeling the degradation pattern. Good experimental design and practices are needed to minimize the risk
of biases and reduce the amount of random error during data collection. Testing should be performed at time intervals that
encompass the target shelf life and must be continued for a period after the product degrades below specification. It is also
required that at least three lots of material be used in stability testing to capture lot-to-lot variation, an important source
of product variability.1,2
The true degradation pattern of a certain product, assuming that it degrades via a first-order reaction, can be described
as follows:

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation1
<span class="article-articlebody" />

The observed result (Y) of each lot has a random component φ associated with that lot, as well as a random experimental error,
ε.

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation2
<span class="article-articlebody" />

Both α and δ represent the fixed parameters of the model that need to be estimated from the data, while φ and ε are assumed
to be normally distributed with mean = 0, and standard deviations of σφ and σ.ε respectively. Equation 2 is a nonlinear mixed model. Details on the estimation process are outside the scope of this paper.8,9
Let C represent a critical level where the essential performance characteristics of the product are within the specification.
A product is considered to be stable when Y ≥ C. Product is not stable when Y < C, while Y < C occurs at ts. The manufacturer determines the value of C. The estimated time that the product is stable is calculated as

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation3
<span class="article-articlebody" />

Here, a and d are the estimated values of the intercept and the degredation rate. The standard error of the estimated time
can be obtained from the Taylor series approximation method and is used to calculate confidence limits. The labeled shelf
life of the product is the lower confidence limit of the estimated time.8 Public safety is paramount, that is why we use the lower confidence limit. Lots should be modeled separately when lot-to-lot
variability is large. More details on this issue are found in references 9 and 10.
Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Chart_thumb
Figure 2. A set of simulated data showing degradation of product at four different temperatures.
We simulated data for three lots tested for a total period of 600 days (Table 1 and Figure 1). The product loses its activity
as it ages, but it is considered to be performing within the specification until it reaches 80% of its activity (C = 0.Cool.
The estimated lot-to-lot standard deviation is 0.000104, and the estimate of experimental error is 0.000262. Therefore, the
shelf life of the product was determined to be 498 days. This represents the lower 95% confidence limit corresponding to the
estimated time of 541 days.
Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Chart_thumb
Table 3. Predictions of parameters at 25°C based on the Arrhenius equation.
Accelerated Stability Tests
In accelerated stability testing, a product is stored at elevated
stress conditions. Degradation at recommended storage conditions could
be predicted based on the degradation at each stress condition and
known relationships between the acceleration factor and the degradation
rate. A product may be released based on accelerated stability data,
but the real-time testing must be done in parallel to confirm the
shelf-life prediction.1
Sometimes the amount of error of the predicted stability is so large
that the prediction itself is not useful. Design your experiments
carefully to reduce this error. It is recommended that several
production lots should be stored at various acceleration levels to
reduce prediction error. Increasing the number of levels is a good
strategy for reducing error.

Temperature is probably the most
common acceleration factor used for chemicals, pharmaceuticals, and
biological products since its relationship with the degradation rate is
well characterized by the Arrhenius equation. This equation describes a
relationship between temperature and the degradation rate as in
Equation 4.

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation4
<span class="article-articlebody" />

This relationship can be used in accelerated stability studies when the following conditions are met:


  • A zero- or
    first-order kinetics reaction takes place at each elevated temperature
    as well as at the recommended storage temperature.7
  • The same model is used to fit the degradation patterns at each temperature.7,8
These requirements do not fully guarantee that the Arrhenius equation can be used to predict the degradation rate at storage
temperature, but they are a good start. Do not compromise the analytical accuracy during the course of the study to distinguish
between the degradation rates at each temperature.
Select
temperature levels based on the nature of the product and the
recommended storage temperature. The selected temperatures should
stimulate relatively fast degradation and quick testing but not destroy
the fundamental characteristics of the product. It is not reasonable to
test at very high temperatures for a very short period of time, since
the mechanisms of degradation at high temperatures may be very
different than those at the recommended storage temperature. Choose the
adjacent levels appropriately so that degradation trends are larger
than experimental variability. Choosing levels depends on the nature of
the product and analytical accuracy, but other practical implications
may be considered. Testing should be performed at time intervals that
encompass the target stability at each elevated temperature. Acquire
some data below C so that the degradation trend can be determined.
Humidity and pH can be used along with temperature to accelerate degradation, but modeling of multi-factor degradation is
very complex. A model for parameter estimation and prediction of shelf life when temperature and pH are used as acceleration
factors is given by Some et al.11
Arrhenius Prediction
Assuming that the degradation pattern follows a first-order reaction as
described in Equation 2, the Arrhenius equation (Equation 4) can be
used to predict the degradation rate at recommended storage
temperature. First, an acceleration factor, λ, is calculated as the
ratio of the degradation rate at elevated temperature to the
degradation rate at storage temperature.9 This ratio, which can be worked out easily from Equation 4, can be expressed as

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation5
<span class="article-articlebody" />

The true degradation pattern at storage temperature can be expressed as

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Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation6



(Here, λ indicates this was evaluated from accelerated tests.) The
testing result (Y) will include random components representing
lot-to-lot variability and experimental error. Once the estimates of α
and δ are obtained, stability time is calculated in a similar fashion
as in real-time stability testing. Shelf life is the lower confidence
limit of the estimated time.
Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Chart_thumb
Nomenclature
An example.
Simulated data for three lots, each aged at four elevated temperatures
for 300 days, are shown in Table 2. The performance of each lot at each
time point is measured in three replicates. A critical level of C = 0.8
is the criterion. Data and trends are presented in Figure 2, with the
estimates of degradation rates and days given in Table 2. The estimated
degradation rate is observed to increase with temperature. The number
of days that product performs within the specifications (C = 0.Cool is
217 days when stored at 35°C. Stability time will drop down to 24.8
days when product is stored at 65°C. The estimated activation energy is
15.4 kcal/mol. Predictions at 25°C based on the Arrhenius equation are
presented in Table 3. The product will perform within specification for
an estimated 572 days. Using the lower limit, the recommended shelf
life is 561 days.
Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Chart_thumb
Unstable Weather Conditions and Shelf-Life
Bracket Method
Activation energy is usually estimated from the accelerated stability
data. However, when the activation energy is known, the degradation
rate at storage temperature may be predicted from data collected at
only one elevated temperature. This practice is sometimes preferred in
industry since it reduces the size and time of accelerated stability
tests. Experience indicates that some pharmaceutical analytes have
activation energy in the range of 10 to 20 kcal/mol, but it is unlikely
you will have precise information or be able to make assumptions about
the activation energy of a certain product.12
The bracket method is a straightforward application of the Arrhenius equation that can be used if the value of the activation
energy is known.12 Assuming that stability of a product at 50°C is 32 days, and it will be stored at 25°C, then, te = 32 days, Te = 273 + 50°C = 323K, and Ts = 273 + 25°C = 298K. We know that activation energy is Ea = 10 kcal/mol. Stability at recommended storage temperature is calculated with a modified version of Equation 5 as:

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation7


Calculated stability is highly dependent on the value of activation energy. A stability of 435 days results when Ea = 20 kcal/mol.
The bracket method should not be confused with bracketing, which is an experimental design that allows you to test a minimum
number of samples at the extremes of certain factors, such as strength, container size, and container fill.3,4,6 Bracketing assumes that the stability of any intermediate levels is represented by the stability of the extremes and testing
at those extremes is performed at all time points.4
The Q-Rule The Q-Rule states that the degradation rate decreases by a constant factor when temperature is lowered by certain degrees.
The value of Q is typically set at 2, 3, or 4. This factor is proportional to the temperature change as Qn, where n equals the temperature change in °C divided by 10°C. Since 10°C is the baseline temperature, the Q-Rule is sometimes
referred to as Q10.
To illustrate the application of the Q-Rule, let us assume that the stability of a product at 50°C is 32 days. The recommended
storage temperature is 25°C and n = (50 - 25)/10 = 2.5. Let us set an intermediate value of Q = 3. Thus, Qn = (3)2.5 = 15.6. The predicted shelf life is 32 days 3 15.6 = 500 days. This approach is more conservative when lower values of Q
are used.12 Both Q-Rule and the bracket methods are rough approximations of stability. They can be effectively used to plan elevated
temperature levels as well as the duration of testing in the accelerated stability testing protocol.
High-Order Kinetics Theoretically, the Arrhenius equation does not apply when more than one kind of molecule is involved in reactions. However,
if the degradation rate and temperature are linearly related, the prediction of shelf life can be approximated by the Arrhenius
equation. Statistics that test the appropriateness of this approximation are presented in literature.
Magari et al. used a polynomial model to fit the degradation of a reagent (HmX PAK) for the Coulter HmX Analyzer.13 The following degradation pattern was consistent at all elevated temperatures:

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation8


β0, β1, and β2 are the parameters of the second-degree polynomial and t is time. The degradation rate is a function of time, which is not
constant in this case.

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation9


Degradation at storage temperature can be predicted from the degradation at elevated temperatures as

Assessing Shelf Life Using Real-Time and Accelerated Stability Tests Equation10


The acceleration factor, λ, is based on the Arrhenius equation. Statistical tests indicated that the use of this equation
was appropriate in this case. Shelf-life predictions were also verified by real-time stability testing results.
Similar Products When most of the assumptions required to use the Arrhenius equation are not satisfied, comparisons to a product with a known
stability is performed to assess shelf life. This approach requires having a similar product with a known shelf life to be
used as a control. The new or test product is expected to demonstrate similar behavior to the control since they belong to
the same family and have the same kinetics of degradation. Side-by-side testing of the control and test products at different
elevated temperatures is then performed. It is necessary to assume that the same model can represent the degradation pattern
at each elevated and storage temperature.
If the degradation
patterns of the test and control samples at the same elevated
temperatures are not statistically different, it can be assumed that
they will degrade similarly at the storage temperature. The closer the
elevated temperatures are to the storage temperature, the more
confident we can be in making this statement. The experimental
protocols used are similar to the protocols used with the Arrhenius
equation. Degradation patterns of a family of products at certain
elevated temperatures can be modeled and used to check the behavior of
a new product that belongs to that family.
Data Analysis The complication that was alluded to with Equation 1 is that degradation models are usually nonlinear mixed models, where
lot-to-lot variability is the random component. Estimation of the parameters of the models is important for the accuracy of
shelf-life predictions. We recommend using the maximum likelihood (ML) approach to estimate these parameters.
Since no closed-form solutions for ML estimates exist, an iterative procedure is performed, starting with some initial values
for the parameters and updating them until differences between consecutive iterations are minimal and the estimates converge
to their final value. Initial values are usually chosen by experience. The closer these values are to the final values, the
faster the model will converge. We used PROC NLMIXED of SAS for data analysis.14
Values of the real-time stability model (Equation 2) converged
relatively quickly, while several initial values for the parameters of
the accelerated model (Equation 6) were tried before they converged.
Statistical theory and the applicability of ML estimation are common in
the literature, and many computer routines are available to facilitate
data analysis. However, experience with the modeling and estimation
processes is necessary, since any unexpected results must be
appropriately interpreted. It is quite easy to get useless numbers from
a computer run.
References (1) FDA. Guidelines for submitting documentations for the stability of human drugs and biologics. Rockville (MD); 1987.
(2) ICH. Stability testing for new drug substances and products. Q1A(R). Geneva; 1994.
(3) ICH. Stability testing for new drug substances and products. Q1A(R2). Geneva; 2003.
(4) Tsong Y. Recent issues in stability testing, J Biopharm Stat 2003; 13:vii-ix.
(5) ICH. Stability data evaluation. Q1E. Geneva; 2003.
(6) ICH. Bracketing and matrixing designs for stability testing of new drug substances and products. Q1D. Geneva; 2003.
(7) King SP, et al. Statistical prediction of drug stability based on nonlinear parameter estimation. J Pharm Sci 1984; 73:2332-2344.
(Cool Tydeman MS, Kirkwood TBL. Design and analysis of accelerated degradation tests for the stability of biological standards.
1. Properties of maximum likelihood estimators. J Biol Stand 1984; 12:195-206.
(9) Magari R.
Estimating degradation in real time and accelerated stability tests
with random lot-to-lot variation: a simulation study. J Pharm Sci 2002; 91:893-899.
(10) Tsong Y, et al. Shelf life determination based on equivalence assessment. J Biopharm Stat 2003; 13:431-449.
(11) Some I, et al. Stability parameter estimation at ambient temperature from studies at elevated temperatures. J Pharm Sci 2001; 90:1759-1766.
(12) Anderson G, Scott M. Determination of product shelf life and activation energy for five drugs of abuse. Clin Chem 1991; 37:398-429.

(13) Magari R, et al. Accelerated stability model for predicting shelf-life. J Clin Lab Anal 2002; 16: 221-226.
(14) SAS Institute. SAS/stat user's guide, vers. 8. Cary (NC); 2000. BPI
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