Assessing Shelf Life Using RealTime 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: realtime stability tests and accelerated stability
tests. In realtime 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.
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 physicalchemical 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.^{13} 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}
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 secondorder
reaction mechanisms.^{6}
In zeroorder reactions, degradation is independent of the
concentration of remaining intact molecules; in firstorder reactions,
degradation is proportional to that concentration.^{6,7}
Zero and firstorder reactions involve only one kind of molecule, and
can be described with linear or exponential relationships. Second and
higherorder 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 higherorder
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 realtime stability tests and accelerated stability tests. The realtime
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.
RealTime Stability Tests In realtime stability tests, a product is stored at recommended storage conditions and monitored for a period of time (t_{test}). Product will degrade below its specification, at some time, denoted t_{s}, and we must also assure that t_{s} is less than or equal to t_{test}. The estimated value of t_{s} 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 lottolot variation, an important source
of product variability.^{1,2} The true degradation pattern of a certain product, assuming that it degrades via a firstorder reaction, can be described
as follows:
<span class="articlearticlebody" />
The observed result (Y) of each lot has a random component φ associated with that lot, as well as a random experimental error,
ε.
<span class="articlearticlebody" />
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 σ_{φ} 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 t_{s}. The manufacturer determines the value of C. The estimated time that the product is stable is calculated as
<span class="articlearticlebody" />
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 lottolot
variability is large. More details on this issue are found in references 9 and 10.
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..
The estimated lottolot 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.
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 realtime testing must be done in parallel to confirm the
shelflife 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.
<span class="articlearticlebody" />
This relationship can be used in accelerated stability studies when the following conditions are met:
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 multifactor 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 firstorder 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
<span class="articlearticlebody" />
The true degradation pattern at storage temperature can be expressed as
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: realtime stability tests and accelerated stability
tests. In realtime 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.
Figure 1. A simulated set of stability results also showing the estimated degradation and 95% confidence limits. 
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 physicalchemical 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.^{13} 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}
Table 1. Estimates of the degradation model and Table 2. Estimates of degradation rates, days of stability and 95% confidence limits. 
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 secondorder
reaction mechanisms.^{6}
In zeroorder reactions, degradation is independent of the
concentration of remaining intact molecules; in firstorder reactions,
degradation is proportional to that concentration.^{6,7}
Zero and firstorder reactions involve only one kind of molecule, and
can be described with linear or exponential relationships. Second and
higherorder 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 higherorder
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 realtime stability tests and accelerated stability tests. The realtime
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.
RealTime Stability Tests In realtime stability tests, a product is stored at recommended storage conditions and monitored for a period of time (t_{test}). Product will degrade below its specification, at some time, denoted t_{s}, and we must also assure that t_{s} is less than or equal to t_{test}. The estimated value of t_{s} 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 lottolot variation, an important source
of product variability.^{1,2} The true degradation pattern of a certain product, assuming that it degrades via a firstorder reaction, can be described
as follows:

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

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 σ_{φ} 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 t_{s}. The manufacturer determines the value of C. The estimated time that the product is stable is calculated as

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 lottolot
variability is large. More details on this issue are found in references 9 and 10.
Figure 2. A set of simulated data showing degradation of product at four different temperatures. 
as it ages, but it is considered to be performing within the specification until it reaches 80% of its activity (C = 0..
The estimated lottolot 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.
Table 3. Predictions of parameters at 25°C based on the Arrhenius equation. 
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 realtime testing must be done in parallel to confirm the
shelflife 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.

This relationship can be used in accelerated stability studies when the following conditions are met:
 A zero or
firstorder 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}
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 multifactor 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 firstorder 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

The true degradation pattern at storage temperature can be expressed as