Summer 2012 Volume 16 Number 3 43

Peer reviewed: Stabilit y

INTRODUCTIONIn August 2002, United States Food and Drug

Administration announced a new initiative, Phar-maceutical Current Good Manufacturing Practices (cGMPs) for the 21st Century (1). This initiative, cou-pled with the publications of the International Con-ference on Harmonisation (ICH) Q8 Pharmaceutical Development, 2006, ICH Q9 Quality Risk Manage-ment, 2007, ICH Q10 Pharmaceutical Quality Sys-tems, 2007, ICH Q11 Concept Paper, 2011 (2 – 5), and the long-awaited FDA Guidance for Industry on Process Validation: General Principles and Practices, 2011 (6), represented a significant shift of regulatory requirements from the traditional “test to compli-ance” to the current “quality by design”. It ushers in a life cycle and risk-based approach to process and product development. ICH Q8 states “…quality can-

not be tested into products; quality should be built in by design” (2). The approach is most apparent in the new regulatory definition for process valida-tion: “…the collection and evaluation of data, from the process design through commercial production, which establishes scientific evidence that a process is capable of consistently delivering quality.” (6). As stability of a drug product is a quality attribute that could affect drug safety and efficacy, it plays an im-portant role in the new risk-based paradigm for pro-cess and product development, as well as for lifecycle management.

Stability testing is also a regulatory requirement. Currently there are several regulatory guidelines re-lated to stability testing of new drug and biological substances and products. FDA issued the first sta-bility guideline in 1984. More specific requirements on statistical design and analysis became available three years later (7). In an effort to harmonize stabil-ity testing in the European Union, Japan, and the United States, a series of ICH guidelines have been developed and published since 1993 (8 – 12). How-ever, these guidelines primarily focus on studies per-formed under real storage conditions, in real-time, but fall short on specifics concerning stability design and analysis at different stages of drug development. In 2002 a working group was set up by World Health Organization (WHO) to evaluate the issue, in the context of vaccine stability testing. The effort led to the publication of the WHO Guidelines on Stability Evaluation of Vaccines (13), which recommends a life cycle approach to stability evaluation. Although the guidelines were intended to provide general guid-ance for vaccine stability testing, many of the princi-

Stability studies play a critical role at every stage of a drug product life cycle. As the entire pharmaceutical industry is moving towards a risk-based paradigm for process and product development, full utilization of stability studies not only increases the likelihood of product quality assurance and regulatory compliance, but also minimizes the risk of untoward rejection of good product lots or acceptance of compromised lots. This paper discusses how novel statistical method-ologies such as Arrhenius modeling, simulation, and Bayesian analysis can be effectively used in stability testing to achieve both quality assurance and cost reduction objectives.

Ensure Product Quality and Regulatory Compliance through Novel Stability Design and AnalysisHarry Yang

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ples and applications are suitable for drug and other biological products as well. In the past several years, two stability workshops, one sponsored by Korean FDA and other by International Association for Bio-logicals (IABS), were held to prompt deeper under-standing of the WHO Guidelines and life cycle and risk-based philosophy for stability testing. Summa-ries and contributions of the workshops are included in a special issue of Biologicals (14).

Stability studies are conducted during develop-ment, licensure, and post-marketing phases for vari-ous purposes. Effective utilization of stability testing to aid process and product development starts from a clear understanding of these objectives throughout the life cycle of the product. During early develop-ment, stability studies are performed to understand degradation pathways of the product and estimate potency of clinical trial materials, whereas in late de-velopment, it is shelf-life and release potency of the product that becomes the primary focus of stability evaluations, in support of licensure and the prod-uct label insert. After the product is approved for marketing, stability studies serve multiple purposes, including 1) bridging stability of marketed product and clinically evaluated product to ensure relevance of shelf life and release limit; 2) updating shelf life and/or release limit, if needed, to warrant product quality through (a shortened or extended) dating period; 3) providing quality assurance of robustness of manufacturing process after process changes, and other changes such as site, scale, formulation, stor-age, shipping conditions, and delivery device; and 4) aiding in evaluation and removal of non-stability in-dicating tests. While stability testing can help manu-facturers achieve a broad range of objectives related to process and product development, stability stud-ies tend to be time-consuming and costly. As drug products, especially biologics, are liable to variations in raw materials and manufacturing process, are susceptible to environmental changes such as tem-perature and humidity, and often need to be pack-aged, stored, handled, and shipped at different tem-peratures, the stability testing program can become colossal. It is essential for the manufacturer to ex-plore alternative stability experimental designs and

analyses. This will not only ensure product quality and regulatory compliance but also minimize the risk of untoward rejection of good product lots or ac-ceptance of compromised lots. Through several case examples, this paper discusses how to achieve such a goal through novel applications of Arrhenius mod-eling, statistical simulation, and Bayesian analysis.

This paper assumes that the drug product is a vaccine that has a claimed shelf life of 20 months under normal storage temperature 5oC ± 3oC. This paper also concentrates on product potency as an in-dicator of stability. It is assumed that the following linear model is used for describing the relationship between the measured potency value y

i of a lot and

test time :

[Model 1]

where a and b (<0) are the intercept and degra-dation slope parameters, and are measurement errors which are assumed to be independently and identically distributed (iid) according to a normal distribution .

DESIGN SPACE OF STORAGE TEMPERATUREQuality by design starts with identification of crit-

ical quality attributes (CQAs), which are attributes of the product under development having significant impact on product safety and efficacy. CQAs evolve from targeted product profile, scientific understand-ing of mechanism of action of the molecule, and data from animal and human studies. After defining CQAs, it is critical to establish a design space for pro-cess parameters that enables the process to produce product of the desired CQAs. In ICH Q8 guideline, “design space” is defined as “The multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality” (2). It states further, “Working within the design space is not considered as a change. Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process. Design space is proposed by the ap-plicant and is subject to regulatory assessment and

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Ha r r y Yang

approval” (2). The intent of establishing the design space is to render quality manufacturing of the prod-uct without extensive regulatory oversight.

Although a design space is usually constructed for process parameters such as temperature, pH and feeding time in formulation development, the concept can be used in a broad sense to establish a design space for other parameters such as product storage temperature, which are not directly related to the manufacturing process. Per regulatory re-quirements, a drug product has to be kept under the storage conditions in the product label insert during production, storage, handling, transporta-tion and use to ensure its quality. However, excur-sions outside of the approved limits may occur, in particular, when the drug is shipped to regions with high temperatures. Should such deviations occur, the manufacturer is required to conduct an investigation to evaluate the impact of the excur-sion and file a biological product deviation report (BPDR) with the regulatory authority. Not only is this often a costly exercise but also it potentially would delay the release of the product; as regula-tory review and approval is often time-consuming. Establishment of a design space for the storage tem-perature beforehand enables the manufacturer to ensure product quality in the event of an excursion of the temperature outside of the approved limits but within the space, without the need of regula-tory filing.

For the vaccine discussed in this paper, histori-cal data and empirical knowledge of the product stability indicate that a lot, which was inadver-tently exposed to an exaggerated temperature for a certain time period, continues to be acceptable if its degradation rate, which measures how fast the product potency degrades (the absolute value of degradation slope b in Model 1) does not exceed 0.122 log

10 titer/month. Based on this knowledge,

a design space (DS) of temperature can be defined as the range of temperature at which the one-sided upper 95% confidence limit of degradation rate is bounded by 0.122 log

10 titer/month. This design

space is constructed in accordance with ICH Q8 definition of “design space” as it warrants that

change of the temperature within the space would not result in degradation rate exceeding the accept-able limit 0.122 log

10 titer/month with 95% confi-

dence. To determine the design space, one needs to establish the dependence of the degradation rate on temperature. This can be accomplished through the Arrhenius equation and accelerated stability testing (15). An accelerated stability test is a short-term stability study conducted under exaggerated (or stressed) conditions to increase the rate of chemi-cal or physical degradation of a drug substance or drug product. As the product degrades much more rapidly under the exaggerated conditions, the ac-celerated studies can be completed in a short time period. Data from the studies allows for estimation of kinetic parameters of the degradation rate mod-eled through the Arrhenius equation, which, in turn, can be used to predict the degradation rate at temperatures untested. Specifically let k

T denote the

degradation rate at temperature T in Kelvin (K = oC +273.15). According to the Arrhenius equation, k

T,

and T have the following relationship:

[Equation 1]

where R is the universal gas constant (8.314) and ΔH is activation energy. Taking the natural log of both sides of Model 2 linearizes the relationship:

[Equation 2]

with

If an estimate of kT is available at a selection of

temperatures outside of the approved limit, thus we have

[Model 2]

where is the measurement error in the estimate of following a normal distribution with mean 0 and variance By fitting Model 2 to the log-trans-formed observed degradation rates estimates

of the model parameters can be obtained. The estimated regression line

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[Equation 3]

can be used to predict degradation rates at tem-peratures outside the approved limits, allowing for construction of the Design Space for storage tem-perature.

To illustrate the method, four sets of stability data are generated at temperature T = 20oC, 30oC, 40oC, and 50oC, and listed in Table I. The four tem-peratures are outside of the normal range of storage temperature 5 oC ± 3 oC. The time points at which potency values are generated are months 0, 3, and 6, which are in line with the recommendation of ICH Q1A (R2) (10).

For each of the four sets of data, by fitting data in Table 1 to Model 1, we obtain an estimate of the degradation slope , which represents potency loss per month, at temperature T. The results are given in Table 2.

Note that Fitting data in Table II to Model 2 results in estimates 15.467, -5300.4 and

0.2337 for the model parameters , respectively. Based on the estimated regression line,

[Equation 4]

log degradation rates at any other temperatures can be predicted. An approximate one-sided upper 95% confidence limit of is calculated to be:

[Equation 5]

where is the 95th percentile of the t-dis-tribution with 2 degrees of freedom, Ti =20oC, 30oC, 40oC, and 50oC for i = 1, 2, 3, 4, respectively, and

Therefore the design

space is determined by

[Equation 6]

which is equivalent to

T ≤ 17.9°C [Equation 7]

Because the normal storage temperature is 5 oC ± 3 oC, the design space of temperature is determined to be 2 oC – 17.9 oC.

EVALUATION OF STABILITY DESIGNS US-ING SIMULATIONPer regulatory guidelines, the shelf life of a drug product should be supported by real-time stability studies on materials that are representative of the final commercially packaged product. ICH Q1E suggests that three lots be used with stability measure-ments taken at 0, 3, 6, 9, 12, 18, and 24 months as depicted in Table III, and that shelf life be estimated as the time point at

which the lower limit of the one-sided 95% confi-dence interval (CI) for the mean predicted value in-

TABLE I: Simulated potency values from four acceler-ated stability studiesTime Point Temperature

20 °C 30 °C 40 °C 50 °C

0 6.9, 6.8, 7.2

7.2, 7.1, 6.6

6.8, 7.2, 7.0

7.0, 6.9, 7.0

3 6.7, 6.6, 6.5

6.6, 6.9, 6.6

6.5, 6.4, 6.4

6.0, 5.7, 5.7

6 6.6, 6.9, 6.4

6.3, 6.6, 6.7

5.5, 5.5, 5.8

4.1, 4.6, 4.5

TABLE II: Estimated degradation slopes from linear model fittingTemperature (°C) Degradation

Slope b̂T

1/ Temperature (K–1)

Log Degradation rate ln(k̂

T)

20 -0.087 0.003411 -2.44185

30 -0.102 0.003299 -2.28278

40 - 0.232 0.003193 -1.46102

50 -0.432 0.003095 -0.83933

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Ha r r y Yang

tersects with the approved lower specification (11). Use of multiple lots in the study is to ensure general-izability of findings from the lots used in the current study to future lots.

Let be the least square estimators of in Model 1. The one-sided 95% lower

confidence limit for the mean potency value of y at time x, is given by

where is the 95th percentile of the t-distribution with n -2 degrees of freedom,

Let be the estimated shelf life based on the ICH-recommended method. Then it is a root of the fol-lowing equation with respect to x (16),

[Equation 8)

where is the lower specification limit of potency. Clearly the accuracy of the estimated shelf life is dependent on stability design which is characterized by the sample size n and the choices of time points

so is the precision of the estimate The accuracy measures the difference between the

estimated shelf life and the true shelf life of the product which is assumed to be 20 months, and pre-cision is the variability in the estimate If three replicates are to be tested at each time point, the total number of assays based on the full design in Table II is 3 x 3 x 7 =81. In practice, the study may incur a substantial cost. It is desirable to identify an alterna-tive stability design that requires fewer assays.

In general, reduced designs provide an effective way to balance efficiency and representativeness. It works to the best interest of the manufacturer as fewer assays help reduce overall cost of stability test-ing. However, because a lesser amount of data is col-lected, there is a risk that the estimates of stability parameters such as the degradation slope might be less accurate or precise, potentially causing an un-reliable estimate of shelf life. From both compliance and risk management standpoints, it is sensible for the manufacturer to evaluate the risk before adopt-ing a reduced design for determining product shelf life in support of licensure. This can be accomplished through statistical simulation, better known in the literature as Monte Carlo simulation.

Monte Carlo simulations were techniques first introduced by Stanislaw Ulam, an Austrian-born mathematician, along with computer pioneer John Von Neumann, to solve problems associated with random neutron diffusion in nuclear material to build the atomic bomb during World War II. How-ever, it was not until the 1980s, when fast-speed and low-cost computers were developed, did these com-puting-intensive methods start gaining widespread uses in scientific modeling and statistical inferences. In the statistical literature, Monte Carlo methods are often used to solve statistical problems (both point estimation and hypothesis testing) for which either a theoretical solution is too hard to derive or there is limited real-life data. Successful applications of Monte Carlo methods have relied on the efficiency of random number generators and estimation of probability distributions which are features offered by many commercially available software packages (e.g., SAS) (17). In the context of stability design evaluation, stability data sets under different designs can be repeatedly simulated based on a degrada-

Table III: Full stability design recommended in ICH Q1ETime 0 3 6 9 12 18 24

Lot 1 x* x x x x x x

Lot 2 x x x x x x x

Lot 3 x x x x x x x

* “x” = time point where potency value is measured.

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tion model such as Model 1, and input parameters that are usually estimated from devel-

opment data. For each round of simulation, shelf life can be estimated for each of the designs under evalu-ation. The repeated simulations generate large sets of shelf lives, making it possible to calculate accuracy and precision of the shelf life estimate based on each design, and assess the appropriateness of using re-duced designs for the stability study in support of product licensure.

Tables IV and V list two reduced designs of inter-est, one specified in ICH Q1E and the other similar to what is suggested in (18), assuming that four lots of product are available for stability testing.

We assume the lower potency specification limit is 6.5 log

10 titer/dose. Based on a release limit of 7.0 log

10

titer/dose, degradation rate of 0.025 log10 titer/month,

the true shelf life is (7.0 – 6.5)/0.025 = 20 months. As-suming that the lot to lot variability of 0.05 log

10 titer,

and assay variability of 0.01 log10 titer, 1000 stability

data are simulated, using Model 1 and the full and re-duced matrix designs in Tables III – V. The first simu-lated data set for each design is presented in Table VI.

For each design and each simulation, a regression analysis is conducted to estimate the shelf life of the

product. Let denote the estimated shelf life from the ith simulation, . The mean estimated shelf life, range, accuracy and precision are calcu-lated as follows:

[Equation 9]

The results are summarized in Table VII. Two ob-servations can be made from the Table: 1) The ac-curacy of the shelf life estimates based on the three designs are comparable; 2) The mean shelf life es-timates of three designs all underestimate the true shelf life of 20-months by approximately 1 month. This is expected as shelf life determined from each simulation using the ICH Q1E recommended regres-

Table IV: Reduced stability design with three lotsTime 0 3 6 9 12 18 24

Lot 1 x* x x x x

Lot 2 x x x x

Lot 3 x x x x x

* “x” = time point where potency value is measured.

Table V: Reduced stability design with four lotsTime 0 3 6 9 12 18 24

Lot 1 x* x x x x

Lot 2 x x x x

Lot 3 x x x x

Lot 4 x x x x

* “x” = time point where potency value is measured.

Table VI: Sample data sets simulated from Model 1 and three stability designsTime Point(Month)

ICH Q1E(Lots 1, 2, 3)

Reduced Design with 3 Lots(Lots 1, 2, 3)

Reduced Design with 4 Lots(Lots 1, 2, 3, 4)

0 6.97, 7.00, 7.06

6.97, 6.92, 7.05

6.98, 6.94, 7.11, 7.06

3 6.90, 6.92, 7.01

6.88, NG* , NG

6.91, NG, NG, NG

6 6.84, 6.84, 6.92

NG, 6.77, NG NG, 6.79, NG,NG

9 6.75,6.76,6.84 NG, NG, 6.82 NG, NG, 6.90,NG

12 6.66, 6.68, 6.76

6.68, 6.62, 6.74

6.68, 6.64, 6.79, 6.76

18 6.52, 6.56, 6.62

6.52, NG, 6.59 6.55, NG, NG, 6.61

24 6.37, 6.39, 6.47

6.37, 6.32, 6.43

6.39, 6.35, 6.51, 6.46

* NG = “Not generated” as per the design.

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Ha r r y Yang

sion method is an estimate of the lower 95% confi-dence bound of the true shelf life as opposed to the true shelf life itself (17). In terms of precision, the reduced design with four lots results in the most pre-cise shelf life estimate as evidenced by a narrower range of shelf life estimates (15.81 – 22.41) and a smaller precision (1.05). As design consists of a total of 51 assays, it has about 37% [=(81 – 51)/81] few-er tests than the ICH Q1E design. Therefore, it is a more economical stability study to conduct. Because it maintains about the same level of quality assur-ance to shelf life estimation, it is a good alternative design to adopt for the annual stability stu

QUALITY ASSURANCE THROGH COMBINED DATAProduct manufacturers are mandated by regula-tions to have an annual stability program in place. Each year one lot of product is randomly selected and put on stability study under the approved condi-tions. Data generated from this lot will be analyzed to assess product and manufacturing process con-sistency. As stability sample testing is an on-going process, the complete data set will not be available until the end of the study. To better manage risks associated with unforeseen causes, the manufacturer is interested in not only timely estimation of stabil-ity parameters such as degradation slope and shelf life, but also the predictive probability for the true

stability parameters of the lot to meet acceptance cri-teria. Although data from the current study can be analyzed based on Model 1 in a timely fashion to obtain estimates of the stability parameters, calcula-tion of the aforesaid predictive probability requires combining the prior knowledge of the stability pa-rameters with information obtained from the cur-rent stability testing. To put this in the right context, suppose that potency measurements of the lot placed on annual stability are taken at 0, 3, 6, 9, 12, 18, and 24 months. Upon the collection of data at month 9, a regression analysis is performed. It is noted that the estimated degradation slope is -0.027 log

10 titer/

month. This estimate alone would not give the man-ufacturer the assurance that the true degradation slope would be no worse than an acceptable limit, say, -0.025 log

10 titer/month, which corresponds to a

true shelf life of 20-month. Because this slope esti-mate was computed from only four data points, it is a very imprecise estimate of the slope that would be estimated if all seven-time points were available. On the other hand, the manufacturer does have knowl-edge about the degradation slope from stability stud-ies conducted during product development. How to combine the historical information with the current degradation slope estimate to approximate the prob-ability for the true degradation slope to become ac-ceptable is crucial.

A usual tool in statistics called Bayesian analysis can be used to resolve this issue. The method, first developed by Reverend Thomas Bayes, provides a general framework for making statistical inference based on newly collected experimental evidence and historical knowledge (19). In the context of the above annual stability evaluation, the new data consists of measured potency values up to nine months from the current lot, and stability parameter estimates such as slope which is -0,027 log

10 tier/month. His-

torical knowledge includes acceptable limit of -0.025 log

10 titer/month, and stability characteristics of the

product cumulated from product development, and past experience with commercial lots. The Bayes-ian analysis provides a formal way of calculating the probability for the degradation slope of the lot to be above the acceptable limit of -0.025 log

10 titer/

TABLE VII: Results of simulation to compare efficiency of ICH Q1E-suggested design and two reduced designsDesign Estimated

Mean Shelf Life (Month)

Range (Min – Max) (Month)

Accuracy (Month)

Precision (Month)

ICH Q1E 19.16 15.62 – 23.52

0.84 1.19

Reduced Design with three Lots

18.94 14.40-23.29

1.06 1.24

Reduced Design with four Lots

19.02 5.81 – 22.41

0.92 1.05

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month, conditional on the 9-month stability data or slope estimate. To carry out the calculation, we need to introduce some formal notations.

Let denote the potency data col-lected up to time point and is the estimate of degradation slope based on To es-timate the probability that the degradation slope is no worse than the acceptable limit conditional on

calculate

[Equation 10]

The cumulative stability data indicates that the degradation slope b of commercial lots has a nor-mal distribution Because also follows a normal distribution with mean b and variance

where with

(20), the posterior distribution of b

is given by (21)

[Equation 11]

Thus we have

[Equation 12]

where Φ is the cumulative probability function of the standard normal distribu-tion. At month 9 (m = 9), it is estimated that

Historical data pro-vides estimates of -0.01 and 0.012 for the prior mean and variance respectively, which implies that the product is a very stable product. The data also suggest assay variability Using these estimates, it is calculated that

[Equation 13]

Although the first 9 months of data seem to sug-gest that this lot of the product appears to degrade faster than expected, the slope estimate was impre-cise as it was computed from only four data points. By combining the current test results with the his-torical data it is predicted that the probability for the true degradation rate of the lot to be above the acceptable limit -0.025 is greater than 90%. This renders sufficient assurance to the quality of the product lot.

SUMMARYDrug product development has become more and more complex. Regardless how comprehensive the post process testing, including stability evaluation, might be, there is always risk that the product might fail to meet quality standards. To mitigate such risk, it is crucial for the manufacturer to use knowledge of the process and product, including potential risks and limitations, to guide the design of the process and product and implement quality control mea-sures throughout the development. Only in this way can quality be built into the product. Stability testing, as an integral part of drug product develop-ment, plays a very important role in process design, control and end product testing. If effectively uti-lized, it enables the manufacturer to build efficiency in the product development while ensuring com-pliance. The attainment of this goal requires novel applications of statistical methodologies. Through several case examples, this paper demonstrates use of Arrhenius modeling, statistical simulation and Bayesian analysis in stability design and analysis to ensure quality assurance and regulatory compli-ance, and also minimize costs associated with sta-bility testing.

ACKNOWLEGEMENTThe author thanks the reviewer for very helpful com-ments. The author also thanks Drs. Jianchun (Ja-son) Zhang and Lanju Zhang for their assistance in statistical simulation for the second case example, and Dr. Laura Richman for review of the manuscript.

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Ha r r y Yang

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ABOUT THE AUTHORHarry Yang, Ph.D., is a senior director at MedImmune, LLC, where he heads the Non-Clinical Biostatistics Group. He can be reached at YangH@MedImmune.