Guidance for Industry

Q1E Evaluation of

Stability Data

U.S. Department of Health and Human Services

Food and Drug Administration

Center for Drug Evaluation and Research (CDER)

Center for Biologics Evaluation and Research (CBER)

June 2004

ICH
Guidance for Industry

Q1E Evaluation of

Stability Data

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Office of Communication, Training, and

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 http://www.fda.gov/cber/guidelines.htm.

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U.S. Department of Health and Human Services

Food and Drug Administration

Center for Drug Evaluation and Research (CDER)

Center for Biologics Evaluation and Research (CBER)

June 2004

ICH
TABLE OF CONTENTS

I. INTRODUCTION (1.0)........................................................................................................ 1

II. EVALUATION OF STABILITY DATA (2.0) .................................................................. 2

A. General Principles (2.1).................................................................................................................2

B. Data Presentation (2.2) ..................................................................................................................3

C. Extrapolation (2.3) .........................................................................................................................4

D. Data Evaluation for Retest Period or Shelf Life Estimation for Drug Substances or Products

Intended for Room Temperature Storage (2.4)...........................................................................4

E. Data Evaluation for Retest Period or Shelf Life Estimation for Drug Substances or Products

Intended for Storage Below Room Temperature (2.5) ...............................................................6

F. General Statistical Approaches (2.6)............................................................................................8

Appendix A: Decision Tree for Data Evaluation for Retest Period or Shelf Life Estimation for

Drug Substances or Products (Excluding Frozen Products)....................................................10

Appendix B: Examples of Statistical Approaches to Stability Data Analysis................................11
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Guidance for Industry1

Q1E Evaluation of Stability Data

This guidance represents the Food and Drug Administration's (FDA's) current thinking on this topic. It

does not create or confer any rights for or on any person and does not operate to bind FDA or the public.

An alternative approach may be used if such approach satisfies the requirements of the applicable statutes

and regulations. If you want to discuss an alternative approach, contact the FDA staff responsible for

implementing this guidance. If you cannot identify the appropriate FDA staff, call the appropriate

number listed on the title page of this guidance.

I. INTRODUCTION (1.0)2

This guidance provides recommendations on how to use stability data generated in accordance

with the principles detailed in the ICH guidance Q1A(R2) Stability Testing of New Drug

Substances and Products (parent guidance) to propose a retest period or shelf life in a

registration application. This guidance describes when and how extrapolation can be considered

when proposing a retest period for a drug substance or a shelf life for a drug product that extends

beyond the period covered by available data from the stability study under the long-term storage

condition (long-term data).

FDA's guidance documents, including this guidance, do not establish legally enforceable

responsibilities. Instead, guidances describe the Agency's current thinking on a topic and should

be viewed only as recommendations, unless specific regulatory or statutory requirements are

cited. The use of the word should in Agency guidances means that something is suggested or

recommended, but not required.

The recommendations in the evaluation and statistical analysis of stability data provided in the

parent guidance are brief in nature and limited in scope. The parent guidance states that

regression analysis is an appropriate approach to analyzing quantitative stability data for retest

 

1 This guidance was developed within the Expert Working Group (Quality) of the International Conference on

Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) and has been

subject to consultation by the regulatory parties, in accordance with the ICH process. This document has been

endorsed by the ICH Steering Committee at Step 4 of the ICH process, February 2003. At Step 4 of the process, the

final draft is recommended for adoption to the regulatory bodies of the European Union, Japan, and the United

States.

2 Arabic numbers reflect the organizational breakdown in the document endorsed by the ICH Steering Committee at

Step 4 of the ICH process, February 2003.
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period or shelf life estimation and recommends that a statistical test for batch poolability be

performed using a level of significance of 0.25. However, the parent guidance includes few

details and does not cover situations where multiple factors are involved in a full- or reduceddesign study. This guidance expands the recommendations presented in the evaluation sections

of the parent guidance.

This guidance covers:

• The evaluation of stability data that should be submitted in registration applications for new

molecular entities and associated drug products.

• Recommendations on the establishment of retest periods and shelf lives for drug substances

and drug products intended for storage at or below room temperature.*

• Stability studies using single- or multi-factor designs and full or reduced designs.

*Note: The term room temperature refers to the general customary environment and should not

be inferred to be the storage statement for labeling.

ICH Q6A and Q6B should be consulted for recommendations on the setting and justification of

acceptance criteria, and ICH Q1D should be referenced for recommendations on the use of fullversus reduced-design studies.

II. EVALUATION OF STABILITY DATA (2.0)

A. General Principles (2.1)

The design and execution of formal stability studies should follow the principles outlined in the

parent guidance. The purpose of a stability study is to establish, based on testing a minimum of

three batches of the drug substance or product, a retest period or shelf life and label storage

instructions applicable to all future batches manufactured and packaged under similar

circumstances. The degree of variability of individual batches affects the confidence that a

future production batch will remain within acceptance criteria throughout its retest period or

shelf life.

Although normal manufacturing and analytical variations are to be expected, it is important that

the drug product be formulated with the intent to provide 100 percent of the labeled amount of

the drug substance at the time of batch release. If the assay values of the batches used to support

the registration application are higher than 100 percent of label claim at the time of batch release,

after taking into account manufacturing and analytical variations, the shelf life proposed in the

application can be overestimated. On the other hand, if the assay value of a batch is lower than

100 percent of label claim at the time of batch release, it might fall below the lower acceptance

criterion before the end of the proposed shelf life.

A systematic approach should be adopted in the presentation and evaluation of the stability

information. The stability information should include, as appropriate, results from the physical,

chemical, biological, and microbiological tests, including those related to particular attributes of

the dosage form (for example, dissolution rate for solid oral dosage forms). The adequacy of the
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mass balance should be assessed. Factors that can cause an apparent lack of mass balance should

be considered, including, for example, the mechanisms of degradation and the stabilityindicating capability and inherent variability of the analytical procedures.

The basic concepts of stability data evaluation are the same for single- versus multi-factor studies

and for full- versus reduced-design studies. Data from formal stability studies and, as

appropriate, supporting data should be evaluated to determine the critical quality attributes likely

to influence the quality and performance of the drug substance or product. Each attribute should

be assessed separately, and an overall assessment should be made of the findings for the purpose

of proposing a retest period or shelf life. The retest period or shelf life proposed should not

exceed that predicted for any single attribute.

The decision tree in Appendix A outlines a stepwise approach to stability data evaluation and

when and how much extrapolation can be considered for a proposed retest period or shelf life.

Appendix Bprovides (1) information on how to analyze long-term data for appropriate

quantitative test attributes from a study with a multi-factor, full, or reduced design, (2)

information on how to use regression analysis for retest period or shelf life estimation, and (3)

examples of statistical procedures to determine poolability of data from different batches or other

factors. Additional guidance can be found in the references listed; however, the examples and

references do not cover all applicable statistical approaches.

In general, certain quantitative chemical attributes (e.g., assay, degradation products,

preservative content) for a drug substance or product can be assumed to follow zero-order

kinetics during long-term storage (Carstensen 1977). Data for these attributes are therefore

amenable to the type of statistical analysis described in Appendix B, including linear regression

and poolability testing. Although the kinetics of other quantitative attributes (e.g., pH,

dissolution) is generally not known, the same statistical analysis can be applied, if appropriate.

Qualitative attributes and microbiological attributes are not amenable to this kind of statistical

analysis.

The recommendations on statistical approaches in this guidance are not intended to imply that

use of statistical evaluation is preferred when it can be justified to be unnecessary. However,

statistical analysis can be useful in supporting the extrapolation of retest periods or shelf lives in

certain situations and can be critical in verifying the proposed retest periods or shelf lives in

other cases.

B. Data Presentation (2.2)

Data for all attributes should be presented in an appropriate format (e.g., tabular, graphical,

narrative) and an evaluation of such data should be included in the application. The values of

quantitative attributes at all time points should be reported as measured (e.g., assay as percent of

label claim). If a statistical analysis is performed, the procedure used and the assumptions

underlying the model should be stated and justified. A tabulated summary of the outcome of

statistical analysis and/or graphical presentation of the long-term data should be included.
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C. Extrapolation (2.3)

Extrapolation is the practice of using a known data set to infer information about future data.

Extrapolation to extend the retest period or shelf life beyond the period covered by long-term

data can be proposed in the application, particularly if no significant change is observed at the

accelerated condition. Whether extrapolation of stability data is appropriate depends on the

extent of knowledge about the change pattern, the goodness of fit of any mathematical model,

and the existence of relevant supporting data. Any extrapolation should be performed in such a

way that the extended retest period or shelf life will be valid for a future batch released with test

results close to the release acceptance criteria.

An extrapolation of stability data assumes that the same change pattern will continue to apply

beyond the period covered by long-term data. The correctness of the assumed change pattern is

critical when extrapolation is considered. When estimating a regression line or curve to fit the

long-term data, the data themselves provide a check on the correctness of the assumed change

pattern, and statistical methods can be applied to test the goodness of fit of the data to the

assumed line or curve. No such internal check is possible beyond the period covered by longterm data. Thus, a retest period or shelf life granted on the basis of extrapolation should always

be verified by additional long-term stability data as soon as these data become available. Care

should be taken to include in the protocol for commitment batches a time point that corresponds

to the end of the extrapolated retest period or shelf life.

D. Data Evaluation for Retest Period or Shelf Life Estimation for Drug

Substances or Products Intended for Room Temperature Storage (2.4)

A systematic evaluation of the data from formal stability studies should be performed as

illustrated in this section. Stability data for each attribute should be assessed sequentially. For

drug substances or products intended for storage at room temperature, the assessment should

begin with any significant change at the accelerated condition and, if appropriate, at the

intermediate condition, and progress through the trends and variability of the long-term data.

The circumstances are delineated under which extrapolation of retest period or shelf life beyond

the period covered by long-term data can be appropriate. A decision tree is provided in

Appendix A as an aid.

1. No significant change at accelerated condition (2.4.1)

Where no significant change occurs at the accelerated condition, the retest period or shelf life

would depend on the nature of the long-term and accelerated data.

a. Long-term and accelerated data showing little or no change over time and

little or no variability (2.4.1.1)

Where the long-term data and accelerated data for an attribute show little or no change over time

and little or no variability, it might be apparent that the drug substance or product will remain

well within the acceptance criteria for that attribute during the proposed retest period or shelf

life. In these circumstances, a statistical analysis is normally considered unnecessary but
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justification for the omission should be provided. Justification can include a discussion of the

change pattern or lack of change, relevance of the accelerated data, mass balance, and/or other

supporting data as described in the parent guidance. Extrapolation of the retest period or shelf

life beyond the period covered by long-term data can be proposed. The proposed retest period or

shelf life can be up to twice as long as, but should not be more than 12 months beyond, the

period covered by long-term data.

b. Long-term or accelerated data showing change over time and/or variability

(2.4.1.2)

If the long-term or accelerated data for an attribute show change over time and/or variability

within a factor or among factors, statistical analysis of the long-term data can be useful in

establishing a retest period or shelf life. Where there are differences in stability observed among

batches or among other factors (e.g., strength, container size, and/or fill) or factor combinations

(e.g., strength-by-container size and/or fill) that preclude the combining of data, the proposed

retest period or shelf life should not exceed the shortest period supported by any batch, other

factor, or factor combination. Alternatively, where the differences are readily attributed to a

particular factor (e.g., strength), different shelf lives can be assigned to different levels within the

factor (e.g., different strengths). A discussion should be provided to address the cause for the

differences and the overall significance of such differences on the product. Extrapolation beyond

the period covered by long-term data can be proposed; however, the extent of extrapolation

would depend on whether long-term data for the attribute are amenable to statistical analysis.

• Data not amenable to statistical analysis

Where long-term data are not amenable to statistical analysis, but relevant supporting data are

provided, the proposed retest period or shelf life can be up to one-and-a-half times as long as, but

should not be more than 6 months beyond, the period covered by long-term data. Relevant

supporting data include satisfactory long-term data from development batches that are (1) made

with a closely related formulation to, (2) manufactured on a smaller scale than, or (3) packaged

in a container closure system similar to, that of the primary stability batches.

• Data amenable to statistical analysis

If long-term data are amenable to statistical analysis but no analysis is performed, the extent of

extrapolation should be the same as when data are not amenable to statistical analysis. However,

if a statistical analysis is performed, it can be appropriate to propose a retest period or shelf life

of up to twice as long as, but not more than 12 months beyond, the period covered by long-term

data, when the proposal is backed by the result of the analysis and relevant supporting data.

2. Significant change at accelerated condition (2.4.2)

Where significant change* occurs at the accelerated condition, the retest period or shelf life will

depend on the outcome of stability testing at the intermediate condition, as well as at the longterm condition.
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*Note: The following physical changes can be expected to occur at the accelerated condition

and would not be considered significant change that calls for intermediate testing if there is no

other significant change:

• Softening of a suppository that is designed to melt at 37oC, if the melting point is clearly

demonstrated.

• Failure to meet acceptance criteria for dissolution for 12 units of a gelatin capsule or gelcoated tablet if the failure can be unequivocally attributed to cross-linking.

However, if phase separation of a semi-solid dosage form occurs at the accelerated condition,

testing at the intermediate condition should be performed. Potential interaction effects should

also be considered in establishing that there is no other significant change.

a. No significant change at intermediate condition (2.4.2.1)

If there is no significant change at the intermediate condition, extrapolation beyond the period

covered by long-term data can be proposed; however, the extent of extrapolation would depend

on whether long-term data for the attribute are amenable to statistical analysis.

• Data not amenable to statistical analysis

When the long-term data for an attribute are not amenable to statistical analysis, the proposed

retest period or shelf life can be up to 3 months beyond the period covered by long-term data, if

backed by relevant supporting data.

• Data amenable to statistical analysis

When the long-term data for an attribute are amenable to statistical analysis but no analysis is

performed, the extent of extrapolation should be the same as when data are not amenable to

statistical analysis. However, if a statistical analysis is performed, the proposed retest period or

shelf life can be up to one-and-half times as long as, but should not be more than 6 months

beyond, the period covered by long-term data, when backed by statistical analysis and relevant

supporting data.

b. Significant change at intermediate condition (2.4.2.2)

Where significant change occurs at the intermediate condition, the proposed retest period or shelf

life should not exceed the period covered by long-term data. In addition, a retest period or shelf

life shorter than the period covered by long-term data can be appropriate.

E. Data Evaluation for Retest Period or Shelf Life Estimation for Drug

Substances or Products Intended for Storage Below Room Temperature (2.5)
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1. Drug substances or products intended for storage in a refrigerator (2.5.1)

Data from drug substances or products intended to be stored in a refrigerator should be assessed

according to the same principles as described in section II.D for drug substances or products

intended for room temperature storage, except where explicitly noted in the section below. The

decision tree in Appendix A can be used as an aid.

a. No significant change at accelerated condition (2.5.1.1)

Where no significant change occurs at the accelerated condition, extrapolation of retest period or

shelf life beyond the period covered by long-term data can be proposed based on the principles

outlined in section II.D.1, except that the extent of extrapolation should be more limited.

If the long-term and accelerated data show little change over time and little variability, the

proposed retest period or shelf life can be up to one-and-a-half times as long as, but should not

be more than 6 months beyond, the period covered by long-term data normally without the

support of statistical analysis.

Where the long-term or accelerated data show change over time and/or variability, the proposed

retest period or shelf life can be up to 3 months beyond the period covered by long-term data if

(1) the long-term data are amenable to statistical analysis but a statistical analysis is not

performed, or (2) the long-term data are not amenable to statistical analysis but relevant

supporting data are provided.

Where the long-term or accelerated data show change over time and/or variability, the proposed

retest period or shelf life can be up to one-and-a-half times as long as, but should not be more

than 6 months beyond, the period covered by long-term data if (1) the long-term data are

amenable to statistical analysis and a statistical analysis is performed, and (2) the proposal is

backed by the result of the analysis and relevant supporting data.

b. Significant change at accelerated condition (2.5.1.2)

If significant change occurs between 3 and 6 months’ testing at the accelerated storage condition,

the proposed retest period or shelf life should be based on the long-term data. Extrapolation is

not considered appropriate. In addition, a retest period or shelf life shorter than the period

covered by long-term data could be appropriate. If the long-term data show variability,

verification of the proposed retest period or shelf life by statistical analysis can be appropriate.

If significant change occurs within the first 3 months’ testing at the accelerated storage

condition, the proposed retest period or shelf life should be based on long-term data.

Extrapolation is not considered appropriate. A retest period or shelf life shorter than the period

covered by long-term data could be appropriate. If the long-term data show variability,

verification of the proposed retest period or shelf life by statistical analysis can be appropriate.

In addition, a discussion should be provided to address the effect of short-term excursions

outside the label storage condition (e.g., during shipping or handling). This discussion can be
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supported, if appropriate, by further testing on a single batch of the drug substance or product at

the accelerated condition for a period shorter than 3 months.

2. Drug substances or products intended for storage in a freezer (2.5.2)

For drug substances or products intended for storage in a freezer, the retest period or shelf life

should be based on long-term data. In the absence of an accelerated storage condition for drug

substances or products intended to be stored in a freezer, testing on a single batch at an elevated

temperature (e.g., 5°C ± 3°C or 25°C ± 2°C) for an appropriate time period should be conducted

to address the effect of short-term excursions outside the proposed label storage condition (e.g.,

during shipping or handling).

3. Drug substances or products intended for storage below -20°C (2.5.3)

For drug substances or products intended for storage below -20°C, the retest period or shelf life

should be based on long-term data and should be assessed on a case-by-case basis.

F. General Statistical Approaches (2.6)

Where applicable, an appropriate statistical method should be employed to analyze the long-term

primary stability data in an original application. The purpose of this analysis is to establish, with

a high degree of confidence, a retest period or shelf life during which a quantitative attribute will

remain within acceptance criteria for all future batches manufactured, packaged, and stored

under similar circumstances.

In cases where a statistical analysis was employed to evaluate long-term data due to a change

over time and/or variability, the same statistical method should also be used to analyze data from

commitment batches to verify or extend the originally approved retest period or shelf life.

Regression analysis is considered an appropriate approach to evaluating the stability data for a

quantitative attribute and establishing a retest period or shelf life. The nature of the relationship

between an attribute and time will determine whether data should be transformed for linear

regression analysis. The relationship can be represented by a linear or nonlinear function on an

arithmetic or logarithmic scale. In some cases, a nonlinear regression can better reflect the true

relationship.

An appropriate approach to retest period or shelf life estimation is to analyze a quantitative

attribute (e.g., assay, degradation products) by determining the earliest time at which the 95

percent confidence limit for the mean intersects the proposed acceptance criterion.

For an attribute known to decrease with time, the lower one-sided 95 percent confidence limit

should be compared to the acceptance criterion. For an attribute known to increase with time,

the upper one-sided 95 percent confidence limit should be compared to the acceptance criterion.

For an attribute that can either increase or decrease, or whose direction of change is not known,

two-sided 95 percent confidence limits should be calculated and compared to the upper and

lower acceptance criteria.
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The statistical method used for data analysis should take into account the stability study design to

provide a valid statistical inference for the estimated retest period or shelf life. The approach

described above can be used to estimate the retest period or shelf life for a single batch or for

multiple batches when the data are combined after an appropriate statistical test. Examples of

statistical approaches to the analysis of stability data from single or multi-factor, full- or reduceddesign studies are included in Appendix B. References to current literature sources can be

found in Appendix B.6.

APPENDICES (3)
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Appendix A: Decision Tree for Data Evaluation for Retest Period or Shelf Life

Estimation for Drug Substances or Products (Excluding Frozen Products)

Tabulate and/or plot

stability data on all

attributes at all storage

conditions and evaluate

each attribute separately

Intended

to be stored in a

refrigerator?

No No

Yes to both

Y= up to 2X, but not

exceeding X + 12 months;

 or if refrigerated,

Y = up to 1.5X, but not

exceeding X + 6 months

Significant

change

at intermediate

condition?

No to (1)

or (2)

No extrapolation; shorter

retest period or shelf life

can be appropriate;

statistical analysis if longterm data show variability

If backed by statistical

analysis and relevant

supporting data: Y = up to

2X, but not exceeding X +

12 months; or if refrigerated,

Y = up to 1.5X, but not

exceeding X + 6 months

(1) Long- term

data amenable to

statistical analysis and

(2) statistical analysis

performed?

Yes

No to (1) or

(2) or both

If backed by statistical

analysis and relevant

supporting data: Y = up

to 1.5X, but not

exceeding X + 6 months

(1) Long- term

data amenable to

statistical analysis and

(2) statistical analysis

performed?

Yes to both

Statistical analysis

is normally

unnecessary

Yes

Long- term

data show: (1) little or

no change over time

and (2) little or no

variability?

Accelerated

data show: (1) little or

no change over time

and (2) little or no

variability?

No to (1)

or (2)

Yes to both

If backed by relevant

supporting data: Y = up

to 1.5X, but not

exceeding X + 6 months;

or if refrigerated, Y = up

to X + 3 months

If backed by relevant

supporting data:

Y = up to X + 3 months

No to (1) or

(2) or both

Yes to both

Significant

change at

accelerated

condition within

6 months?

No

Significant

change at

accelerated

condition within

3 months?

No extrapolation; shorter

retest period or shelf life and

data covering excursions

can be appropriate;

statistical analysis if longterm data show variability

Y = Proposed retest period or shelf life

X = Period covered by long-term data

No

Yes

Yes
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Appendix B: Examples of Statistical Approaches to Stability Data Analysis

Linear regression, poolability tests, and statistical modeling, described below, are examples of

statistical methods and procedures that can be used in the analysis of stability data that are

amenable to statistical analysis for a quantitative attribute for which there is a proposed

acceptance criterion.

B.1 Data Analysis for a Single Batch

In general, the relationship between certain quantitative attributes and time is assumed to be

linear(Carstensen 1977). Figure 1 (page 18) shows the regression line for assay of a drug

product with upper and lower acceptance criteria of 105 percent and 95 percent of label claim,

respectively, with 12 months of long-term data and a proposed shelf life of 24 months. In this

example, two-sided 95 percent confidence limits for the mean are applied because it is not

known ahead of time whether the assay would increase or decrease with time (e.g., in the case of

an aqueous-based product packaged in a semi-permeable container). The lower confidence limit

intersects the lower acceptance criterion at 30 months, while the upper confidence limit does not

intersect with the upper acceptance criterion until later. Therefore, the proposed shelf life of 24

months can be supported by the statistical analysis of the assay, provided the recommendations

in sections II.D and II.E are followed.

When data for an attribute with only an upper or a lower acceptance criterion are analyzed, the

corresponding one-sided 95 percent confidence limit for the mean is recommended. Figure 2

(page 18) shows the regression line for a degradation product in a drug product with 12 months

of long-term data and a proposed shelf life of 24 months, where the acceptance criterion is not

more than 1.4 percent. The upper one-sided 95 percent confidence limit for the mean intersects

the acceptance criterion at 31 months. Therefore, the proposed shelf life of 24 months can be

supported by statistical analysis of the degradation product data, provided the recommendations

in sections II.D and II.E are followed.

If the above approach is used, the mean value of the quantitative attribute (e.g., assay,

degradation products) can be expected to remain within the acceptance criteria through the end

of the retest period or shelf life at a confidence level of 95 percent.

The approach described above can be used to estimate the retest period or shelf life for a single

batch, individual batches, or multiple batches when combined after appropriate statistical tests

described in Appendix sections B.2 through B.5.

B.2 Data Analysis for One-Factor, Full-Design Studies

For a drug substance or for a drug product available in a single strength and a single container

size and/or fill, the retest period or shelf life is generally estimated based on the stability data

from a minimum of three batches. When analyzing data from such one-factor, batch-only, fulldesign studies, two statistical approaches can be considered.
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• The objective of the first approach is to determine whether the data from all batches support

the proposed retest period or shelf life.

• The objective of the second approach, testing for poolability, is to determine whether the data

from different batches can be combined for an overall estimate of a single retest period or

shelf life.

B.2.1 Evaluating whether all batches support the proposed retest period or shelf life

The objective of this approach is to evaluate whether the estimated retest periods or shelf lives

from all batches are longer than the one proposed. Retest periods or shelf lives for individual

batches should first be estimated using the procedure described in Appendix section B.1 with

individual intercepts, individual slopes, and the pooled mean square error calculated from all

batches. If each batch has an estimated retest period or shelf life longer than that proposed, the

proposed retest period or shelf life will generally be considered appropriate, as long as the

guidance for extrapolation in sections II.D and II.E is followed. There is generally no need to

perform poolability tests or identify the most reduced model. If, however, one or more of the

estimated retest periods or shelf lives are shorter than that proposed, poolability tests can be

performed to determine whether the batches can be combined to estimate a longer retest period

or shelf life.

Alternatively, the above approach can be taken during the pooling process described in Appendix

section B.2.2. If the regression lines for the batches are found to have a common slope and the

estimated retest periods or shelf lives based on the common slope and individual intercepts are

all longer than the proposed retest period or shelf life, there is generally no need to continue to

test the intercepts for poolability.

B.2.2 Testing for poolability of batches

B.2.2.1 Analysis of covariance

Before pooling the data from several batches to estimate a retest period or shelf life, a

preliminary statistical test should be performed to determine whether the regression lines from

different batches have a common slope and a common time-zero intercept. Analysis of

covariance (ANCOVA) can be employed, where time is considered the covariate, to test the

differences in slopes and intercepts of the regression lines among batches. Each of these tests

should be conducted using a significance level of 0.25 to compensate for the expected low power

of the design due to the relatively limited sample size in a typical formal stability study.

If the test rejects the hypothesis of equality of slopes (i.e., if there is a significant difference in

slopes among batches), it is not considered appropriate to combine the data from all batches.

The retest periods or shelf lives for individual batches in the stability study can be estimated by

applying the approach described in Appendix section B.1 using individual intercepts and

individual slopes and the pooled mean square error calculated from all batches. The shortest

estimate among the batches should be chosen as the retest period or shelf life for all batches.
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If the test rejects the hypothesis of equality of intercepts but fails to reject that the slopes are

equal (i.e., if there is a significant difference in intercepts but no significant difference in slopes

among the batches), the data can be combined for the purpose of estimating the common slope.

The retest periods or shelf lives for individual batches in the stability study should be estimated

by applying the approach described in Appendix section B.1, using the common slope and

individual intercepts. The shortest estimate among the batches should be chosen as the retest

period or shelf life for all batches.

If the tests for equality of slopes and equality of intercepts do not result in rejection at a level of

significance of 0.25 (i.e., if there is no significant difference in slope and intercepts among the

batches), the data from all batches can be combined. A single retest period or shelf life can be

estimated from the combined data by using the approach described in Appendix section B.1 and

applied to all batches. The estimated retest period or shelf life from the combined data is usually

longer than that from individual batches because the width of the confidence limit(s) for the

mean will become narrower as the amount of data increases when batches are combined.

The pooling tests described above should be performed in a proper order such that the slope

terms are tested before the intercept terms. The most reduced model (i.e., individual slopes,

common slope with individual intercepts, or common slope with common intercept, as

appropriate) can be selected for retest period or shelf life estimation.

B.2.2.2 Other methods

Statistical procedures(Ruberg and Stegeman 1991; Ruberg and Hsu 1992; Shao and Chow 1994;

Murphy and Weisman 1990; Yoshioka et al. 1997) other than those described above can be used

in retest period or shelf life estimation. For example, if it is possible to decide in advance the

acceptable difference in slope or in mean retest period or shelf life among batches, an appropriate

procedure for assessing the equivalence in slope or in mean retest period or shelf life can be used

to determine the data poolability. However, such a procedure should be prospectively defined,

evaluated, and justified and, where appropriate, discussed with the regulatory authority. A

simulation study can be useful, if applicable, to demonstrate that the statistical properties of the

alternative procedure selected are appropriate (Chen et al. 1997).

B.3 Data Analysis for Multi-Factor, Full-Design Studies

The stability of the drug product could differ to a certain degree among different factor

combinations in a multi-factor, full-design study. Two approaches can be considered when

analyzing such data.

• The objective of the first approach is to determine whether the data from all factor

combinations support the proposed shelf life.

• The objective of the second approach, testing for poolability, is to determine whether the data

from different factor combinations can be combined for an overall estimate of a single shelf

life.
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B.3.1 Evaluating whether all factor combinations support the proposed shelf life

The objective of this approach is to evaluate whether the estimated shelf lives from all factor

combinations are longer than the one proposed. A statistical model that includes all appropriate

factors and factor combinations should be constructed as described in Appendix section

B.3.2.2.1, and the shelf life should be estimated for each level of each factor and factor

combination.

If all shelf lives estimated by the original model are longer than the proposed shelf life, further

model building is considered unnecessary and the proposed shelf life will generally be

appropriate as long as the guidance in sections II.D and II.E is followed. If one or more of the

estimated shelf lives fall short of the proposed shelf life, model building as described in

Appendix section B.3.2.2.1 can be employed. However, it is considered unnecessary to identify

the final model before evaluating whether the data support the proposed shelf life. Shelf lives

can be estimated at each stage of the model building process, and if all shelf lives at any stage are

longer than the one proposed, further attempts to reduce the model are considered unnecessary.

This approach can simplify the data analysis of a complicated multi-factor stability study

compared to the data analysis described in Appendix section B.3.2.2.1.

B.3.2 Testing for poolability

The stability data from different combinations of factors should not be combined unless

supported by statistical tests for poolability.

B.3.2.1 Testing for poolability of batch factor only

If each factor combination is considered separately, the stability data can be tested for poolability

of batches only, and the shelf life for each non-batch factor combination can be estimated

separately by applying the procedure described in Appendix section B.2. For example, for a

drug product available in two strengths and four container sizes, eight sets of data from the 2x4

strength-size combinations can be analyzed and eight separate shelf lives should be estimated

accordingly. If a single shelf life is desired, the shortest estimated shelf life among all factor

combinations should become the shelf life for the product. However, this approach does not take

advantage of the available data from all factor combinations, thus generally resulting in shorter

shelf lives than does the approach in Appendix section B.3.2.2.

B.3.2.2 Testing for poolability of all factors and factor combinations

If the stability data are tested for poolability of all factors and factor combinations and the results

show that the data can be combined, a single shelf life longer than that estimated based on

individual factor combinations is generally obtainable. The shelf life is longer because the width

of the confidence limit(s) for the mean will become narrower as the amount of data increases

when different factors, such as batches, strengths, container sizes, and/or fills, are combined.
Contains Nonbinding Recommendations

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B.3.2.2.1 Analysis of covariance

Analysis of covariance can be employed to test the difference in slopes and intercepts of the

regression lines among factors and factor combinations (Chen et al. 1997; Fairweather et al.

1995). The purpose of the procedure is to determine whether data from multiple factor

combinations can be combined for the estimation of a single shelf life.

The full statistical model should include the intercept and slope terms of all main effects and

interaction effects and a term reflecting the random error of measurement. If it can be justified

that the higher order interactions are very small, there is generally no need to include these terms

in the model. In cases where the analytical results at the initial time point are obtained from the

finished dosage form prior to its packaging, the container intercept term can be excluded from

the full model because the results are common among the different container sizes and/or fills.

The tests for poolability should be specified to determine whether there are statistically

significant differences among factors and factor combinations. Generally, the pooling tests

should be performed in a proper order such that the slope terms are tested before the intercept

terms and the interaction effects are tested before the main effects. For example, the tests can

start with the slope and then the intercept terms of the highest order interaction, and proceed to

the slope and then the intercept terms of the simple main effects. The most reduced model,

obtained when all remaining terms are found to be statistically significant, can be used to

estimate the shelf lives.

All tests should be conducted using appropriate levels of significance. It is recommended that a

significance level of 0.25 be used for batch-related terms, and a significance level of 0.05 be

used for non-batch-related terms. If the tests for poolability show that the data from different

factor combinations can be combined, the shelf life can be estimated according to the procedure

described in Appendix section B.1 using the combined data.

If the tests for poolability show that the data from certain factors or factor combinations should

not be combined, either of two alternatives can be applied: (1) a separate shelf life can be

estimated for each level of the factors and of the factor combinations remaining in the model; or

(2) a single shelf life can be estimated based on the shortest estimated shelf life among all levels

of factors and factor combinations remaining in the model.

B.3.2.2.2 Other methods

Alternative statistical procedures (Ruberg and Stegeman 1991; Ruberg and Hsu 1992; Shao and

Chow 1994; Murphy and Weisman 1990; Yoshioka et al. 1997) to those described above can be

applied. For example, an appropriate procedure for assessing the equivalence in slope or in

mean shelf life can be used to determine the data poolability. However, such a procedure should

be prospectively defined, evaluated, properly justified, and, where appropriate, discussed with

the regulatory authority. A simulation study can be useful, if applicable, to demonstrate that the

statistical properties of the alternative procedure selected are appropriate (Chen et al. 1997).
Contains Nonbinding Recommendations

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B.4 Data Analysis For Bracketing Design Studies

The statistical procedures described in Appendix section B.3 can be applied to the analysis of

stability data obtained from a bracketing design study. For example, for a drug product available

in three strengths (S1, S2, and S3) and three container sizes (P1, P2, and P3) and studied

according to a bracketing design where only the two extremes of the container sizes (P1 and P3)

are tested, six sets of data from the 3x2 strength-size combinations will be obtained. The data

can be analyzed separately for each of the six combinations for shelf life estimation according to

Appendix section B.3.2.1, or tested for poolability prior to shelf life estimation according to

Appendix section B.3.2.2.

The bracketing design assumes that the stability of the intermediate strengths or sizes is

represented by the stability at the extremes. If the statistical analysis indicates that the stability

of the extreme strengths or sizes is different, the intermediate strengths or sizes should be

considered no more stable than the least stable extreme. For example, if P1 from the above

bracketing design is found to be less stable than P3, the shelf life for P2 should not exceed that

for P1. No interpolation between P1 and P3 should be considered.

B.5 Data Analysis For Matrixing Design Studies

A matrixing design has only a fraction of the total number of samples tested at any specified time

point. Therefore, it is important to ascertain that all factors and factor combinations that can

have an impact on shelf life estimation have been appropriately tested. For a meaningful

interpretation of the study results and shelf life estimation, certain assumptions should be made

and justified. For instance, the assumption that the stability of the samples tested represents the

stability of all samples should be valid. In addition, if the design is not balanced, some factors or

factor interactions might not be estimable. Furthermore, for different levels of factor

combinations to be poolable, it might have to be assumed that the higher order factor interactions

are negligible. Because it is usually impossible to statistically test the assumption that the higher

order terms are negligible, a matrixing design should be used only when it is reasonable to

assume that these interactions are indeed very small, based on supporting data.

The statistical procedure described in Appendix section B.3 can be applied to the analysis of

stability data obtained from a matrixing design study. The statistical analysis should clearly

identify the procedure and assumptions used. For instance, the assumptions underlying the

model in which interaction terms are negligible should be stated. If a preliminary test is

performed for the purpose of eliminating factor interactions from the model, the procedure used

should be provided and justified. The final model on which the estimation of shelf life will be

based should be stated. The estimation of shelf life should be performed for each of the terms

remaining in the model. The use of a matrixing design can result in an estimated shelf life

shorter than that resulting from a full design.

Where bracketing and matrixing are combined in one design, the statistical procedure described

in Appendix section B.3 can be applied.

B.6 References
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Carstensen, J.T., “Stability and Dating of Solid Dosage Forms,” Pharmaceutics of Solids and

Solid Dosage Forms, Wiley-Interscience, 182-185, 1977.

Chen, J.J., Ahn, H., and Tsong, Y., “Shelf-life Estimation for Multifactor Stability Studies,”

Drug Inf. Journal, 31:573-587, 1997.

Fairweather, W., Lin, T.D., and Kelly, R., “Regulatory, Design, and Analysis Aspects of

Complex Stability Studies,” J. Pharm. Sci., 84:1322-1326, 1995.

Murphy, J.R. and Weisman, D., “Using Random Slopes for Estimating Shelf-life,”

Proceedings of American Statistical Association of the Biopharmaceutical Section, 196-

200, 1990.

Ruberg, S.J. and Hsu, J.C., “Multiple Comparison Procedures for Pooling Batches in Stability

Studies,” Technometrics, 34:465-472, 1992.

Ruberg, S.J. and Stegeman, J.W., “Pooling Data for Stability Studies: Testing the Equality of

Batch Degradation Slopes,” Biometrics, 47:1059-1069, 1991.

Shao, J. and Chow, S.C., “Statistical Inference in Stability Analysis,” Biometrics, 50:753-763,

1994.

Yoshioka, S., Aso, Y., and Kojima, S., “Assessment of Shelf-life Equivalence of Pharmaceutical

Products,” Chem. Pharm. Bull., 45:1482-1484, 1997.
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18

B.7 Figures

Figure 1

Shelf life Estimation with Upper and Lower Acceptance Criteria Based on Assay at 

25C/60%RH

80

85

90

95

100

105

110

115

120

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

Time Point (Months)

Assay (% of Label Claim)

Raw Data

Upper confidence limit

Lower confidence limit

Regression line 

Upper acceptance 

criterion: 105

Lower acceptance 

criterion: 95

Figure 2

Shelf life Estimation with Upper Acceptance Criterion Based on a Degradation 

Product at 25C/60%RH

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

Time Point (Months)

Degradation Product (%)

Raw Data

Upper confidence limit

Regression line 

Upper acceptance 

criterion: 1.4