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GUIDANCE FOR INDUSTRY 
 
Statistical Evaluation Of Stability Data 
 
VICH GL51 
 
 
Submit comments on this guidance at any time.  Submit written comments to the Division of 
Dockets Management (HFA-305), Food and Drug Administration, 5630 Fishers Lane, Room 
1061, Rockville, MD 20852.  Submit electronic comments  on the guidance to  
http://www.regulations.gov.  You should identify all comments with Docket No. FDA-2012-
D-0288. 
 
For further information regarding this document, contact Mai Huynh, Center for Veterinary 
Medicine, (HFV-142), Food and Drug Administration, 7500 Standish Place, Rockville, 
MD  20855, 240-402-0669; email:  Mai.huynh@fda.hhs.gov. 
 
Additional copies of this guidance document may be requested from the Communications 
Staff (HFV-12), Center for Veterinary Medicine, Food and Drug Administration, 7519 
Standish Place, Rockville, MD 20855, and may be viewed on the Internet at either 
http://www.fda.gov/AnimalVeterinary/default.htm or http://www.regulations.gov. 
 
 
U.S. Department of Health and Human Services 
Food and Drug Administration 
Center for Veterinary Medicine 
May 2014  Contains Nonbinding Recommendations 
 
VICH GL51 (QUALITY:  STABILITY DATA) 
February 2013 
For Implementation at Step 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
S E S
TATISTICAL  VALUATION OF  TABILITY 
D  
ATA
 
 
 
Adopted at Step 7 of the VICH Process by the VICH Steering Committee 
in February 2013 
for implementation by 28 February 2014 
 
 
 
 
 
THIS GUIDANCE HAS BEEN DEVELOPED BY THE APPROPRIATE VICH EXPERT WORKING GROUP 
AND IS SUBJECT TO CONSULTATION BY THE PARTIES, IN ACCORDANCE WITH THE VICH PROCESS. 
AT STEP 7 OF THE PROCESS THE FINAL DRAFT IS RECOMMENDED FOR ADOPTION TO THE 
REGULATORY BODIES OF THE EUROPEAN UNION, JAPAN AND USA. 
 
   
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TABLE OF CONTENTS 
 
1.  INTRODUCTION............................................................................................................... 4 
1.1  Objectives of the Draft Guidance................................................................................. 4 
1.2  Background .................................................................................................................. 4 
1.3  Scope of the Draft Guidance ........................................................................................ 4 
2.  GUIDANCE ......................................................................................................................... 5 
2.1  General Principles ........................................................................................................ 5 
2.2  Data presentation ......................................................................................................... 6 
2.3  Extrapolation ................................................................................................................ 6 
2.4  Data Evaluation for Retest Period or Shelf Life Estimation for Drug Substances or 
Veterinary Medicinal Products Intended for Room Temperature Storage .................. 7 
2.5  Data Evaluation for Retest Period or Shelf Life Estimation for Drug Substances or 
Veterinary Medicinal Products Intended for Storage Below Room Temperature ....... 9 
2.6  General Statistical Approaches .................................................................................. 11 
3.  APPENDICES ................................................................................................................... 12 
Appendix A:  Decision Tree for Data Evaluation for Retest Period or Shelf Life  
  Estimation for Drug Substances or Veterinary Medicinal Products (excluding 
Frozen Products) ........................................................................................................ 12 
Appendix B:  Examples of Statistical Approaches to Stability Data Analysis ............... 13 
 
   
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GUIDANCE FOR INDUSTRY 
STATISTICAL EVALUATION OF STABILITY DATA 
 
This guidance represents the Food and Drug Administrations (FDAs) 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.  You can use an alternative approach if the approach satisfies the requirements of the 
applicable statutes and regulations.  If you want to discuss an alternative approach, contact the 
appropriate FDA staff.  If you cannot identify the appropriate FDA staff, call the appropriate number 
listed on the title page of this guidance. 
 
1.  INTRODUCTION 
 
1.1  Objectives of the Guidance 
 
This guidance is intended to provide recommendations on how to use stability data generated 
in accordance with the principles detailed in the VICH guidance entitled, Stability Testing 
of New Veterinary Drug Substances and Medicinal Products, GL3(R) (hereafter referred to 
as the 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 veterinary medicinal product that 
extends beyond the period covered by available data from the stability study under the long-
term storage condition (hereafter referred to as long-term data). Application of this guidance 
is entirely optional and it is up to the applicant to decide whether or not to use statistical 
analysis to support the claimed retest period/shelf-life. 
 
FDAs guidance documents, including this guidance, do not establish legally enforceable 
responsibilities.  Instead, guidances describe the Agencys 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. 
 
1.2  Background 
 
The guidance on the evaluation and statistical analysis of stability data provided in the parent 
guidance is 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 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 reduced-design 
study. 
 
This guidance is an expansion of the guidance presented in the Evaluation sections of the 
parent guidance. 
 
1.3  Scope of the Guidance 
 
This guidance addresses the evaluation of stability data that should be submitted in 
registration applications for new molecular entities and associated veterinary medicinal 
products. The  guidance provides recommendations on establishing retest periods and shelf 
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  Contains Nonbinding Recommendations 
 
lives for drug substances and veterinary medicinal products intended for storage at or below 
room temperature*. It covers 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. 
 
The VICH guidances entitled, Specifications: Test Procedures and Acceptance Criteria for 
New Veterinary Drug Substances and New Medicinal Products: Chemical Substances, VICH 
GL39 and Specifications: Test Procedures and Acceptance Criteria for New 
Biotechnological/Biological Veterinary Medicinal Products, GL40 should be consulted for 
recommendations on the setting and justification of acceptance1 criteria, and the VICH draft 
guidance entitled, Bracketing and Matrixing Designs for Stability Testing of New 
Veterinary Drug Substances and Medicinal Products, VICH GL45 should be referenced for 
recommendations on the use of full- versus reduced-design studies. 
 
2.  GUIDANCE 
 
2.1  General Principles 
 
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 the veterinary medicinal 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 veterinary medicinal 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 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 stability-indicating capability and inherent variability of the analytical procedures. 
 
                                                 
1 The term acceptance criteria is defined in the VICH guidance entitled, Specifications: Test Procedures and 
Acceptance Criteria for New Veterinary Drug Substances and New Medical Products: Chemical Substances, 
VICH GL39. 
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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 the veterinary 
medicinal 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 B provides (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 a veterinary medicinal product can be assumed 
to follow zero-order kinetics during long-term storage1. 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 called for to verify the proposed retest periods or shelf lives in 
other cases. 
 
2.2  Data presentation 
 
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. 
 
2.3  Extrapolation  
 
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 
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  Contains Nonbinding Recommendations 
 
such 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 
long-term 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. 
 
2.4  Data Evaluation for Retest Period or Shelf Life Estimation for Drug Substances 
or Veterinary Medicinal Products Intended for Room Temperature Storage 
 
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 veterinary medicinal 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. 
 
2.4.1  No significant change at accelerated condition  
 
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. 
 
2.4.1.1  Long-term and accelerated data showing little or no change over time and little or 
no variability 
 
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 the veterinary 
medicinal 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 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, but should not be 
more than 12 months beyond, the period covered by long-term data. 
 
2.4.1.2  Long-term or accelerated data showing change over time and/or variability 
 
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 
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  Contains Nonbinding Recommendations 
 
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, 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, 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. 
 
2.4.2  Significant change at accelerated condition 
  
Where significant change* occurs at the accelerated condition, the retest period or shelf life 
would depend on the outcome of stability testing at the intermediate condition, as well as at 
the long-term condition. 
 
*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 gel-
coated 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. 
 
   
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2.4.2.1  No significant change at intermediate condition 
 
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, 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. 
 
2.4.2.2  Significant change at intermediate condition 
 
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 could be called for. 
 
2.5  Data Evaluation for Retest Period or Shelf Life Estimation for Drug Substances 
or Medicinal Products Intended for Storage Below Room Temperature 
 
2.5.1  Drug substances or veterinary medicinal products intended for storage in a 
refrigerator 
 
Data from drug substances or veterinary medicinal products intended to be stored in a 
refrigerator should be assessed according to the same principles as described in Section 2.4 
for drug substances or veterinary medicinal 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. 
 
2.5.1.1  No significant change at accelerated condition 
 
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 2.4.1, 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, but should not be more 
than 6 months beyond, the period covered by long-term data normally without the support of 
statistical analysis. 
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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, 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. 
 
2.5.1.2  Significant change at accelerated condition 
 
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 called for. 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 called for. 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 supported, if appropriate, by further testing on a single batch of the drug 
substance or the veterinary medicinal product at the accelerated condition for a period shorter 
than 3 months. 
 
2.5.2  Drug substances or veterinary medicinal products intended for storage in a freezer 
 
For drug substances or veterinary medicinal 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 veterinary medicinal products intended to be stored 
in a freezer, testing on a single batch at an elevated temperature (e.g., 5C  3C or 25C  
2C) 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). 
 
2.5.3  Drug substances or veterinary medicinal products intended for storage below -20C 
 
For drug substances or veterinary medicinal products intended for storage below -20C, the 
retest period or shelf life should be based on long-term data and should be assessed on a case-
by-case basis.   
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2.6  General Statistical Approaches 
 
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 non-linear 
function on an arithmetic or logarithmic scale. In some cases, a non-linear 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. 
 
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 reduced-design studies are included in Appendix B.  References to current literature 
sources can be found in Appendix B.6.   
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3.  APPENDICES 
 
Appendix A: Decision Tree for Data Evaluation for Retest Period or Shelf Life 
Estimation for Drug Substances or Veterinary Medicinal Products (excluding 
Frozen Products) 
 
 
  Tabulate and/or plot 
stability data on all  No extrapolation; shorter 
  attributes at all storage  retest period or shelf life and 
  conditions and evaluate  data covering excursions 
each attribute separately  can be called for; statistical 
  analysis if long-term data 
Yes  show variability 
 
 
  Significant 
change at  No 
  accelerated 
condition within 
 
3  months? 
 
 
 
Yes 
   
Significant  Intended  Significant  No extrapolation; shorter 
change at  Yes  to be stored in a  No  change  Yes  retest period or shelf life 
accelerated  refrigerator?  at intermediate  can be called for; statistical 
condition within   condition?  analysis if long-term data 
6 months?  show variability 
No 
No 
Long- term  (1)Long- term 
data show: (1) little or  No to (1) or  data amenable to  No to (1)   If backed by relevant 
no change over time  statistical analysis and  supporting data: 
and (2) little or no  (2) or both  (2) statistical analysis  or (2)  Y = up to X + 3 months  
variability?  performed? 
Yes to both 
Yes to both 
Accelerated  (1)Long- term  If backed by statistical 
data show: (1) little or  No to (1) or   data amenable to  No to (1)  analysis and relevant 
no  change over time  statistical analysis and  supporting data: Y = up 
and (2) little or no  (2) or both  (2) statistical analysis  or (2)  to 1.5X, but not 
variability?  performed?  exceeding X + 6 months  
Yes to both 
Yes to both 
Statistical analysis  Y = Proposed retest period or shelf life 
is normally  X = Period covered by long-term data 
unnecessary   
If backed by statistical 
analysis and relevant  If backed by relevant 
Y= up to 2X, but not  supporting data: Y = up to  supporting data: Y = up 
exceeding X + 12 months;  2X, but not exceeding X +  to 1.5X, but  not 
 or if refrigerated,  12 months; or if refrigerated,  exceeding X + 6 months; 
Y = up to 1.5X, but not   Y = up to 1.5X, but not  or if refrigerated, Y = up 
exceeding X + 6 months  exceeding X + 6 months   to X + 3  months  
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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 
linear1. Figure 1 shows the regression line for assay of a veterinary medicinal 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 2.4 and 2.5 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 shows the regression line for a degradation product in a veterinary medicinal 
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 2.4 and 2.5 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 Sections B.2 through B.5. 
 
B.2  Data Analysis for One-Factor, Full-Design Studies 
 
For a drug substance or for a veterinary medicinal 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, full-design studies, two statistical approaches can be considered. 
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. 
 
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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 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 2.4 and 2.5 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 
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 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. 
 
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 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 
14 
  Contains Nonbinding Recommendations 
 
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 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 procedures2-6 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 appropriate7. 
 
B.3  Data Analysis for Multi-Factor, Full-Design Studies 
 
The stability of the veterinary medicinal 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. 
 
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 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 2.4 and 2.5 is followed. If one or more of the 
estimated shelf lives fall short of the proposed shelf life, model building as described in 
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 
15 
  Contains Nonbinding Recommendations 
 
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 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 Section B.2.  For example, for a 
veterinary medicinal 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 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 batches, strengths, container sizes and/or fills, etc. are 
combined. 
 
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 combinations7, 8. 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 
16 
  Contains Nonbinding Recommendations 
 
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 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 procedures2-6 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 appropriate7. 
 
B.4  Data Analysis For Bracketing Design Studies 
 
The statistical procedures described in Section B.3 can be applied to the analysis of stability 
data obtained from a bracketing design study.  For example, for a veterinary medicinal 
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 Section B.3.2.1, or tested for poolability 
prior to shelf life estimation according to 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 
17 
  Contains Nonbinding Recommendations 
 
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 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 Section B.3 can be applied. 
 
B.6  References 
 
1.  Carstensen,  J.T.,  Stability  and  Dating  of  Solid  Dosage  Forms  
Pharmaceutics of Solids and Solid Dosage Forms, Wiley-Interscience, 182-185, 1977 
 
2.  Ruberg,  S.J.  and  Stegeman,  J.W.,  Pooling  Data  for  Stability  Studies:  Testing  the 
Equality of Batch Degradation Slopes Biometrics, 47:1059-1069, 1991 
 
3.  Ruberg, S.J. and Hsu, J.C., Multiple Comparison Procedures for Pooling Batches in 
Stability Studies Technometrics, 34:465-472, 1992 
 
4.  Shao,  J.  and  Chow,  S.C.,  Statistical  Inference  in  Stability  Analysis  
Biometrics, 50:753-763, 1994 
 
5.  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 
 
6.  Yoshioka,  S.,  Aso,  Y,  and  Kojima,  S.,  Assessment  of  Shelf-life  Equivalence  of 
Pharmaceutical Products Chem. Pharm. Bull., 45:1482-1484, 1997 
 
7.  Chen,  J.J.,  Ahn,  H.,  and  Tsong,  Y.,  Shelf-life  Estimation  for  Multifactor  Stability 
Studies Drug Inf. Journal, 31:573-587, 1997 
 
8.  Fairweather, W., Lin, T.D., and Kelly, R., Regulatory, Design, and Analysis Aspects of 
Complex Stability Studies J. Pharm. Sci., 84:1322-1326, 1995 
18 
  Contains Nonbinding Recommendations 
 
B.7 Figures 
 
Figure 1 
 
 
 
Shelf life Estimation with Upper and Lower Acceptance Criteria Based on Assay at 
 
25C/60%RH
 
120
 
115
 
m) 110 
ai
Cl  
el  105  
b Raw Data
a  
L 100  
f  Upper confidence limit
o
%  95  Lower confidence limit 
(
say  90  Regression line 
s  
A Upper acceptance 
 
  criterion: 105
85
  Lower acceptance 
80  
criterion: 95
                                 
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
 
Time Point (Months)
 
 
Figure 2 
 
 
 
Shelf life Estimation with Upper Acceptance Criterion Based on a Degradation 
 
Product at  25C/60%RH
 
3.0
 
2.5
 
%)
(
ct  2.0 
u
d
o
r
P  
n  1.5 Raw Data 
o
ati Upper confidence limit 
d 1.0 
a
r Regression line 
g
e  
D Upper acceptance 
 
0.5  
criterion: 1.4
 
0.0
                                 
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
 
Time Point (Months)
 
19