Guidance for Industry

Q1D Bracketing and Matrixing 

Designs for Stability Testing of New 

Drug Substances and Products

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)

January 2003

ICH
Guidance for Industry

Q1D Bracketing and Matrixing 

Designs for Stability Testing of New 

Drug Substances and Products

Additional copies are available from:

Center for Drug Evaluation and Research (CDER),

Division of Drug Information (HFD-240),

5600 Fishers Lane, Rockville, MD 20857

(Tel) 301-827-4573

http://www.fda.gov/cder/guidance/index.htm

or

Office of Communication, Training, and

Manufacturers Assistance (HFM-40),

Center for Biologics Evaluation and Research (CBER)

1401 Rockville Pike, Rockville, MD 20852-1448,

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

(Voice Information) 800-835-4709 or 301-827-1800

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)

January 2003

ICH
i

TABLE OF CONTENTS

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

A. Objectives of the Guidance (1.1)...........................................................................................1

B. Background (1.2)..................................................................................................................1

C. Scope of the Guidance (1.3)..................................................................................................1

II. GUIDANCE (2)......................................................................................................................2

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

B. Applicability of Reduced Designs (2.2).................................................................................2

C. Bracketing (2.3)....................................................................................................................2

D. Matrixing (2.4).....................................................................................................................4

E. Data Evaluation (2.5)............................................................................................................8
GUIDANCE FOR INDUSTRY1

Q1D Bracketing and Matrixing Designs for Stability Testing of New Drug Substances and 

Products

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.

I. INTRODUCTION (1)

A. Objectives of the Guidance (1.1)

This guidance is intended to address recommendations on the application of bracketing and 

matrixing to stability studies conducted in accordance with principles outlined in the ICH 

guidance Q1A(R) Stability Testing of New Drug Substances and Products (the parent 

guidance).

B. Background (1.2)

The parent guidance notes that the use of matrixing and bracketing can be applied, if justified, 

to the testing of new drug substances and products, but provides no further guidance on the 

subject. 

C. Scope of the Guidance (1.3)

This document provides guidance on bracketing and matrixing study designs. Specific 

principles are defined in this guidance for situations in which bracketing or matrixing can be 

applied. Sample designs are provided for illustrative purposes and should not be considered the 

only, or the most appropriate, designs in all cases.

 

1

 This guidance was developed within the Expert Working Group (Quality) of the International Conference on Harmonisat ion 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 7, 2002. 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.

Arabic numbers reflect the organizational breakdown in the document endorsed by the ICH Steering Committee at Step 4 of the 

ICH process, February 7, 2002. 
2

II. GUIDANCE (2)

A. General (2.1)

A full study design is one in which samples for every combination of all design factors are 

tested at all time points. A reduced design is one in which samples for every factor 

combination are not all tested at all time points. A reduced design can be a suitable alternative 

to a full design when multiple design factors are involved. Any reduced design should have the 

ability to adequately predict the retest period or shelf life. Before a reduced design is 

considered, certain assumptions should be assessed and justified. The potential risk should be 

considered of establishing a shorter retest period or shelf life than could be derived from a full 

design due to the reduced amount of data collected.

During the course of a reduced design study, a change to full testing or to a less reduced design 

can be considered if a justification is provided and the principles of full designs and reduced 

designs are followed. However, proper adjustments should be made to the statistical analysis, 

where applicable, to account for the increase in sample size as a result of the change. Once the 

design is changed, full testing or less reduced testing should be carried out through the 

remaining time points of the stability study.

B. Applicability of Reduced Designs (2.2)

Reduced designs can be applied to the formal stability study of most types of drug products, 

although additional justification should be provided for certain complex drug delivery systems 

where there are a large number of potential drug-device interactions. For the study of drug 

substances, matrixing is of limited utility and bracketing is generally not applicable.

Whether bracketing or matrixing can be applied depends on the circumstances, as discussed in 

detail below. The use of any reduced design should be justified. In certain cases, the 

conditions described in this guidance are sufficient justification for use, while in other cases, 

additional justification should be provided (see sections II.C.1 and II.D.1). The type and level 

of justification in each of these cases will depend on the available supporting data. Data 

variability and product stability, as shown by supporting data, should be considered when a 

matrixing design is applied.

Bracketing and matrixing are reduced designs based on different principles. Therefore, careful 

consideration and scientific justification should precede the use of bracketing and matrixing 

together in one design.

C. Bracketing (2.3)

As defined in the glossary to the parent guidance, bracketing is the design of a stability 

schedule such that only samples on the extremes of certain design factors (e.g., strength, 

container size and/or fill) are tested at all time points as in a full design. The design assumes 

that the stability of any intermediate levels is represented by the stability of the extremes tested. 
3

The use of a bracketing design would not be considered appropriate if it cannot be 

demonstrated that the strengths or container sizes and/or fills selected for testing are indeed the 

extremes.

1. Design Factors (2.3.1)

Design factors are variables (e.g., strength, container size and/or fill) to be evaluated in a study 

design for their effect on product stability.

a. Strength (2.3.1.1)

Bracketing can be applied to studies with multiple strengths of identical or closely related 

formulations. Examples include but are not limited to (1) capsules of different strengths made 

with different fill plug sizes from the same powder blend, (2) tablets of different strengths 

manufactured by compressing varying amounts of the same granulation, and (3) oral solutions 

of different strengths with formulations that differ only in minor excipients (e.g., colorants, 

flavorings).

With justification, bracketing can be applied to studies with multiple strengths where the 

relative amounts of drug substance and excipients change in a formulation. Such justification 

can include a demonstration of comparable stability profiles among the different strengths of 

clinical or development batches. 

In cases where different excipients are used among strengths, bracketing generally should not 

be applied. 

b. Container Closure Sizes and/or Fills (2.3.1.2)

Bracketing can be applied to studies of the same container closure system where either 

container size or fill varies while the other remains constant. However, if a bracketing design is 

considered where both container size and fill vary, it should not be assumed that the largest and 

smallest containers represent the extremes of all packaging configurations. Care should be 

taken to select the extremes by comparing the various characteristics of the container closure 

system that may affect product stability. These characteristics include container wall thickness, 

closure geometry, surface area to volume ratio, headspace to volume ratio, water vapor 

permeation rate or oxygen permeation rate per dosage unit or unit fill volume, as appropriate. 

With justification, bracketing can be applied to studies for the same container when the closure 

varies. Justification could include a discussion of the relative permeation rates of the bracketed 

container closure systems.

2. Design Considerations and Potential Risks (2.3.2)

If, after starting the studies, one of the extremes is no longer expected to be marketed, the study 

design can be maintained to support the bracketed intermediates. A commitment should be 

provided to carry out stability studies on the marketed extremes postapproval.
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Before a bracketing design is applied, its effect on the retest period or shelf life estimation 

should be assessed. If the stability of the extremes is shown to be different, the intermediates 

should be considered no more stable than the least stable extreme (i.e., the shelf life for the 

intermediates should not exceed that for the least stable extreme).

3. Design Example (2.3.3)

An example of a bracketing design is given in Table 1. This example is based on a product 

available in three strengths and three container sizes. In this example, it should be 

demonstrated that the 15-milliliter (ml) and 500-ml high-density polyethylene container sizes 

truly represent the extremes. The batches for each selected combination should be tested at 

each time point as in a full design.

Table 1: Example of a Bracketing Design

Strength 50 mg 75 mg 100 mg

Batch 1 2 3 1 2 3 1 2 3

15 ml T T T T T T

100 ml 

Container size

500 ml T T T T T T

Key: T = Sample tested 

D. Matrixing (2.4)

As defined in the glossary of the parent guidance, matrixing is the design of a stability schedule 

such that a selected subset of the total number of possible samples for all factor combinations 

would be tested at a specified time point. At a subsequent time point, another subset of 

samples for all factor combinations would be tested. The design assumes that the stability of 

each subset of samples tested represents the stability of all samples at a given time point. The 

differences in the samples for the same drug product should be identified as, for example, 

covering different batches, different strengths, different sizes of the same container closure 

system, and possibly, in some cases, different container closure systems.

When a secondary packaging system contributes to the stability of the drug product, matrixing 

can be performed across the packaging systems.

Each storage condition should be treated separately under its own matrixing design. Matrixing 

should not be performed across test attributes. However, alternative matrixing designs for

different test attributes can be applied if justified. 
5

1. Design Factors (2.4.1)

Matrixing designs can be applied to strengths with identical or closely related formulations. 

Examples include but are not limited to (1) capsules of different strengths made with different 

fill plug sizes from the same powder blend, (2) tablets of different strengths manufactured by 

compressing varying amounts of the same granulation, and (3) oral solutions of different 

strengths with formulations that differ only in minor excipients (e.g., colorants or flavorings).

Other examples of design factors that can be matrixed include batches made by using the same 

process and equipment, and container sizes and/or fills in the same container closure system.

With justification, matrixing designs can be applied, for example, to different strengths where 

the relative amounts of drug substance and excipients change or where different excipients are 

used or to different container closure systems. Justification should generally be based on 

supporting data. For example, to matrix across two different closures or container closure 

systems, supporting data could be supplied showing relative moisture vapor transmission rates 

or similar protection against light. Alternatively, supporting data could be supplied to show 

that the drug product is not affected by oxygen, moisture, or light.

2. Design Considerations (2.4.2)

A matrixing design should be balanced as far as possible so that each combination of factors is 

tested to the same extent over the intended duration of the study and through the last time point 

prior to submission. However, due to the recommended full testing at certain time points, as 

discussed below, it may be difficult to achieve a complete balance in a design where time

points are matrixed. 

In a design where time points are matrixed, all selected factor combinations should be tested at 

the initial and final time points, while only certain fractions of the designated combinations 

should be tested at each intermediate time point. If full long-term data for the proposed shelf 

life will not be available for review before approval, all selected combinations of batch, 

strength, container size, and fill, among other things, should also be tested at 12 months or at 

the last time point prior to submission. In addition, data from at least three time points, 

including initial, should be available for each selected combination through the first 12 months 

of the study. For matrixing at an accelerated or intermediate storage condition, care should be 

taken to ensure testing occurs at a minimum of three time points, including initial and final, for 

each selected combination of factors.

When a matrix on design factors is applied, if one strength or container size and/or fill is no 

longer intended for marketing, stability testing of that strength or container size and/or fill can 

be continued to support the other strengths or container sizes and/or fills in the design.
6

3. Design Examples (2.4.3)

Examples of matrixing designs on time points for a product in two strengths (S1 and S2) are 

shown in Table 2. The terms one-half reduction and one-third reduction refer to the reduction 

strategy initially applied to the full study design. For example, a one-half reduction initially 

eliminates one in every two time points from the full study design and a one-third reduction 

initially removes one in every three. In the examples shown in Table 2, the reductions are less 

than one-half and one-third due to the inclusion of full testing of all factor combinations at 

some time points as discussed in section II.D.2 (2.4.2). These examples include full testing at 

the initial, final, and 12-month time points. The ultimate reduction is therefore less than onehalf (24/48) or one-third (16/48), and is actually 15/48 or 10/48, respectively.

Table 2: Examples of Matrixing Designs on Time Points for a Product with Two 

Strengths

 One-Half Reduction

Time point (months) 0 3 6 9 12 18 24 36

Batch 1 T T T T T T

Batch 2 T T T T T T

S1

Batch 3 T T T T T

Batch 1 T T T T T

Batch 2 T T T T T T

 S

 t

 r

 e

 n

 g

 t

 h

S2

Batch 3 T T T T T

Key: T = Sample tested

 One-Third Reduction

Time point (months) 0 3 6 9 12 18 24 36

Batch 1 T T T T T T

Batch 2 T T T T T T

S1

Batch 3 T T T T T T T

Batch 1 T T T T T T T

Batch 2 T T T T T T

 S

 t

 r

 e

 n

 g

 t

 h

S2

Batch 3 T T T T T T

Key: T = Sample tested

Additional examples of matrixing designs for a product with three strengths and three container 

sizes are given in Tables 3a and 3b. Table 3a shows a design with matrixing on time points 

only and Table 3b depicts a design with matrixing on time points and factors. In Table 3a, all 
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combinations of batch, strength, and container size are tested, while in Table 3b, certain 

combinations of batch, strength and container size are not tested. 

Tables 3a and 3b: Examples of Matrixing Designs for a Product With Three Strengths 

and Three Container Sizes

 3a Matrixing on Time Points

Strength S1 S2 S3

Container size A B C A B C A B C

Batch 1 T1 T2 T3 T2 T3 T1 T3 T1 T2

Batch 2 T2 T3 T1 T3 T1 T2 T1 T2 T3

Batch 3 T3 T1 T2 T1 T2 T3 T2 T3 T1

 3b Matrixing on Time Points and Factors

Strength S1 S2 S3

Container size A B C A B C A B C

Batch 1 T1 T2 T2 T1 T1 T2

Batch 2 T3 T1 T3 T1 T1 T3

Batch 3 T3 T2 T2 T3 T2 T3

Key:

Time-point 

(months)

0 3 6 9 12 18 24 36

T1 T T T T T T T

T2 T T T T T T

T3 T T T T T T

S1, S2, and S3 are different strengths. 

A, B, and C are different container sizes.

T = Sample tested 

4. Applicability and Degree of Reduction (2.4.4)

The following, although not an exhaustive list, should be considered when a matrixing design is 

contemplated: 

• knowledge of data variability 

• expected stability of the product

• availability of supporting data 

• stability differences in the product within a factor or among factors

and/or 

• number of factor combinations in the study
8

In general, a matrixing design is applicable if the supporting data indicate predictable product 

stability. Matrixing is appropriate when the supporting data exhibit only small variability. 

However, where the supporting data exhibit moderate variability, a matrixing design should be 

statistically justified. If the supportive data show large variability, a matrixing design should

not be applied. 

A statistical justification could be based on an evaluation of the proposed matrixing design with 

respect to its power to detect differences among factors in the degradation rates or its precision 

in shelf life estimation.

If a matrixing design is considered applicable, the degree of reduction that can be made from a 

full design depends on the number of factor combinations being evaluated. The more factors 

associated with a product and the more levels in each factor, the larger the degree of reduction 

that can be considered. However, any reduced design should have the ability to adequately 

predict the product shelf life.

5. Potential Risk (2.4.5)

Due to the reduced amount of data collected, a matrixing design on factors other than time 

points generally has less precision in shelf life estimation and yields a shorter shelf life than the 

corresponding full design. In addition, such a matrixing design may have insufficient power to 

detect certain main or interaction effects, thus leading to incorrect pooling of data from 

different design factors during shelf life estimation. If there is an excessive reduction in the 

number of factor combinations tested and data from the tested factor combinations cannot be 

pooled to establish a single shelf life, it may be impossible to estimate the shelf lives for the 

missing factor combinations. 

A study design that matrixes on time points only would often have similar ability to that of a 

full design to detect differences in rates of change among factors and to establish a reliable 

shelf life. This feature exists because linearity is assumed and because full testing of all factor 

combinations would still be performed at both the initial time point and the last time point prior 

to submission.

E. Data Evaluation (2.5)

Stability data from studies in a reduced design should be treated in the same manner as data 

from full design studies.