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
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or
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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)
January 2003
ICH 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
i 1
GUIDANCE FOR INDUSTRY
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 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 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. 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.
2 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.
3 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
Container size 15 ml T T T T T T
100 ml
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.
4 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.
5 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 one-
half (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
  S S1 Batch 1 T T T T T T
  t
Batch 2 T T T T T T
  r
  e Batch 3 T T T T T
  n
  g S2 Batch 1 T T T T T
  t
Batch 2 T T T T T T
  h
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
  S S1 Batch 1 T T T T T T
  t
Batch 2 T T T T T T
  r
  e Batch 3 T T T T T T T
  n
  g S2 Batch 1 T T T T T T T
  t
Batch 2 T T T T T T
  h
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
6 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 0 3 6 9 12 18 24 36
(months)
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
7 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.
8