#198 
 
Guidance for Industry 
 
Bracketing and Matrixing Designs 
for Stability Testing of New Veterinary Drug 
Substances and Medicinal Products 
 
VICH GL45 
 
Submit comments on this guidance at any time.  Submit  electronic comments on the guidance 
to http://www.regulations.gov.   Submit written comments to the Division  of Dockets 
Management (HFA-305), Food and Drug Administration,  5630 Fishers Lane, Room 1061, 
Rockville,  MD  20852.  All written comments should be identified  with the Docket No. FDA-
2009-D-0309. 
 
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, 240-402-0670,  email:   mai.huynh@fda.hhs.gov. 
 
Additional  copies of this guidance document may be requested from the Policy and 
Regulations Staff (HFV-6), 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 
July 2015 
  Contains Non-Binding Recommendations 
VICH GL 45 (Quality)  Bracketing and Matrixing 
April 2010 
For implementation at Step 7 
 
 
 
 
 
 
 
Quality:  Bracketing and Matrixing 
Designs for Stability Testing of 
New Veterinary Drug Substances 
and Medicinal Products 
     
 
 
 
 
 
 
 
Adopted at Step 7 of the VICH Process 
by the VICH Steering Committee 
in April 2010 
for implementation  by April 2011 
 
 
 
 
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 the USA. 
 
 
 
 
   
2  Contains Non-Binding Recommendations 
Table of Contents 
 
 
1.  INTRODUCTION ......................................................................................................... 4 
1.1 Objectives of the Guidance ............................................................................................ 4 
1.2 Background................................................................................................................. 4 
1.3 Scope of the Guidance .................................................................................................. 4 
2.  GUIDANCE ................................................................................................................. 4 
2.1 General....................................................................................................................... 4 
2.2 Applicability of Reduced Designs ................................................................................... 5 
2.3 Bracketing .................................................................................................................. 5 
2.3.1 Design Factors....................................................................................................... 5 
2.3.2 Design Considerations and Potential Risks ................................................................. 6 
2.3.3 Design Example..................................................................................................... 7 
2.4 Matrixing .................................................................................................................... 7 
2.4.1 Design Factors....................................................................................................... 7 
2.4.2 Design Considerations ............................................................................................ 8 
2.4.3 Design Examples ................................................................................................... 8 
2.4.4 Applicability and Degree of Reduction .....................................................................11 
2.4.5 Potential Risk .......................................................................................................11 
2.5 Data Evaluation ..........................................................................................................11 
   
3  Contains Non-Binding Recommendations 
Guidance for Industry 
 
Bracketing and Matrixing Designs for Stability Testing of New Veterinary 
Drug Substances and Medicinal Products 
 
This guidance represents the current thinking of the Food and Drug Administration (FDA or 
Agency) on this topic.  It does not establish any rights for any person and is not binding on FDA 
or the public.  You can use an alternative approach if it satisfies the requirements of the 
applicable statutes and regulations.  To discuss an alternative approach, contact the FDA staff 
responsible for this guidance as listed on the title page. 
 
   
1.  INTRODUCTION 
 
1.1 Objectives of the Guidance 
 
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 
Harmonised Tripartite guidance on Stability Testing of New Veterinary Drug Substances and 
Medicinal Products (Revision) VICH GL3(R) (hereafter referred to as the VICH GL3(R)). 
 
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 
 
VICH GL3(R) notes that the use of matrixing  and bracketing can be applied,  if justified,  to 
the testing  of new veterinary  drug substances  and medicinal  products,  but  provides  no 
further guidance on the subject. 
 
1.3 Scope of the Guidance 
 
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. 
 
2.  GUIDANCE 
 
2.1 General 
 
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 
4  Contains Non-Binding Recommendations 
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. 
 
2.2 Applicability of Reduced Designs 
 
Reduced designs can be applied  to the formal stability  study of most types of new veterinary 
medicinal  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 new veterinary 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.   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. 
 
2.3 Bracketing 
 
As defined  in  the glossary  to  VICH GL3(R),  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. 
 
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. 
 
2.3.1 Design Factors 
 
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. 
   
5  Contains Non-Binding Recommendations 
2.3.1.1 Strength 
 
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. 
 
2.3.1.2 Container Closure Sizes and/or Fills 
 
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, and 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. 
 
2.3.2 Design Considerations and Potential Risks 
 
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 post-approval. 
 
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). 
 
   
6  Contains Non-Binding Recommendations 
2.3.3 Design Example 
 
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  15 ml  T  T  T        T  T  T 
size 
100 ml                   
500 ml  T  T  T        T  T  T 
 
Key: T = Sample tested 
 
2.4 Matrixing 
 
As defined in the  glossary  of  the  VICH GL3(R),  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  is 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 medicinal  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 veterinary 
medicinal  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. 
 
2.4.1 Design Factors 
 
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). 
 
   
7  Contains Non-Binding Recommendations 
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 medicinal  product is not affected by oxygen, moisture, or 
light. 
 
2.4.2 Design Considerations 
 
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. 
 
2.4.3 Design Examples 
 
Examples of matrixing  designs on time points for a medicinal  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 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. 
   
8  Contains Non-Binding Recommendations 
Table 2:  Examples of Matrixing Designs on Time Points for a Medicinal Product 
with Two Strengths 
 
One-Half Reduction 
 
Time point (months)  0  3  6  9  12  18  24  36 
Strength  S1  Batch 1  T  T    T  T    T  T 
Batch 2  T  T    T  T  T    T 
Batch 3  T    T    T  T    T 
S2  Batch 1  T    T    T    T  T 
Batch 2  T  T    T  T  T    T 
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 
Strength  S1  Batch 1  T  T    T  T    T  T 
Batch 2  T  T  T    T  T    T 
Batch 3  T    T  T  T  T  T  T 
S2  Batch 1  T    T  T  T  T  T  T 
Batch 2  T  T    T  T    T  T 
Batch 3  T  T  T    T  T    T 
 
Key: T = Sample tested 
 
Additional  examples  of matrixing  designs  for a medicinal  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 combinations  of batch, strength, and container size are tested, 
while in Table 3b, certain combinations  of batch, strength and container size are not tested. 
   
9  Contains Non-Binding Recommendations 
Tables 3a and 3b:  Examples of Matrixing Designs for a Medicinal 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) 
T 1  T    T  T  T  T  T  T 
T 2  T  T    T  T    T  T 
T 3  T  T  T    T  T    T 
 
S 1, S2, and S3 are different strengths. A, B, and C are different container sizes. 
T = Sample tested 
   
10  Contains Non-Binding Recommendations 
2.4.4 Applicability and Degree of Reduction 
 
The following,  although not an exhaustive list,  should be considered when a matrixing 
design is contemplated: 
 
  knowledge of data variability 
  expected stability  of the medicinal  product 
  availability  of supporting  data 
  stability  differences in the medicinal  product within  a factor or among 
factors and/or 
  number of factor combinations  in the study 
 
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 supporting  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. 
 
2.4.5 Potential Risk 
 
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. 
 
2.5 Data Evaluation 
 
Stability  data from studies in a reduced design should be treated in the same manner as data 
from full design studies. 
11