Design of an Efficient Stability Programme -Bracketing and Matrixing

Stability in Business as Motivation in Stone Wall

We will focus mostly on the following guideline:

Q1D Bracketing and Matrixing Designs for Stability Testing of Drug Substances and Products (2003.2.7)


Key factors such as batch, strength, package size and fill can affect the specification attribute.
In addition to how the specification attribute may change with storage, these factors may have to be taken into consideration. For example if the % label claim is to considered in 3 batches and at 2 strengths then there is a total of 3 X 2 = 6 combinations. Each of these combinations may have to be monitored at each of 8 time points i.e. [0,3,6,9, 12, 18,24,36] months. Such a full study design would require at least 6 X 8 assays!


Requirements are specified in ICH Q1D A design in which samples for every factor combination are not tested at all time points. Two types of reduced design; “bracketing and “matrixing”. Can be applied to most types of drug products. For drug substances (APIs), matrixing is of limited applicability and bracketing is not generally applicable.


Bracketed designs are such that only samples at the extremes of certain design factors are tested at all times. This leads to economy on assay determinations but care must be taken as such reduced designs make assumptions that the assays either only increase or only decrease between the extremes. As an example lets look at the % label claim for three batches at 3 strengths and 3 container sizes. A full design would require 3 X 3 X 3 = 27 assays at any one time point.

A bracketed design using the extremes could reduce the design to only 12 assays:

Strength Low Medium High
Batch 1 2 3 1 2 3 1 2 3
Small Container T T T — — — T T T
Medium Container — — — — — — — — —
Large Container T T T — — — T T T

Where ‘T’ denotes assay test and ‘–‘ denotes no assay test. This is a big saving on the number of assays to be undertaken but we would need to be confident that nothing unusual happens at the medium levels!

Bracketed designs can be applied as follows:

  • To studies with multiple strengths of identical or closely related formulations
  • To studies of the same container closure system where either container size or fill varies while the other remains constant
    • If both container size and fill vary; take care in selecting extremes (ICH 01 D

Matrixing designs are such that only a subset of all possible factor combinations may be collected at particular time points. At a subsequent time point a different subset of factor combinations are normally collected. Care must be taken in selecting the samples for testing to ensure the design is balanced and representative.

It is recommended that:

  • All factor combinations are collected at the start and end time points
  • All factor combinations be tested at 12 months, or the most recent time point when all full-term data are unavailable before review
  • Data should be available from at least three time points during the first 12 months

A matrix design with one half reduction on time points:

Time point (months) 0 3 6 9 12 18 24 36
Strength Low Half Data Collected Half Data Collected
Batch 1 T T T T T T
Batch 2 T T T T T T
Batch 3 T T T T T
Strength High All Data Collected All Data Collected All Data Collected
Batch 1 T T T T T
Batch 2 T T T T T T
Batch 3 T T T T T

Where ‘T’ denotes assay test and ‘–‘ denotes no assay test.

Matrixing designs are applicable if:

  • Previous data indicates predictable product stability
  • Previous data exhibit moderate variability
  • They are of appropriate statistical design
REDUCED DESIGNS – rules of thumbRule of thumb

At first you will find it easier to use a full design. Use a bracket design when you are confident that nothing unusual happens between extremes. Use the matrix design to cut down on numbers of assays at each time point. Read the ICH Guidelines. These are not easy because of the many different factors that can effect storage and shelf life but after repeated reading it should fall into place.