The role of bracketing and matrixing in efficient design of stability protocols

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Pharmaceutical Technology Europe

Pharmaceutical Technology Europe, Pharmaceutical Technology Europe-12-01-2005, Volume 17, Issue 12

This article looks at the use of bracketing and matrixing to lower the number of stability samples required and, consequently, reduce the cost of sample production, testing and management. There is a common misconception that regulatory authorities will not accept such methods, but there is actually an International Conference on Harmonization guideline (ICH Q1D) on the subject. In fact, many of these designs have already been accepted and FDA members were among the first to describe matrixing.

Stability testing is a vital part of product development. It is, however, quite resource consuming and, with 12 months' stability data generally required for a new product licence, is also often on the critical path of development. Therefore, it is vital that stability protocols are designed both properly, to ensure regulatory approval, and efficiently to minimize the time and resource required.

Fortunately, there are well-accepted procedures, namely bracketing and matrixing (B&M), to reduce the amount of stability testing required. These are procedures for reducing the number of samples of product tested for stability which, when correctly applied, should result in neither loss of data quality produced nor a significant change in the predicted shelf life. Such procedures are also theoretically applicable to drug substances, but, as there tend to be fewer presentations or batches tested than for products, the opportunities and benefits are more restricted.

Stability samples must be manufactured, labelled and stored, so reducing the number of stability samples can also potentially save in sample production and management costs, especially since storage facilities are quite expensive to set-up and maintain.

Bracketing, in particular, and matrixing have already been routinely applied to stability studies for some time now and are the subject of an International Conference on Harmonization (ICH) paper, Q1D issued in 2002.1 Preceding that there was a Committee for Proprietary Medicinal Products (CPMP) paper in 1997 on B&M and the Center for Drug Evaluation and Research (CDER) draft stability guidelines, issued in 1998, which also included these topics.2,3 Despite this, there is still much feeling in industry that the regulatory authorities will be reluctant to accept reduced stability protocols. In practice, I have had experience of submitting many reduced stability protocols with B&M without encountering any resistance from the reviewers; in fact, some were praised for their good design. I have also had conversations with regulators who have queried why more submissions do not include reduced stability designs, particularly matrixing. In fact, matrixing was described some time ago in papers authored by FDA staff.4,5


B&M are performed across different presentations of an active in a given product type, that is across different factors such as strength, pack, fill volume and packing site. The definitions as given in ICH are as follows:

Bracketing. "The design of a stability schedule such that only samples on the extremes of certain design factors (e.g., strength and package size) are tested at all time points as in a full design. The design assumes that the stability of any intermediate level is represented by the stability of the extremes tested."

For example, this indicates that for a product with three different strengths, say tablets at 2, 4 and 6 mg, it may be possible to omit testing of the 4 mg tablets.

Matrixing. "The design of a stability schedule such that a selected subset of the total number of possible samples for all factor combinations is 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."

Therefore, at a given time point (other than the initial or final ones) not every batch on stability needs to be tested.



B&M can be applied to virtually any formulation, although for more complex delivery systems with a large number of potential drug–device interactions, such as metered-dose inhalers (MDIs), multidose dry powder inhalers (MDPIs) and transdermal delivery systems, additional justification will be required. Indeed, FDA appears reluctant to accept reduced designs for inhaled devices although other regulatory bodies have accepted them.

ICH Q1D guidelines give some direction on the applicability of B&M. The existence of multiple strengths of a formulation is an obvious target for such reduced designs and the guidelines specifically allow this without justification when the different strengths have identical formulations. For example, tablets with identical formulations, but different compression weights, and capsules of different strengths made with identical power blends, but different fill plug sizes. Different strengths made with closely related formulations can be subject to B&M with some justification. What constitutes a closely related formulation is not defined, but examples could be:

  • Different strengths are obtained by minor changes in one excipient (say for 2, 4 and 6 mg tablets where one excipient changes to accommodate the varying active).

  • Different coatings on otherwise identical tablets.

The justification might be a statement confirming that either experiments demonstrating that varying the excipient or coating has no effect on the active, or that earlier development stability studies showed the changes are unlikely to have any effect upon stability.

B&M can also be applied to studies of the same closure system where either container or fill size varies. For bracketing, care must be taken to ensure that the intermediate condition is correctly identified as it might not necessarily be that the largest and smallest container represent the extreme configurations. Consideration should be given to wall thickness, closure geometry, surface area to volume ratio, headspace to volume ratio, water vapour and oxygen permeation rate per dosage unit.

Even when the closure varies bracketing and matrixing is possible with some justification. Such justification might be a demonstration that the product is not water sensitive or a discussion of the relative permeation rates of the closure systems.

Many regulatory authorities welcome the opportunity to comment on stability protocols prior to formal submissions and I would recommend in all instances where B&M are applied (and even when they aren't) that the applicant takes advantage of this, especially with FDA.

B&M can still be applied when all batches cannot be placed on storage simultaneously. The allowable difference in start times should be decided case by case as a business risk, because identification of any stability differences between batches will be delayed; as a guide up to 2 months' spread appears reasonable. Clearly, if studies are not started simultaneously the efficiency gains will be reduced.


Bracketing. Bracketing designs are fairly straightforward and have been around for longer than matrixed designs. A typical example of bracketing, as given in the CPMP paper, is reproduced as Table 1. This example is a product available in three different strengths, two different packs and for one of these packs, three different sizes. In this instance it would be necessary to demonstrate that the 30 and 500 high density polyethylene (HDPE) sizes bracket the 100 size as discussed earlier.

Table 1 Example of a bracketing design.

If, subsequent to commencing studies, it is decided not to register one of the extreme presentations, it is permissible to maintain the stability study to support any intermediate presentations that have not been placed on stability. A commitment should then be provided to place the omitted presentations on stability.

Matrixing. For matrixing, each storage condition should be treated separately under its own matrixing design. Accelerated conditions can be matrixed, but at least three time points, including initial and final, must be analysed, therefore, gains are minimal and personally I prefer full testing as accelerated conditions may provide early warning of any unexpected events.

As far as possible a matrixing design should be balanced so that each presentation (of strength, pack, fill volume etc.) is tested to the same extent over the intended study period. Full testing must be performed at the maximum storage period at the time of submission, frequently rendering exact balancing impossible. However, the design should be approximately balanced at least.

Examples of simple matrixed designs for a product in two strengths are shown in Table 2 (assuming submission with 12 months' data). Table 2(a) shows a one-half matrix design (or one-half reduction) and Table 2(b) — a two-thirds design (one-third reduction), giving reductions in the number of test samples of 31% and 21% respectively. These examples are for definitive stability and hence three batches are tested. Fewer batches may be permissible for follow up stability, or an abbreviated new application, but matrixing is still allowable.

Table 2 (a) One-half matrix design. (b) Two-thirds matrix design.

Note that these designs have assumed 36 months as the longest time point. The 36-month (and 48-month) time point could also be matrixed if one intends to test up to 48 months (or 60 months).

Note that in 2(b) interchanging the Xs and Os, excluding the initial, 12 month and final time points, makes it a one-third matrix (two-thirds reduction, a 42% reduction).

With matrixing, designs can be complete (matrixing on time points alone), whereby all batches tested in all possible presentations, or incomplete (matrixing on time points and factors), whereby some batches are not tested in some presentations. The larger the number of different presentations the more likely it is that an incomplete design is acceptable. An example of a more complex design, with six factors (three strengths and three packs) using a one-half design with full testing at 12 months is given in Table 3. Table 3(a) shows a complete reduced design and 3(b) an incomplete reduced design. In 3b, while all combinations of strength and pack are tested, each individual batch of product is not tested in all strength/pack combinations.

Table 3 (a) Complete reduced design (matrixing on time points alone) for three strengths and three packs. (b) Incomplete reduced design (matrixing on time points and factors) for three strengths and three packs.

ICH Q1D provides other example designs. It should be noted that it is permissible to combine B&M in a single design.

If, during the course of a matrixed stability study, it becomes apparent that the matrix is no longer appropriate, for example, if the required expiry period might not be achieved, you can revert to full testing or to a smaller reduction in testing. However, once matrixing is reduced it is not permissible subsequently to reinstate the original matrix. Therefore, it is good practice to put all samples on stability, including those that are not to be tested under the matrix design. In practice, for full stability, extra samples are usually stored to allow for any repeat analyses, so when storing samples for a reduced design you only need a sufficient amount for full testing, or a very small excess, to save on samples stored yet have enough to cover emergencies.

It is also worth noting that should the worst happen, such as when reaching a key storage time it is found that the reduced data do not support the required shelf life, then extra replicate analyses can be performed to obtain an improved shelf life estimate. Any statistical treatment should allow for the extra data at the last time point.

Different tests may be matrixed to varying extents. For example, if the test for active content is highly reproducible and the active is stable, then this test may be subjected to a one-half, or possibly even a one-third, matrix design. If, however, the test for a key impurity shows significant variability and there is an indication that the impurity might increase on storage, then a two third matrix, or possibly no matrix at all, may be more appropriate. In practice, I usually kept things simple and matrixed all tests to the same extent.

Degree of reduction

The degree of reduction in testing is dependent on the variability between, and homogeneity within, batches and the precision of the test method. Generally, greater numbers of presentations support larger test reductions. The intrinsic stability of the formulation is also very important as reductions in the number of samples tested may result in wider confidence intervals and, therefore, a shorter shelf life estimate. Hence, for a product likely to have an inherently short shelf life B&M should be minimal, while greater reductions may be appropriate for a product likely to significantly exceed a 36-month shelf life.

Table 4 gives some qualitative feel for the reductions that may be applied according to variability and anticipated expiry period (EP).

Table 4 Degree of reduction in bracketing and matrixing.

Data evaluation

Stability data from bracketed and/or matrixed studies should be treated in the same way as data from nonreduced studies. If inspection of the data clearly shows that there is no significant change in a parameter then no statistical analysis is required. Where statistical analysis is required the data from different batches and presentations should first be tested for poolability. If pooling is not justified then the shortest EP obtained should be applied to all batches and presentations. If pooling is justified then the predicted EP applies to all presentations.


The use of bracketing and matrixing for optimizing the design of stability protocols has been described. They can potentially provide considerable savings in stability studies costs as the amount of testing required is reduced, fewer samples have to be labelled and placed on storage, and consequently the space required to store them is also reduced.

The procedures are easy to apply, well established, accepted by the regulatory authorities and are described in ICH guidelines. Therefore, there is no reason why their application should not be widespread throughout the pharmaceutical industry.


1. International Conference on Harmonization ICH Q1D (2002)

2. Committee for Proprietary Medicinal Products, "Reduced Stability Testing Plans — Bracketing and Matrixing," CPMP/QWP/157/96 (1997) (Withdrawn).

3. FDA, "Stability Testing of Drug Substances and Drug Products," Draft Guidance for Industry (1998)

4. E. Nordbrock, J. Biopharm. Stat.2, 91–113 (1992)

5. W. Fairweather, T.D. Lin and R. Kelly, J. Pharm. Sci.84, 1322–1326 (1995)

Ray Munden is Principal at Munden Consultancy in Royston, UK.