What is the Difference between Bracketing and Matrixing?

In the context of stability studies, bracketing and matrixing strategies allow for a reduction in testing effort without significantly compromising the integrity of the results – provided they are scientifically justified and documented in accordance with regulatory requirements.

Definitions according to ICH Q1A(R2)

A key foundation for both concepts is the ICH Q1A(R2) Guideline Stability Testing of New Drug Substances and Products, which defines bracketing and matrixing as follows:

• Bracketing: The design of a stability schedule such that only samples on the extremes of certain design factors, e.g., strength, package size, 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. Where a range of strengths is to be tested, bracketing is applicable if the strengths are identical or very closely related in composition (e.g., for a tablet range made with different compression weights of a similar basic granulation, or a capsule range made by filling different plug fill weights of the same basic composition into different size capsule shells). Bracketing can be applied to different container sizes or different fills in the same container closure system.
• 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. 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.

In short, bracketing is a design strategy in which only the extremes (e.g., highest and lowest strengths, largest and smallest pack sizes) of a product range are tested. The assumption here is that the stability of the intermediate values is represented by the tested extremes.

Matrixing, by contrast, involves testing only a subset of the total sample combinations at specific time points. The samples are selected in such a way that all combinations are tested at least once over the course of the study. Matrixing is particularly suitable for products with a large number of variables (e.g., batches, container types, filling quantities).

ICH Q1D and Q1E

More detailed guidance on the application of bracketing and matrixing in stability studies is provided in the ICH Q1D – Bracketing and Matrixing designs for Stability Testing of Drug Substances and Drug Products. This guideline includes sample table layouts and highlights key considerations for study planning. It also specifies the conditions under which reduced designs are acceptable, the statistical aspects to be considered, and when a conventional full design should be preferred.

In addition, ICH Q1E – Evaluation of Stability Data provides guidance for the statistical evaluation of stability data. This guideline is particularly important in assessing whether data from a bracketing or matrixing design are sufficient to justify a product’s shelf life.

Scientific Prerequisites

Both strategies require that their underlying assumptions are supported by existing data or can be adequately justified as part of a risk assessment. It is particularly important that neither bracketing nor matrixing is applied without solid scientific justification. The selection of samples and the testing strategy must be well documented and scientifically substantiated—especially when both strategies are combined in a single design.

As stated in ICH Q1D:

• Whether bracketing or matrixing can be applied depends on the circumstances [...]. The use of any reduced design should be justified.
• 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.
• 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.
• 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.

This makes it clear: variability in the stability data is a critical factor when deciding whether to apply matrixing. Only when data exhibit low variability can full testing reasonably be reduced. In cases of high variability, the risk increases that degradation processes or trends may remain undetected in untested combinations.

Bracketing, too, is not universally applicable. The tested samples must clearly represent the extremes—e.g., with respect to drug concentration, fill volume, or container size. Otherwise, there is a risk that relevant stability issues in intermediate configurations may be missed.