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Bracketing and Matrixing for Stability Testing in Pharmaceuticals

What is Bracketing and Matrixing?
Bracketing and matrixing are statistical approaches used in stability testing of pharmaceutical products.

Bracketing: refers to the practice of testing a product at the beginning, middle, and end of its shelf life. This approach allows for the determination of the product's stability over time by comparing the results from each test. By testing at different points in time, bracketing can identify any changes in the product's stability profile and determine if it remains within the established acceptance criteria throughout its shelf life.

Matrixing: is similar to bracketing in that it is a statistical approach for evaluating stability. However, matrixing involves testing multiple products or formulations at the same time, rather than at different points in time. This allows for the simultaneous evaluation of multiple products or formulations in a single test, which can be more cost-effective and efficient than testing each product or formulation separately.

Both bracketing and matrixing are used in stability testing to optimize the number of samples and test conditions while maintaining a high level of confidence in the results. These approaches are widely used in the pharmaceutical industry to comply with regulatory requirements and ensure the quality and safety of drug products.

It is worth noting that the International Conference on Harmonization (ICH) guidelines provide guidance on how to use bracketing and matrixing in stability testing, including the conditions under which these approaches are appropriate, and the requirements that should be met for their use.


According to the ICH Q1A(R2) Glossary, bracketing is defined as "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." 


Matrixing is "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."


Bracketing and Matrixing for Stability Testing in Pharmaceuticals
The practice of bracketing and matrixing in pharmaceutical stability has been comprehensively covered in various forums interested in the testing of new drug products in accordance with the standards and regulations guiding the industry.

Bracketing and matrixing can be done in full study designs that aim to test the new drug substances for every combination of all design factors included in the technical guidelines, or in reduced study designs that focus on testing some of the drug samples or components while ignoring others.

Although a reduced study design is often considered as an appropriate option for a full study design in cases whereby a multiplicity of design factors come into play, it is important for professionals in the pharmaceutical industry to ensure that the reduced or partial design has the capacity to sufficiently envisage the retest interlude or shelf life of the drug substance.

Available documentation demonstrates that bracketing and matrixing in pharmaceutical stability are reduced designs anchored on divergent standards, hence the need to be vigilant and also to use scientific justifications in deciding which design to use. Bracketing has been described as the design of a stability plan which is only interested in examining the samples on the extremes of specific design aspects at all available time positions as would be the case in a complete design.

The bracketing design makes a presumption that the stability of intermediary points is well covered by the stability of peripheral points being tested. In drugs packaged in container sizes ranging from 15 mg to 500 mg, for example, bracketing can be used to test the extreme batches at each time position as would be the case in a full design. In such an arrangement, the stability of the intermediaries (container sizes of 100 mg, 200 mg, 300 mg and 400 mg) is solely dependent on the stability of the extreme container sizes (15 mg and 500 mg).


Matrixing, on the other hand, concerns the design of a stability plan whereby a selected compartment of the entire number of prospective samples for all design factor combinations is assessed at a specific time position. This process is repeated at an ensuing time position, whereby another compartment of samples for all design factor combinations are assessed. This process presumes that the steadiness or stability of each compartment of samples assessed embodies the stability of all product samples at a predetermined time position.

Consequently, the variations in the samples of a similar medicine should be acknowledged as, for instance, covering diverse batches, diverse potency, and even diverse container closure procedures. This means that similar drug formulations with different levels of strength or potency can be tested through matrixing, particularly in instances where they have been manufactured using similar processes and equipment.

Overall, bracketing and matrixing in pharmaceutical product stability testing are important processes in minimizing the quantities of samples of drug formulations and products assessed for stability. Although these processes use reduced designs as opposed to full designs, they are nevertheless effective in ensuring the stability of new drug products in a timely and cost-effective manner.



Is Bracketing/Matrixing Acceptable During Generic Drug Development?
Bracketing and matrixing can be acceptable during generic drug development, but it depends on the specific circumstances and the regulatory requirements of the country where the drug is being developed.

In general, the goal of generic drug development is to demonstrate bioequivalence to an already approved reference product, and therefore, the stability testing of a generic drug should be conducted in a similar manner to the reference product.

The FDA guidelines for generic drug development state that if the innovator product has been stability tested according to ICH guidelines, then the generic product should also be tested according to the same guidelines, and the same stability protocols should be used. This includes the use of bracketing and matrixing, if the innovator product used these approaches.

Additionally, the FDA also permits bracketing and matrixing for Generic Drug Development when the abbreviated stability protocols are used for submission, as long as the abbreviated stability data are sufficient to support the proposed shelf-life and storage conditions for the drug product.

However, it's important to note that the acceptance of Bracketing/Matrixing approach may vary among different regulatory agencies. Therefore, it is important to check the specific guidelines of the country where the generic drug is being developed to ensure compliance with the applicable regulations.


In summary, Bracketing/Matrixing can be acceptable during Generic Drug Development, but it should follow the guidelines of ICH or the regulatory agency of the country where the drug is being developed, and the stability testing of a generic drug should be conducted in a similar manner to the reference product.


Reference Guideline for Bracketing and Matrixing
The use of bracketing and matrixing in stability testing is generally accepted by regulatory agencies worldwide, but it is important to check the specific guidelines of the country where the drug is being developed to ensure compliance with the applicable regulations.

The International Conference on Harmonization (ICH) provides guidelines on the use of bracketing and matrixing in stability testing in its Q1A (R2) guideline on Stability Testing of New Drug Substances and Products. The guideline provides information on the conditions under which these approaches are appropriate, as well as the requirements that should be met for their use.

Additionally, the FDA has also issued guidelines for the use of bracketing and matrixing in stability testing in the Code of Federal Regulations (CFR) Title 21 Part 211.166. The guideline provides information on the conditions under which these approaches are appropriate, as well as the requirements that should be met for their use.

It is important to note that although bracketing and matrixing are generally accepted, the use of these approaches may be limited in certain situations. For example, if the product is intended for use in a critical population or for a critical indication, a full stability study may be required.

In summary, Bracketing and Matrixing are widely accepted approach in stability testing by regulatory agencies worldwide and are generally considered as cost-effective and efficient way of testing. But it's important to check the specific guidelines of the country where the drug is being developed to ensure compliance with the applicable regulations. The ICH guideline Q1A (R2) and FDA guideline 21 CFR 211.166 are the reference guidelines for these approaches.


Design Factors for Bracketing and Matrixing
Design factors are variables that are considered during the design of a stability study for their potential effect on the stability of a product. These factors can include:

Strength: The concentration or potency of the active ingredient in the product. Changes in strength can affect the stability of the product and may require different storage conditions.

Container size and/or fill: The size and amount of product in each container can affect the stability of the product. Larger containers may have more headspace and may require different storage conditions than smaller containers.

Formulation: The composition of the product, including the excipients used, can affect the stability of the product. Different formulations may require different storage conditions.


Packaging: The type of packaging used, such as glass bottles, plastic containers, or blister packs, can affect the stability of the product. Different packaging materials may have different permeability characteristics, which can affect the stability of the product.

Storage conditions: The conditions under which the product is stored, such as temperature, humidity, and light, can affect the stability of the product. Different storage conditions may require different testing protocols.

Shelf life: The expected shelf life of the product, which is the period of time during which the product is expected to remain stable under specific storage conditions.

Route of administration: The way the product is intended to be administered, such as oral, topical, or parenteral, can affect the stability of the product.

These factors must be taken into account during the design of a stability study to ensure that the study adequately assesses the stability of the product under different conditions and that the results of the study are meaningful.

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 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


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. 

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 t r e n g t h

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



t r e n g t h

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 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.

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 (months)

0

3

6

9

12

18

24

36

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


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