Save Money By Using Bracketing and Matrixing

The process of validating a stability claim can be a very costly and time-consuming exercise.  Therefore, it is important that a significant amount of thought be put into the study design.  When appropriate, one also needs to take advantage of acceptable methodologies for reducing the overall cost of these studies.  This article will summarize FDA Guidance on “Q1D Bracketing and Matrixing Designs for Stability Testing of New Drug Substances and Products”.  The of use bracketing and matrixing is an approach used by manufacturers in many industries, including the pharmaceutical industry, to reduce the costs of stability studies.


A Full Study Design is one in which every combination of all design factors (i.e. strength, package size, fill volume etc) are tested at all time points.  If the company designing the study had only one configuration for their product, and they planned on selling millions of units of that one configuration, a full study design, even though it is more expensive, is a low risk approach for conducting stability studies. For companies with multiple product lines, each having multiple configurations, the option of using a Reduced Study Design that utilizes Bracketing and/or Matrixing is an important consideration.  When considering a reduced study design, known attributes of the product configuration must be taken into consideration.  For example…

  • Does the active pharmaceutical ingredient (API) have inherent stability issues?
  • Are the materials of composition the same for the different package sizes?
  • Is the head space for different package sizes similar?
  • Does the API have known interactions with the container closure system (CCS)?

Subtle differences in the components (i.e. container closure system) within product line, especially for products with inherent stability issues, may translate into instability of the product, and therefore must be examined.  Reduced studies need to be scientifically justified, regardless of whether they are based on bracketing, matrixing, or a combination both.


Bracketing is a reduced study where the extremes of the various design factors are tested at all time points.

  • Strength of the drug is a design factor where bracketing can be used to reduce the cost of a study. A bracketed study tests the highest and lowest strengths of a specific product formulation.  Examples of products where this would be a consideration are pellets, tablets, and capsules with identical or similar formulations but different plug or capsule sizes. Bracketing may also be used for solutions where the formulation remains constant and only the active ingredient varies in concentration.  Bracketing should not be used if the excipients differ between formulas.


  • Container Closure Sizes and/or Fill volume are also design factors where a bracketed study design may be utilized. If both the container closure and the fill volume vary it should not be assumed that the largest and smallest containers represent the extremes.  When constructing a study design, attributes such as wall thickness, surface area and/or headspace to volume ratio, and water vapor and/or oxygen permeation rate may play a factor in stability and will need to be considered.

Upon completion of a bracketed study, the BUD for an intermediate should not exceed the least stable extreme condition.  For example, if the highest strength for a drug is more stable than the lowest strength, then the intermediate strength BUD is based on lowest strength drug.

An example of a bracketed study may be found in Table 1 below.  In this study, Fentanyl Citrate is compounded at 3 different strengths and filled into 3 different size containers with the same materials of compositions.  In this example, all batches and container closure combinations met specification at 90 days except Batch 1 of the 1mL size for Fentanyl Citrate 2mcg/mL, which passed at 60 days but failed the 90-day time point.  The BUD for all container sizes of the 50mcg/mL is 90 days, as is the case for the 10mL container of the 2mcg/mL and 10mcg/mL strength (see green highlighted configurations).  Since the strength for the 1mL package size of the 2mcg/mL passed at 60 days and failed at 90 days it can only be assigned a BUD of 60 days.  Given this information, the intermediate configurations that were not tested in this study (i.e. 1mL and 5mL 10mcg/mL; 5mL 2mcg/mL), can only receive a BUD of 60 days (red highlight configurations).  To assign a BUD of 90 days to these combinations would require that they be tested for stability, which results in essentially a full study design.

Table 1:  Fentanyl Citrate Bracketed Study

T/## – Tested/Last Time Point within Specification


Unlike Bracketing that tests the extremes of design factors at all timepoints, a matrixed design reduces the total cost of a study by testing a subset of the total of number of possible samples for all design factor combinations at specified timepoints.  The premise behind using this approach is the stability of each subset of samples tested, represents the stability of all samples at a given time point, even if all samples were not tested.

An example of a basic matrix study design may be found in Table 2.  This study is comprised of 3 batches of two (2) strengths of a drug tested over a two-year time period.  If the study duration goes beyond 12 months, all batches and strengths are required to be tested at zero time, 12 months, and the final time point (see Table 2).  If any of the batches had an OOS result at 16, 20 or 24-month, the maximum dating that would be given for the strength with the failing result would be 12 months.  In the example below, Batch 3 of Fentanyl Citrate 2mcg/mL was OOS at 24 months.  Therefore, that strength can only get a 12-month BUD.  If any batch had an OOS result at 3, 6, 9 or 12 months for a specific strength, the study for that strength would need to be repeated.  In this example, all three batches of Fentanyl Citrate 50mcg/mL were within specification for all time points tested, so that strength would receive at 24-month BUD.  If there were intermediate strengths of Fentanyl Citrate (i.e. 10mcg/mL), those strengths could only be assigned a BUD of 12months.  If a longer BUD than 12 months was desired, a stability study would need to be performed on the intermediate strength.

Table 2:  Fentanyl Citrate Matrixed Study

T = Tested

Examples of more complicated matrixed stability studies may be found below.  Both studies have three (3) strengths of drug, with each strength filled into three (3) different sized containers, with each strength and container combination having 3 batches.  One is being matrixed on time points only (see Table 3), and the other on time points and design factors (See Table 4).  The key for the time points tested (i.e. T1, T2, T3) may be found in Table 5.

Table 3:  Matrix Design on Time Point Only

Table 4:  Matrix Design on Time Points and Design Factors

Table 5:  Key for Time Points Tested (i.e. T1, T2, T3)

The degree of reduction of a study depends on the number of design factor combinations.  The more design factors and levels for each factor, the greater the opportunity for reduction.  Even though a reduced design is less costly, a higher reduction in study design often correlates with lower BUD’s.  For example, the study represented in Table 4 would be less costly than the Table 3 study but would have a higher likelihood of generating a lower BUD.  It is for this reason that matrix study designs that utilized both time point and design factor reduction be used for products with strong stability profiles.  For products where the supporting data signals significant stability issues, a full design or a bracketed study design is more appropriate.

In summary, bracketing and matrixing are industry accepted methodologies for minimizing the significant costs associate with establishing and maintained stability claims.  If these methodologies are to be employed, careful consideration should be given to the stability profile of the drug before designing a study.  Drugs with strong stability profiles can tolerate greater reduction in the study design.  Whereas, more robust designs such as a full design, bracketing or matrixing on time points should be considered for products with known stability issues.  Lastly, and most importantly, whichever approach is used to design the study, scientific justification for the design used, should be documented.


– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –