Statistical Considerations in Design Space Development (Part I of III) - Pharmaceutical Technology

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Statistical Considerations in Design Space Development (Part I of III)
The authors discuss the statistical tools used in experimental planning and strategy and how to evaluate the resulting design space and its graphical representation.

Pharmaceutical Technology
Volume 34, Issue 7, pp. 66-70

Q2: What role do experimental design and DoE play in establishing a design space?

A: There are underlying mathematical models to all scientific endeavors: compound properties, formulation development, and process development. Good approximate models can be developed to understand the effect of process parameters and material inputs on formulation and processing quality attributes, so that acceptable outcomes can be assured. One efficient and effective means to determine these approximate models, which are causal and not merely correlative, is through DoE. Causality in the relationship between factors and responses is a consequence of having observed specific changes in the responses as factor levels are varied. Applying DoE principles in conjunction with mechanistic understanding through the use of first principles when available provides a model-based scientific understanding of the system and process. A design space can be thought of as a summary of such understanding (i.e., a andquot;region of goodness andquot;). Other desirable DoE properties include maximizing the information with a minimum number of runs, exploring interactions between factors in an efficient way, allowing model testing and the ability to apply randomization and blocking principles to minimize biases.

Q3: How should responses (e.g., impurity level, particle size) be selected and what are the consequences if the responses are not appropriate or not well defined?

A: The first step in designing an experiment is to decide on the purpose of the study. The purpose may be to study the effect of certain factors on the responses, to estimate a predictive model that relates factors to responses, to screen factors, or to optimize the process. Once there is agreement on the purpose of the study, determine the most appropriate responses to measure.

Table I: Considerations in selecting responses when developing a design space.
Choosing responses that may be the CQAs or closely related to them is fundamental. It is therefore essential to decide on the candidate process parameters and CQAs as early as possible. It is important to think critically about which responses to measure so that during the statistical analysis one does not discover that a key response was not collected. In addition, there could be significant consequences if certain important data attributes are not considered when choosing the relevant responses. Some important considerations and consequences are listed in Table I.

Q4a: How should factors be selected?

A: Typically, Ishikawa charts or fishbone diagrams are useful in listing potential factors that could explain the variability in the key responses. Following a risk-based approach, one can choose a subset of potentially important primary factors. These factors can be classified as:

  • Controllable (e.g., equivalents of starting material, processing speed)
  • Mixture (i.e., when the independent factors are proportions of different components of a blend [e.g., amounts of excipients])
  • Blocking (i.e., when the experiment is carried out across several groups of runs [e.g., days might be a block when the experimental runs are carried out across several days])
  • Measurable, but not controlled or controlled within a range (e.g., amount of water in the reagent, % loss on drying)
  • Noise or nuisance (e.g., ambient temperature or humidity, that cannot be controlled and may not be capable of being measured): These factors are not accounted for in the statistical model and their overall effect is contained within the random residual variability estimate.

Q4b: What are the consequences if factors are not selected properly?

A: Ultimately, the factors selected for a DoE are those that experts involved in the risk assessment and historical review suggest could have an effect on the responses. It is possible for the selection to be incorrect, with the effect of the error varying from situation to situation, as outlined below.

  • It may be that for a particular study, important factors or their interactions were not included. They are important in the sense that had they been included, they would have shown substantial effects on the response(s). Because design space is limited to the region defined by the factor ranges considered in the study, the effect of factors not included in the study is unknown. For factors held constant during the study, additional trials would be needed to evaluate what effect, if any, they have on the response.
  • Those factors which are not controlled in the initial study (i.e., noise or nuisance factors), may affect the ability to accurately estimate and understand the impact of those factors studied in the initial design. The effect of a factor which had not been studied may appear later when it does vary. As a result, problem-solving work may be necessary, leading to a project delay. Although special designs can be conducted to address noise factors, this topic is out of scope in this article.
  • Including a factor in a DoE and finding that it has no effect on the responses may appear to be a waste of resources. In fact, there may be great value in learning about this lack of sensitivity because this factor can be set to minimize cost or increase convenience.

Q5: What is an appropriate number of factors to study in a designed experiment?

A: There is no strict requirement on the number of factors to be included in a study. The number of factors has to be balanced against the goal of the study (i.e., optimization or effect estimation and#8212;see Questions 8-18 in Part II of this series) and the required information for establishing a design space versus any time or resource constraints that are imposed on the experimenters. Fishbone diagrams and a risk-based approach could lead to identifying factors as those that have a high probability of impact, potential to impact, and also those that are very unlikely to impact the responses of interest. Time and resources are typically determined based on the number of factors, as considering more factors or desiring a more detailed understanding of the impact of the factors (e.g., response surface estimation) leads to a larger experiment.


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