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
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.
Table I: Considerations in selecting responses when developing a design space.
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
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
- 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
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.