Statistical Considerations in Design Space Development (Part II of III)

The authors discuss the statistical tools used in experimental planning and stategy and how to evaluate the resulting design space and its graphical representation.

Part I of this article appeared in the July 2010 issue of Pharmaceutical Technology and discussed experimental design planning (1). This article, Part II, addresses design and analysis in statistical design of experiments (DoE). Part III, to be published in the September 2010 issue of Pharmaceutical Technology, will cover how to evaluate a design space.

Design space is part of the US Food and Drug Administration's quality initiative for the 21st century which seeks to move toward a new paradigm for pharmaceutical assessment as outlined in the International Conference on Harmonization's quality guidelines Q8, Q9, and Q10. The statistics required for design-space development play an important role in ensuring the robustness of this approach.

This article provides concise answers to frequently asked questions (FAQs) related to the statistical aspects of determining a design space as part of quality-by-design (QbD) initiatives. These FAQs reflect the experiences of a diverse group of statisticians who have worked closely with process engineers and scientists in the chemical and pharmaceutical development disciplines, grappling with issues related to the establishment of a design space from a scientific, engineering, and risk-based perspective. Questions 1–7 appeared in Part I of this series (1). The answers provided herein, to Questions 8–22, constitute basic information regarding statistical considerations and concepts and will be beneficial to a scientist working to establish a design space in collaboration with a statistician.

Statistical experimental design

The following questions address types of experiments and appropriate design choices. The selection of the design depends on the development stage, available resources, and the goal of the experiment. The type and size of the design for an experiment depends on what questions need to be answered by the study. In general, there are three types of experiments: screening experiments to select factors for more experimentation or to demonstrate robustness, interaction experiments to further study interactions between factors of interest, and optimization experiments to more carefully map a region of interest.

Q8: Why are one-factor-at-a-time (OFAT) designs misleading?

A: OFAT experimentation is effective if the error in the measurements is small when compared with the difference one desires to detect and if the factors do not interact with one another. If either of condition is violated, the OFAT methodology will require more resources (experiments, time, and material) to estimate the effect of each factor of interest. In general, the interactions between factors are not estimable from OFAT experiments. Even when there are no interactions, a fractional factorial experiment often results in fewer resources and may provide information on the variability. Experimenters may be able to estimate interactions based on a series of experiments that were not originally designed for that purpose, but this approach may require more sophisticated statistical analyses.

Q9: If I have a model based on mechanistic understanding, should I use experimental design?

A: Experimental design can provide an efficient and effective means for estimating mechanistic model parameters. Further, experimental design can be used to minimize the number of runs required to estimate model coefficients. The underlying functional form of the surface, including interactions, may be known so that the interest is focused on estimating the model coefficients. Random variation should also be estimated and incorporated into the mechanistic models; the incorporation of error is often omitted from these models. General mechanistic understanding can still be used to select factors for evaluation, assist with identifying interactions, and assure that the model is appropriate. The appropriate design to accomplish the goals listed above may differ from factorial designs and may result in levels of factors that are not equally spaced.

Another advantage of using an experimental design is that an empirical model can be fit to the data and compared with the mechanistic model as part of model verification (see Questions 10–13).