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.

Design space is part of the US Food and Drug Administration andapos;s quality initiative for the 21st century which aims to move toward a new paradigm for pharmaceutical assessment as outlined in the International Conference on Harmonization andapos;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.

Figure 1: Areas of common statistical questions regarding the development of a design space. (FIGURE IS COURTESY OF THE AUTHORS)
The objective of this article is to provide 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. The answers provided herein 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 (see Figure 1).

In this series, the authors discuss the statistical tools used in the following: experimental planning and strategy, including the use, analysis, and interpretation of historical information; the analysis of a statistically designed experiment (DoE); defining a design space based on the results of the DoE; and evaluating the resulting design space and its graphical representation. The concept of risk is interwoven throughout the FAQs to emphasize the notion that risk management is inherent in virtually all development decisions (including all phases of development and clinical trials) and that the application of statistical thinking and statistical methods is intended to investigate, mitigate, and control risk.

The role of statistics with respect to the design space is grouped into sections as follows:
  • Experimental design planning (Questions 1-7, Part I of III)
  • The design in statistical DoE (Questions 8-18, Part II of III)
  • The analysis in statistical DoE (Questions 19-22, Part II of III)
  • Presenting a design space (Questions 23-24, Part III of III)
  • Evaluating a design space (Questions 25-29, Part III of III).

The set of questions and answers is not meant to be exhaustive; additional relevant questions could be posed that go into greater detail or scope in studying a design space. Nevertheless, these questions cover a broad enough range and detail to be useful to the practicing scientist or process engineer.


The goal of FDA andapos;s QbD initiatives and current good manufacturing practice (CGMP) for the 21st century is to more effectively and consistently produce high quality products through better scientific understanding and risk assessment of drug-product formulation and drug-product and drug-substance manufacture. Quality systems are modified based on designing quality into the process and product throughout the life cycle. Early in the design of the manufacturing process, it is recommended that a risk assessment be performed by a cross-functional team to identify the critical quality attributes (CQAs) and process parameters believed to affect the CQAs, and the effect of the quality of the incoming materials in the manufacturing processes.

According to ICH guidelines Q8(R2), Q9, and Q10, CQA is defined as a physical, chemical, biological, or microbiological property or characteristic that should be within an appropriate limit, range, or distribution to ensure the desired product quality. A design space is a multidimensional combination of input variables (e.g., material attributes), their interactions, and process parameters that have been demonstrated to provide assurance of quality. A statistical and/or mechanistic model can be used to establish a design space. In addition to the establishment of a design space, a target operating setting within the design space is defined to ensure a certain desired level of consistency of the product and process performance during routine operations. As the operating range of process variables approaches the boundary defining a design space, the risk of failing a specification may increase. Whether or not there is statistical significance to this risk (i.e., effect on quality and, thus, safety and efficacy) depends on the proximity of the operating variables andapos; ranges to the design space boundary and the attenuation of the control strategy to detect and mitigate the risk. The execution of an operating plan, including an appropriate control strategy and appropriate process monitoring, is essential to the success of the overall process and product performance.

Statistics is the science of making decisions in the face of uncertainty. Statistical thinking and methods thereby bring established tools and approaches to the determination of a design space, and help to maintain a process that is in control and capable of producing appropriate high quality product. Statistical experimental design is one especially useful tool for establishing a design space in conjunction with risk-based and other modeling tools. This tool provides an effective and efficient way to simultaneously test for factor effects and interactions and to describe causative relationships between process parameters or input materials with the quality attributes.