Design of Experiments for Analytical Method Development and Validation

Design of experiments (DOE) is a well-proven characterization approach within product and process development and a key aspect of quality by design. Recently, more attention has been placed on applying DOE to analytical methods. DOE for analytical methods has three major applications: method development for new methods or those that need improvement, method validation, and quantitation of the influence of analytical methods on product and process acceptance and out-of-specification (OOS) rates. Method development seeks to understand where critical process parameters are in the analytical method and to minimize their influence on accuracy and precision. DOE for method validation seeks to validate the analytical method for a range of concentrations so that changes in formulation or concentration will not require additional validation as they are changes within a characterized design space. Once methods have been developed, qualified, and validated, the impact they have on OOS rates and process capability needs to be quantified and evaluated to determine their fitness for use.    

A systematic approach for using DOE for analytical method development and validation is discussed in this paper and was written in line with the International Conference of Harmonization (ICH) Q2(R1), Q8(R2), and Q9 guidelines (1-3). A quantitative understanding of the factors that influence resolution, linearity, precision, and accuracy is integral to applying DOE to method development.

Textbook approaches to DOE generally suggest a sequential approach to DOE: screening studies, characterization studies, and optimization of the method or process. This approach applied to analytical methods is often not practical as 10-20 methods are often used for drug substance and drug-product evaluation and the amount of time and materials needed to follow the three steps (i.e., screen, characterize, and optimize) would consume unreasonable amounts of resources. The sequence generally recommended by the author for method development is understanding the purpose of the study, perform risk assessments to screen out factors that may or may not have an influence on the analytical method (screening variables by logic and an examination of their scientific potential for influence), and characterization studies to quantify and minimize their influence on precision, accuracy, and linearity.

Assays and measurement systems must be viewed as a process (see Figure 1). The measurement process is made up of methods, standards, software, materials, chemistry, reagents, analysts, sample preparation methods, environmental conditions, and instrumentation/equipment. Quality risk management and statistical data analysis techniques should be used to examine the process of measurement and identify factors that may influence precision, accuracy, linearity, signal to noise, limits of detection and quantification, and/or any other assay attributes to achieve optimal assay results.

DOE for Method Development
Design of experiments can be applied to many aspects of method development; however, the following will provide the typical steps for designing and analyzing experiments for analytical methods.

• Define the purpose (e.g., repeatability, intermediate precision, accuracy, LOD/LOQ linearity, resolution).  
• Define the range of concentrations the method will be used to measure and the solution matrix it will be measured in.
• Develop/define the reference standards for bias and accuracy studies.
• Define the steps in the method and any associated documentation.
• Determine the responses that are aligned to the purpose of the study.  
• Complete a risk assessment of all materials, equipment, analysts, and method components aligned to the purpose of the study and the key responses that will be quantified.  
• Design the experimental matrix and sampling plan.  
• Identify the error control plan and run the study.
• Analyze the study and determine settings and processing conditions that improve method precision and minimize bias errors. Document the design space of the method and associated limits of key factors.
• Run confirmation tests to confirm settings improve precision, linearity, and bias.  Evaluate the impact of the method on product acceptance rates and process capability.

Identify the Purpose of the Method Experiment
The purpose of the analytical method experiment should be clear (i.e., repeatability, intermediate precision, linearity, resolution). The structure of the study, the sampling plan, and ranges used in the study all depend on the purpose of the study. Designing a study for accuracy determination is very different from a study that is designed to explore and improve precision. Accuracy, for example, does not require sample replicates to estimate the mean change in the response. Precision, however, requires replicates and duplicates to evaluation variation in the sample preparation and in other aspects of the method. The purpose of the study should drive the study design.

Define the Range of Concentrations to be Evaluated
Define the range of concentrations used to measure and the solution matrix it will be measured in. Ranges of the concentration will generate the characterized design space so they should be selected carefully as it will put restrictions on how the method may be used in the future (see Figure 2).  Normally five concentrations should be evaluated per ICH Q2R1.

Define all Reference Standards Used in the Study

Develop/define the reference standards for bias and accuracy studies. Without a well-characterized reference, standard bias/accuracy cannot be determined for the method.  Care should be made in selecting, storing, and using reference materials. Stability of the reference is a key consideration and accounting for degradation when replacing standards is critical.

Identify all Steps in the Analytical Method
Lay out the flow or sequence used in the analytical method. Define the steps in the method (e.g., standard operating procedures [SOPs], procedures, or work instructions), all chemistries, reagents, plates, and materials used in the method and all instruments/sensors and equipment. Identify any steps in the process, materials, analyst techniques, or equipment that may influence bias or precision.

Determine the Reponses
Determine the responses that are aligned to the purpose of the study. Raw data and statistical measures such as bias, intermediate precision, signal to noise ratio, and CV are all responses and should be considered as independent results from the method. Make sure the data table is set up so that it can collect the raw data, the statistics can be easily generated from that raw data, and there is a direct link from the statistics to the data.

Perform a Risk Assessment
A risk assessment of the analytical method is used to identify areas/steps in the method that may influence precision, accuracy, linearity, selectivity, signal to noise, etc.  Specifically, the risk question is: Where do we need characterization and development for this assay? Complete a risk assessment of all materials, equipment, analysts, and method components aligned to the purpose of the study and the key responses.  The outcome of the risk assessment is a small set (3 to 8) of risk-ranked factors that may influence the reportable result of the assay.  There are many kinds of factors, so factor identification and how to treat the factor in the analysis are crucial to designing valid experiments. There are controllable factors: continuous, discrete numeric, categorical, and mixture. There are uncontrollable factors: covariate and uncontrolled. In addition, there are factors used in error control: blocking and constants (see Figure 3).

Design the Experimental Matrix and Sampling Plan
For small studies using two or three factors, a full factorial type design may be appropriate.  When the number of factors rises above three, a D-optimal type custom DOE design should be used to more efficiently explore the design space and determine factors that impact the method. There are many good software programs today that help the user define statistically valid experiments and can be customized to meet the user’s needs.

The experimental matrix is one consideration and the sampling plan is another. Replicates and duplicates are essential to quantification of factor influence on precision.  Replicates are complete repeats of the method including repeats of the sample preparation, duplicates are single sample preparations but with multiple measurements or injections using the final chemistry and instrumentation. Replicates provide total method variation and duplicates provide instrument, plate, and chemistry precision independent of sample preparation errors. If the experiment is designed properly many of the requirements for method validation (Figure 4) can be directly met from the outcomes of the method DOE.

Identify the Error Control Plan
Make sure to measure and record uncontrolled factors during the study. Analyst name, equipment ID, out time, hold times, ambient temperature, temperature at the beginning and end of an operation, transfer times, pH, and incubation time may hold valuable information on factors that impact the method. What factors will be restricted or held constant during the study?  Do you need to block for batch, lot, sample prep, or instruments that may have an influence on the reportable result?

Analyze the DOE and Determine the Settings and Design Space
Use a good multiple regression/analysis of covariance (ANCOVA) software package that allows the DOE factors and any uncontrolled variables to be correctly evaluated. Analyze the study and determine settings and processing conditions that improve method precision and minimize bias errors (see Figure 5). When using statistics from the method (e.g., CV, mean, standard deviation), rather than raw data, make sure to weigh the analysis by the number of replicates or duplicates to assure statistical tests and confidence intervals are meaningful. Determine the design space and allowable ranges for all key factors that influence the method.  

Verify the Model and Determine the Impact of the Method on Specifications and Capability
Run confirmation tests to confirm settings improve precision, linearity, and bias. Evaluate the impact of the method on product acceptance rates and process capability. Using an accuracy-to-precision (ATP) model (4), it is possible to visualize the relationship of precision and accuracy on product acceptance rates.  The ATP model shows how changes in precision and accuracy impact product acceptance rates and the assay error design space relative to product acceptance specification limits.  
The attention paid to method development, validation, and control will greatly improve the quality of drug development, patient safety, and predictable, consistent outcomes (see Figure 6).

Summary
Design of experiment is a powerful and underutilized development tool for method characterization and method validation. Analytical professionals need to be comfortable using it to characterize and optimize the analytical method. If used properly and during development, DOE will provide significant improvements in precision and a reduction in bias errors. It will further help to avoid costly and time consuming validation studies as concentrations are modified in formulations and dosing schemes are changed for drug product and drug substance.  

References
1. ICH, Q2(R1) Validation of Analytical Procedures: Text and Methodology (ICH, 2005).
2. ICH, Q8(R2) Pharmaceutical Development (ICH, 2009)
3. ICH, Q9 Quality Risk Management (ICH, 2006).
4. T.A. Little, Assay Development and Method Validation (2014).

About the Author
Thomas A. Little is president of Thomas A. Little Consulting, [email protected]