How to report the DoE part of a Design Space document - using MODDE for Design of Experiments

Quality by Design and Design Space are concepts that have been around for quite some time in the pharmaceutical industry. Slowly the industry has warmed up to these concepts. Since the authorities provided the industry with guidelines, the interest has increased even more.
The vision of filing a Design Space is ambitious and may feel overwhelming when first pro-posed. However, over the years more and more knowledge has accumulated and the industry seems ready to take the next step. When taking this step a frequently asked question is: “How do we report the DoE part of a Design Space document internally as well as to the authori-ties?”

In Design Space projects different departments are commonly involved. Therefore a Standard Operating Procedure (SOP) to avoid errors due to misunderstandings is necessary.
This white paper will focus on the DoE part of the Design Space, and will also briefly touch on the workflow to establish before creating a successful report.

Establishing a Design Space

Establishing a Design Space is a process starting by defining the Critical Process Parameters (CPP's) and the Critical Quality Attributes (CQA's). Design of Experiments (DoE) is used to identify the important CPP's and their impact on the CQA's.

Case Types

The outcome of the DoE investigations should be judged on two criteria resulting in a case categorization: (1) is the CQA inside or outside the specification limits and (2) is the model statistically significant or not.   

Preparation for a Design Space filing

When starting the project of establishing and filing a Design Space, it is extremely important that the teams from the different departments "start on the same page", communicate and use the same terminology. Structure from the beginning to the end is Alpha and Omega for the filing process to run smoothly. Trivial things, such as an inconsistent naming of the input parameters (CPP's) and output parameters (CQA's) and their abbreviations can lead to numerous rewrites, if not addressed at the beginning.

Communication is Key

Start the project by gathering a representative from each involved department and discuss the topics in this section. Communication is the key and small misunderstandings can take a long time to realize and to correct.

Naming and Abbreviations

Create a file where abbreviations and names are given in alphabetical order.  Make this file accessible to all involved parts in the project. Assign a person from each department to communicate with the other departments so that the used names are unique and not used for another CPP's or CQA's.

The length of the abbreviations should be considered as this can be a limiting issue for plots and graph in the Design of Experiment software.

Traceability

Choose software that allows the name of the experiment to be traceable and visible in all plots.

Reporting a Design Space

Creating the report of the Design Space runs rather smoothly if all critical aspect mentioned earlier in this white paper are addressed correctly. The report can be build around a predefined template, based on the 4 cases mentioned above. A template created by Umetrics and can be accessed by contacting Umetrics. In the sections below this template will be explained and to some extent demonstrated.

Report template general content

The template includes the following general content:

• A list of the CPP's also referred to as the input parameters.
• A list of the CQA's, also referred to as the quality product parameters, and the process performance parameters.
• The used design and the model terms possible to estimate with this type of design.
• The design illustrated as a graph. This makes it easier to understand the design for the (untrained) reader. This can be done with up to 5 factors (CPP's) in Umetrics DoE software MODDE.
• A matrix displaying the design. In many complex processes it can be difficult to perform exactly the experiments suggested by the DoE. In these cases the report should include both the theoretical design and the actual design including an evaluation on whether or not the design has been distorted by the changes. An estimation of the distortion is the condition number.

The four cases

The analysis part of the report template begins with a table summarizing the quality of the models. This table contains the specification limits of the CQA's as well as any experiments that did not fulfill specifications. The quality of the model is described with the R², Q² and validity of the models and the standard deviation of the replicates.

The illustration and decision part of the analysis section is built around the 4 cases mentioned in the beginning of this white paper. For each case, specific plots are suggested.

Below is a list of plots to use for the four cases. Optional plots are also listed with the rational on when to use them.

Note that case 2 has many opportunities for different illustrations. This is of course related to the fact that this case does not represent a robust system as the CQA's are outside specification and there exists a significant relationship between changing the CPP's and the CQA's.

Below is an example of a report for a case 2 investigation. The example is based on GE Healthcares Capto S column. A full description of the analytical work is given in the article "Capto S Cation Exchanger for post-Protein A purification of monoclonal antibodies" at www.gelifesciences.com.

Report example, illustrating case 2

Input parameters (CPP's)

The three input parameters and the upper and lower limits of the design are listed in the table below.

Output parameter

Study design

The design used is a Central Composite Face centered design (CCF) with three input parameters (CPP's). The CCF design allows for all main, interaction and quadratic terms to be resolved in the system. Three center points were added for model diagnostics. Below the design is depicted.

The output parameter (CQA) and the specifications for this parameter are found in the table below.

The theoretical and the actual design plans were identical with a condition number of 4,44, see below.

*Center point

Model diagnostics

Below, the model diagnostics are displayed. We conclude that the investigation is a case 2 investigation as the model is significant (R², Q² and Model validity are close to 1) and 7 runs are outside the specification for the dynamic binding capacity of 10%.

Raw data illustration

The replicate plot is a simple illustration of the raw data. Note that the variation in the center points (N9, N10 and N11) is small compared to the overall variation in the data.

Model illustration

The coefficient plot illustrates which model terms that have the highest influence. In this case it is clear that conductivity and pH have a high influence on the output and residence time has a low influence.

Design Space illustration

A common way of illustrating the Design Space (see ICH Q8) is by using a contour plot. The quadratic term for pH and conductivity and their interaction term are illustrated by selecting them on the inner axes, as these two CPPs are the most important and their interaction is highly significant. The contour plots shows the accepted QB10% larger than 110. 

However, the contour plot point estimate does not show any probability estimate. For a probability estimate Monte Carlo simulations can be used around a process set point. The optimizer tool in MODDE was used to find the set point, followed by the Design Space estimating tool to find the region with low risk of failure.

The list and plots below shows the resulting Design Space.

Conclusion and what to next

Using the CPP settings in the Design Space table the predicted response profile clearly states that the risk of failure is less than 0.1% .

The next step, validation, is to conduct a design using the high and low limits of the estimated Design Space and the optimum as the new center point. This will result in a case 1 or 3 where a design space is possible to establish. A design space validation can then be performed on the design space in order to estimate the risk of failure.