Design of Experiments for Formulation Development

During the 1920s, a British statistician named Ronald Fisher put the finishing touches on a method for making breakthrough discoveries. Some 70 years later, Fisher's method, now known as design of experiments, has become a powerful software tool for engineers and researchers.

But why did it take engineers so long to begin using DOE for innovative problem solving? After all, they were ignoring a technique that would have produced successes similar to the following modern-day examples:

John Deere Engine Works in Waterloo , Iowa , uses DOE software to improve the adhesion of its highly identifiable green paint onto aluminum. In the process, the company has discovered how to eliminate an expensive chromate-conversion procedure. Savings: $500,000 annually.

Ski manufacturer K2 Corp. in Vashon, Washington , is hampered by a new ski's complex design that produces a 30-percent higher scrap rate. DOE finds the reason and the solution. Savings: Press downtime tumbles from 250 labor-hours per week to a mere 2.5.

DOE and design space¹

The applicant can choose to conduct pharmaceutical development studies that can lead to an enhanced knowledge of product performance over a wider range of material attributes, processing options and process parameters. Inclusion of this additional information in this section provides an opportunity to demonstrate a higher degree of understanding of manufacturing processes and process controls. This scientific understanding establishes the design space. In these situations, opportunities exist to develop more flexible regulatory approaches, for example, to facilitate:

· risk based regulatory decisions (reviews and inspections);

· manufacturing process improvements, within the approved design space described in the dossier, without further regulatory review;

· “real time” quality control, leading to a reduction of end-product release testing.

To realise this flexibility, the applicant should demonstrate an enhanced knowledge of product performance over a range of material attributes (e.g. particle size distribution, moisture content, flow properties), processing options and process parameters. This knowledge can be gained by, for example, application of formal experimental designs* or PAT*. Appropriate use of risk management principles can be helpful in prioritising the additional pharmaceutical development studies to collect such knowledge. The below given camparision is chart current conventional approach and quality based design which is scientific approach encouraged by US food and drug administration.

The design and conduct of the pharmaceutical development studies should be consistent with their intended scientific purpose and the stage of the development of the product. It should be recognized that the level of knowledge gained, and not the volume of data,provides the basis for science-based submissions and their regulatory evaluation.

Design Space: the design space is the established range of process parameters that has been demonstrated to provide assurance of quality. In some cases design space can also be applicable to formulation attributes. Working within the design space is not generally considered as a change of the approved ranges for process parameters and formulation attributes. Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process.

Design Space²

The design space is the established range of process parameters and formulation attributes that have been demonstrated to provide assurance of quality. It forms the linkage between development and manufacturing design

Establishment of Design Space through product and process design

Making changes to the formulation and manufacturing process during development generates valuable data that supports establishment of the design space.It is implied that both positive and negative results are important to understanding the design space.

Minimum requirements are to provide data to support the proposed formulation and manufacturing process Reports should identify properties of the active ingredient, excipients and manufacturing process that are critical and that present significant risk to product quality and therefore should be monitored or otherwise controlled. Applicants can choose to perform additional development studies that enhance knowledge of product performance over a wider range of attributes, processing options and process parameters.Sharing such information with the regulatory bodies in the development report provides an opportunity to demonstrate an higher degree of understanding of manufacturing processes and process controls This effectively establishes the design space.

This sharing of knowledge of the design space with the regulatory bodies will open the door to: True risk based reviews and inspections Manufacturing process improvements within the approved design space without further regulatory oversight Real time quality control leading to a reduction in end product release testing.

Regulatory and Business Advantages of using Design Space

Working within the design space is not generally considered as a change of the approved ranges for process parameters and product attributes. Result will clearly be less supplemental regulatory filings. Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process

De-emphasize end product testing and may eliminate certain release tests. Process knowledge can eliminate redundant testing for those attributes that are demonstrated to be controlled in-process Diminish the burden for validating systems by providing more options for justifying and qualifying systems intended to control critical attributes of materials and processes

Challenges and Barriers to Implementation of Design Space

Fear of punishment resulting from sharing of full spectrum of knowledge and data generated to implement the concepts Industry is well experienced in the “current state” of design and needs better guidance on on risk management and quality systems. Potentially higher upfront costs and expanded development timelines

Understanding of DOE :³

Three close friends: Naren, Deepak and Ravi were walking to college together every day, pass a large house with neatly manicured gardens. A young girl (renu) rushes out into the greens and abruptly pauses at the sight of three young men passing her gate.

Renu gives them a dazzling smile and winks at them. Now, this is serious. "But there is a little catch. Who did she wink at? Certainly, she couldn't be winking at all three of them?

The smile and the wink fail to cheer them the next day. They must find out which one of them Renu fancies. They decide to find out through planned experimentation. Instead of all three of them walking together, they decide to go past her house in a well-planned pattern of twos and singles. They already know Renu's response and tabulate it as below:

The data is building up, and they are all set to jump to wishful conclusions. They tell Deepak that she's just playing games, and keep him back at home. Naren and ravi take a confident walk, eager to prove our theory of Renu playing games, but are in for a shock. Renu simply does not make an appearance. Less sure about themselves, they tabulate this result too.

Deepak gives the laugh that love struck boys usually give, and suggests that they now walk one person at a time. Naren and ravi do thier part and encounter Renu's vanishing trick. Results are dutifully tabulated.

Deepak is on cloud nine by now. He puts on his best shirt, shines his shoes, and walks past Renu's house, chin up. He actually walks up and down a couple of times, but Renu still fails to appear. Naren and ravi take pleasure in tabulating this result.

Deepak by now looks like a deflated balloon, and Naren and ravi were frankly perplexed. "What's the meaning of this? Is she trying to twist them around her little finger?" Rather than jumping to conclusions, they decided run this combination of experiments again. At the end of all the runs, they decided analyze the data and form some hypothesis.

They consolidated the results as follows:

They analyzed the results by the change in Renu's response to the presence or absence of each of the Casanovas. Results (discovered later that they are called Effect Plots in the Design of Experiments (DOE) parlance) showed as follows.

Obviously, Deepak is the clear winner.

There were three Factors in this experiment: Naren, Ravi and Deepak. A factor is an independent variable in an experiment whose state can be varied. In a planned experiment, the factors are deliberately varied in a predetermined manner. The response is measured at every run of each combination. In a scientific experiment, pressure and temperature of the reaction could be two of the factors. These are varied across the experimental pattern and the response characteristic (e.g., yield of the reaction) is measured.

Each factor was evaluated at two Levels: the person was Present or Absent. A level is a state of the factor that is deliberately varied. Experimentation is typically done at two, or occasionally three levels for every factor. Combining all factors and their levels can become too large and daunting a task if every factor is changed one at a time. An efficient experimental design that varies multiple factors at the same time can reduce the number of runs to a great extent, still providing enough information for confident results. Levels can be discrete like the Present / Absent levels that our experiment had, or can be numeric, such as 80 degrees / 100 degrees centigrade for the temperature factor in a chemical reaction.

The objective variable that is calculated is the Response, which measures:

The relationship between the change in level of each of the factors and the change in response. Secondly, the change in response for a change in each factor level (sensitivity)

In this experiment, the Response was attribute data expressed as whether Renu winked or not. The Response can also be variable data, such as a change in purity from 90% to 95%, where the numerical value of the response is averaged for each level. The difference in response is called the Effect, and is expressed using an Effects Plot as shown above.

The experiment conducted was Balanced since each factor at each level was evaluated at an equal number of other factor-level combinations. A balanced experiment gives the same evaluation advantage to each factor and helps remove bias that may appear as a result of an unequal amount of data for each factor-level combination.

Randomization was achieved by rolling the dice to determine the sequence of runs. This is important since it gives all external factors an equal chance to affect every run of the experiment. A non-randomized experiment stands a great risk of external factors acting in a systematic manner, adding noise to the response.

Conducting two sets of experimental runs led to Replication, providing more data and greater confidence in evaluating the results.

What then went wrong in run 7 and run 14? Why didn't Renu respond to Deepak's presence?

In the first case (run 7), it was a Lurking Variable that played a role. Renu happened to have a father who had a very foul temper. On the day Deepak went alone in the first Replication, the father had confined Renu to her room for some trivial reason. A lurking variable like Renu's father is an external factor that strikes suddenly and randomly to affect the response and confuse the results. In the second case (run 14), it was Renu herself who was in a foul mood and refused to perform as expected. After all she was human, and couldn't be expected to fall in line with statistics all the time. This represents an Experimental Error commonly encountered in experimentation.

Selection of DOE: ⁴

When selecting DOE software, it's important to look for not only a statistical engine that's fast and accurate but also the following: A simple user interface that's intuitive and easy-to-use. A well-written manual with tutorials to get you off to a quick start. A wide selection of designs for screening and optimizing processes or product formulations. A spreadsheet flexible enough for data entry as well as dealing with missing data and changed factor levels.

Software that randomizes the order of experimental runs. Randomization is crucial because it ensures that "noisy" factors will spread randomly across all control factors. Design evaluation tools that will reveal aliases and other potential pitfalls. Functions such as square root or log base 10 allow users to transform their responses, thus improving the statistical properties of the analysis. Software that lets to control the graphical display by selecting plot axes, variable ranges for response surface designs and contour levels.

Advantages of DOE:⁵

There are several advantages to statistically designed experiments, and when compared with other test methods, the results are striking. One chief reason is that it is strongly favored by regulatory agencies because it justifies the choice of ranges and finds a robust (optimum) region. In addition, it gives the researcher the ability to study interactions between factors. In contrast, merely studying one factor at a time does not allow the researcher to study interactions and is not scalable to production.
It provides a more economical use of resources, especially when many factors exist and provides a greater chance of finding optimum conditions. Finally, predictions can be made about future experiments.

Statistical optimization allows the formulator to study a wide range of independent and dependent variables. Independent variables include formulation issues such as granulating solvent/lubricant/disintegrant /diluent concentrations, etc. or process issues such as tablet compaction pressure, mixer speed, lubrication time, etc.
Dependent Variables; i.e., responses that can be measured, include tablet dissolution/disintegration time/hardness/friability, etc

Types of statiscal design:⁶

There are several types of statistical design for pharmaceutical formulations, including:

• Factorial Designs: (both full and fractional factorials);
• Sequential Simplex Techniques;
• Response Surface Methodology;
• D-Optimal Techniques and
• I-Optimal Techniques.

DOE Methodology :

(1) Choose experimental design
(e.g., full factorial, d-optimal)

(2) Conduct randomized experiments

(3) Analyze data

4) Create multidimensional surface model
(for optimization or control)

Conclusion:

Statistical optimization enables a pharmaceutical scientist to define a formulation with optimum characteristics. A large amount of data can be generated from a limited number of experiments, which facilitate an in-depth understanding of the formulation and its manufacturing process. Statistical optimization can also provide solutions to larger-scale manufacturing problems, which occasionally arise.

Importantly, statistical optimization experimentation and analysis provides strong assurances to Regulatory Agencies regarding superior product quality.

Reference:

1. Q8 Pharmaceutical Development – FDA guidance

2. Design Space and PAT” - Q8 ICH Draft Guidance on Pharmaceutical Development by M. Kovalycsik, AVP, Wyeth Research Vaccines R&D, Quality Operations.

3. Three Romeos And A Juliet An Early Brush With Design Of Experiments By Ravindra Khare

4.How to Select Design of Experiments Software by Rich Burnhamwww.sixsigma.com

5. Role of Statistics in Pharmaceutical Development Using Quality-by-Design Approach – an FDA Perspective by Chi-wan Chen, Ph.D and Christine Moore, Ph.D. office of New Drug Quality AssessmentCDER/FDA.

6. Statistical Optimization of Pharmaceutical Formulations by P.K. Shiromani President Shirman Pharmaceutical Consulting