Unit 5. Design and Analysis of experiments: Factorial Design: Definition, 22, 23design. Advantage of factorial design Response Surface methodology: Central composite design, Historical Design, and Optimization Techniques

Unit-V
1. Design and Analysis of experiments:
2. Factorial Design: Definition, 22
, 23
design. Advantage
of factorial design
3. Response Surface methodology: Central composite
design, Historical Design, and Optimization
Techniques

What is DOE software?
• DOE is a powerful data collection and analysis tool that can be used in various
experimental situations.
• It allows for multiple input factors to be manipulated, determining their effect
on a desired output (response)
• A designed experiment is a type of scientific research where researchers
control variables (factors) and observe their effect on the outcome variable
(dependent variable).
• Design of Experiments (DoE) is a structured approach that examines how
various elements influence a particular result.
• By evaluating multiple factors at once, DoE allows scientists to uncover the
impacts of each element and their combinations, yielding a comprehensive
comprehension of the entire system

Why Is It Always Better to Perform a Design of E
xperiments (DOE) Rather than Change One Fact
or at a Time?

Top 5 Best Design of Experiment
Software
• Here are the top 5 DoE software used by professionals in
industry and academia
• Quantum Boost
• JMP
• DesignExpert
• Minitab
• Modde‍
•Quantum Boost
•JMP

•DesignExpert
•Minitab
•Modde‍

Factorial Design: Biostatistics and Research Methodology
Definition
• A factorial design is a research design used in experiments to
investigate the effects of two or more independent variables
simultaneously on a dependent variable.
• In a factorial design, every level of each independent variable is
combined with every level of the other independent variables to
create all possible combinations or conditions.

• For example, in a 2×2 factorial design, there are two independent
variables, each with two levels.
• The first independent variable has levels A and B, while the second
independent variable has levels X and Y.
• The experiment would include all four possible combinations: AX, AY,
BX, and BY.
• The dependent variable is then measured for each combination.

Introduction
• Factorial design is a type of experimental design in which researchers
manipulate two or more independent variables simultaneously to
observe the effects of each variable and their interaction with the
dependent variable.
• In other words, factorial design allows researchers to examine the
effect of each independent variable on the dependent variable while
controlling for the other independent variable(s).

• Factorial design can be represented in a matrix format, where each row
represents a unique combination of the independent variables, and the
cells within the matrix represent the experimental conditions.
• For example, in a 2×2 factorial design, there are four possible
combinations of the two independent variables, resulting in four
experimental conditions.
• Factorial design is commonly used in psychology, sociology, and other
social sciences to test the effects of different factors on human
behavior, attitudes, and perceptions.
• It is also used in other fields, such as medicine, engineering, and
agriculture, to study the effects of different treatments or interventions
on biological, mechanical, or environmental systems.

Types of Factorial design in Pharmaceuticals
• In pharmaceutical research and development, factorial designs are
commonly used to investigate the effects of multiple factors or variables on a
particular outcome or response. Here are some types of factorial designs
frequently employed in pharmaceutical studies:
1. Full Factorial Design: In a full factorial design, all possible combinations of
factor levels are studied. For example, if there are two factors, each with
two levels, a full factorial design would involve four treatment groups
representing all possible combinations of the factor levels. This design
allows for the evaluation of main effects (individual effects of each factor)
and interaction effects (combined effects of multiple factors).

• Fractional Factorial Design: Fractional factorial designs are used when
studying a large number of factors or when there are resource limitations.
These designs involve selecting a subset of factor combinations to be studied,
thereby reducing the number of treatment groups required. Fractional
factorial designs allow for the estimation of main effects and some, but not all,
of the possible interaction effects.

3. Plackett-Burman Design: Plackett-Burman designs are efficient
screening designs used to identify the most influential factors among a large
number of potential factors. These designs are particularly useful when the
number of factors is much larger than the available resources. Plackett-Burman
designs involve selecting a subset of factor combinations based on a specific
criterion, such as orthogonal arrays, to estimate main effects without
considering interaction effects.
4. Taguchi Design: Taguchi designs, also known as robust designs, are
used to optimize a process or formulation with respect to multiple factors while
minimizing the variability of the response. These designs consider both the
mean and variability of the response to identify the optimal factor levels.
Taguchi designs often employ an orthogonal array, allowing for efficient
experimentation with a reduced number of runs.

5. Central Composite Design (CCD): CCD is a type of response surface
design used to investigate the relationship between factors and response
variables. It involves studying factor combinations at the extremes and center
points of the design space. CCD allows for the evaluation of both linear and
quadratic effects of factors and enables the construction of response surface
models to predict optimal factor levels.
• These are some of the commonly employed factorial designs in
pharmaceutical research. The choice of design depends on the specific
research objectives, the number of factors under investigation, available
resources, and the desired level of precision and efficiency in the study.

Factorial design in Pharmaceuticals
• Factorial design is a statistical experimental technique commonly used in
pharmaceutical research and development.
• It involves studying the effects of multiple independent variables, or factors,
on a response variable of interest.
In the context of pharmaceuticals, factorial design offers several advantages
and applications:
• Optimization of Formulation: Factorial design can be used to optimize the
formulation of pharmaceutical products. By simultaneously varying multiple
factors such as excipient composition, drug concentration, pH, or
temperature, researchers can determine the optimal combination of factors
that yield the desired drug properties, stability, bioavailability, or release
characteristics.

• Dosage Optimization: Factorial design can help determine the
optimal dosage of a drug. By examining factors such as drug
concentration, dosing frequency, or administration route in
combination, researchers can identify the most effective and safe
dosage regimen.
• Drug Interaction Studies: Factorial design allows for the investigation
of drug interactions. By considering factors such as drug-drug
interactions, drug-excipient interactions, or drug-food interactions,
researchers can assess how different factors influence drug efficacy,
toxicity, or pharmacokinetics.

• Process Optimization: Factorial design is valuable in optimizing
pharmaceutical manufacturing processes. By varying factors such as
temperature, pressure, mixing speed, or drying time, researchers can
identify the optimal process conditions that yield high-quality
products with desired characteristics and minimal variability.
• Stability Studies: Factorial design can be employed to assess the
stability of pharmaceutical formulations. By considering factors such
as storage temperature, humidity, packaging materials, or light
exposure, researchers can determine the conditions that affect
product stability and identify the most stable formulation.

• Quality Control: Factorial design aids in quality control analysis. By
examining factors such as manufacturing variations, raw material
quality, or analytical method parameters, researchers can assess their
impact on product quality attributes and establish robust quality
control procedures.
• Combination Therapy: Factorial design is useful for studying
combination therapies. By considering factors such as drug
combinations, dosing ratios, or treatment durations, researchers can
evaluate multiple drugs' synergistic or antagonistic effects and
optimize the therapeutic outcomes.

• Overall, factorial design in pharmaceutical research allows for the
systematic exploration of multiple factors and their interactions,
providing valuable insights into formulation optimization, dosage
determination, drug interactions, process optimization, stability
studies, quality control, and combination therapy.
• It helps in making evidence-based decisions and optimizing
pharmaceutical products and processes.

• In pharmaceutical research, factorial design can be used in clinical
trials to investigate the effects of different treatment regimens on
patient outcomes.
• For example, a factorial design can investigate the effects of different
dosages and treatment durations of a drug on the efficacy and safety
outcomes in patients with a specific medical condition.
• Factorial design can also be used in preclinical research to investigate
the effects of different drug formulations, such as different types of
excipients or delivery systems, on the pharmacokinetics and
pharmacodynamics of a drug

• Overall, factorial design can be a powerful tool in
pharmaceutical research.
• It allows researchers to investigate the effects of multiple factors
simultaneously and provides more comprehensive and efficient
information on drugs' efficacy and safety.

2 2
Factorial design
• A 22
factorial design is a type of experimental design used in statistics to
investigate the effects of two factors, each of which has two levels, on a
response variable.
• The factors are typically referred to as factor A and factor B, and each factor
has two levels, which are typically referred to as high (+) and low (-).
• The term “2 2
” refers to the fact that there are two factors, each with two
levels.
• The design is called a factorial design because all possible combinations of
the two levels of each factor are included.

• For example, let’s say we want to study the effects of temperature
and humidity on plant growth. We could set up a 22
factorial design
as follows:
Factor A: Temperature
• High (+): 30°C
• Low (-): 20°C
Factor B: Humidity
• High (+): 70% RH
• Low (-): 50% RH

• We would then randomly assign each plant to one of the four treatment
groups:
1. High temperature, high humidity
2. High temperature, low humidity
3. Low temperature, high humidity
4. Low temperature, low humidity
• We would measure the response variable, plant growth, for each plant in
each treatment group and analyze the data to determine the effects of
temperature and humidity on plant growth and any interactions between
the two factors.

23
Factorial design
• A 23
factorial design is an experimental design that involves manipulating three
independent variables, each with two levels, resulting in a total of 8
experimental conditions.
• The factors are typically denoted as A, B, and C, and each factor has two levels,
which are typically coded as -1 and +1.
• The factorial design is called a (2x 3) design because there are two levels for
each of the three factors, resulting in 2x2x2 = 8 possible combinations.
• The factorial design allows researchers to investigate the main effects of each
factor and their interactions on the dependent variable.

• For example, a (2^3) factorial design could be used to investigate the
effects of three different factors on a plant growth.
• Factor A might represent the type of soil (standard soil vs. nutrient-
rich soil), factor B might represent the amount of water (low vs. high),
and factor C might represent the amount of sunlight (low vs. high).
• Each of the eight experimental conditions would involve a unique
combination of the levels of these three factors, and the plant growth
would be measured as the dependent variable.

• Overall, the (2^3) factorial design is a powerful tool for exploring the
effects of multiple factors on a dependent variable and can be used in
a wide range of research fields, including psychology, sociology,
biology, and engineering.

Advantages of factorial design
• Factorial design is a type of experimental design in which researchers
manipulate two or more independent variables simultaneously to examine
their effects on a dependent variable.
• The following are some advantages of using factorial design in research:
• Efficiency:
Factorial designs are more efficient than conducting multiple experiments to
examine the effects of each independent variable individually. By
manipulating multiple variables at once, researchers can save time and
resources.

• Simultaneous Evaluation of Multiple Factors: In pharmaceutical
research, numerous variables can often influence the outcome of a
study, such as different dosages, formulations, patient characteristics,
and environmental conditions. Traditional one-factor-at-a-time
experiments can be time-consuming and may not capture the
complex interactions between these factors. Factorial design allows
researchers to investigate multiple factors at once, including their
interactions, which can provide a more comprehensive understanding
of a drug’s behavior.

• Optimization of Formulations and Dosages: Factorial design helps
identify optimal combinations of factors (e.g., dosages of multiple
active ingredients) that lead to the desired pharmaceutical outcomes.
By studying these combinations concurrently, researchers can
pinpoint the most effective formulation more quickly and accurately.
This optimization process reduces the need for iterative testing and
minimizes resource wastage.

• Reduced Experimentation Time and Costs: Since factorial design
enables the study of multiple factors in a single experiment, it
significantly reduces the number of experiments needed to gather
relevant data. This reduction in experimentation time and associated
costs is a significant advantage, especially in the highly competitive
and resource-intensive field of pharmaceutical development.

• Detection of Interaction Effects: Factorial design is particularly adept
at detecting interactions between variables. In pharmaceuticals,
factors often interact in complex ways that can impact drug efficacy,
safety, and side effects. Identifying these interactions early in the
research process helps researchers make informed decisions and
design subsequent experiments more effectively.

• Enhanced Statistical Power: The simultaneous study of multiple
factors increases the statistical power of experiments. This means that
researchers can detect smaller yet clinically significant effects that
might be missed in individual experiments. Enhanced statistical power
increases the reliability of research findings and strengthens the basis
for making informed decisions about drug development.

• Comprehensive Data Collection: Factorial design generates
comprehensive datasets that capture a wide range of potential
influences on drug behavior. This rich dataset can provide valuable
insights into the drug’s mechanisms of action, aiding in developing a
deeper understanding of its pharmacology.

Central composite design: Response Surface methodology
• Response surface methodology (RSM) is a collection of statistical and
mathematical techniques.
• Used to study the relationships between a response variable and multiple
predictor variables.
• One of the popular designs in RSM is the Central Composite Design (CCD),
which is a type of experimental design that allows for the estimation of the
curvature of the response surface.

The following are the steps involved in Central Composite Design:
• Identify the factors: Determine the predictor variables that are likely to
affect the response variable.
• Choose the levels of the factors: The levels of the factors should be chosen
based on prior knowledge, experience or experimentation. CCD typically
requires at least five levels (-α, -1, 0, +1, +α) for each factor, where α is the
distance between the center point and the high or low level.
• Determine the number of experimental runs: CCD involves three sets of
runs: factorial, axial and center points. The number of experimental runs is
determined by the number of factors and the number of levels chosen for
each factor. The total number of runs for a CCD is (2k + 2k + n) where k is
the number of factors and n is the number of center points.

• Conduct the experiment: Conduct the experiments according to the
design matrix generated by the CCD.
• Analyze the data: Analyze the data using statistical software to
estimate the response surface and determine the optimal settings of
the predictor variables.
• Validate the model: Validate the model by comparing the predicted
values with the actual values obtained in the experiment. If the model
fits well, it can be used for optimization.

• CCD is a useful experimental design technique for exploring the
relationship between multiple predictor variables and the response
variable.
• Using CCD, the curvature of the response surface can be estimated,
and the optimal settings of the predictor variables can be identified.
• It is important to check that the assumptions of CCD are met before
analyzing the data.

HISTORICAL DESIGN
• The purpose of a historical research design is to collect, verify, and
synthesize evidence from the past to establish facts that defend or refute a
hypothesis.
• It is the study of objects of design in their historical and stylistic contexts.
With a broad definition, the contexts of design history include the social,
the cultural, the economic, the political, the technical, and the aesthetic.
• It uses secondary sources and a variety of primary documentary evidence,
such as diaries, official records, reports, archives, and non-textual
information [maps, pictures, audio and visual recordings]. The limitation is
that the sources must be both authentic and valid

What can we observe from these studies?
• The historical research design is unobtrusive; the research does not
affect the study's results.
• The historical approach is well-suited for trend analysis
• Historical records can add the contextual background required to fully
understand and interpret a research problem.
• There is often no possibility of researcher-subject interaction that
could affect the findings
• Historical sources can be used over and over to study different
research problems or to replicate a previous study

What are the drawbacks of these studies?
• The ability to fulfill the aims of our research is directly related to the amount
and quality of documentation available to understand the research
problem
• Since historical research relies on data from the past, it is impossible to
manipulate it to account for contemporary contexts.
• Interpreting historical sources can be very time-consuming
• The sources of historical materials must be archived consistently to ensure
access. This may be especially challenging for digital or online-only sources.
• Original authors bring their perspectives and biases to the interpretation of
past events, and these biases are more difficult to ascertain in historical
resources

Optimization Techniques in
Response Surface Methodology
• Response Surface Methodology (RSM) is a statistical technique for
optimizing the response of a system or process given a set of input
variables.
• RSM aims to find the optimal input variable set that results in the desired
output response. There are several optimization techniques used in RSM,
including the following:
• Steepest Descent: This is a gradient-based optimization technique used to
identify the direction of the steepest slope in a response surface. The
method involves starting at a point on the response surface and iteratively
moving toward the negative gradient until the minimum point is reached.

• Simplex Method: This is a popular optimization technique that uses
geometric concepts to iteratively move towards the optimal solution.
The method involves creating a simplex, a set of points that define the
corners of a polytope. The simplex is moved toward the minimum
point until the optimal solution is reached.

• Gradient Search: This is another gradient-based optimization
technique that calculates the partial derivatives of the response
function for each input variable. The method involves moving toward
the negative gradient until the minimum point is reached.
• Response Surface Methodology: This popular optimization technique
uses a response surface to model the relationship between the input
variables and the response. The method involves fitting a second-
order polynomial to the data and using the polynomial’s coefficients
to identify the optimal solution.

• Evolutionary Algorithms: These are a class of optimization techniques
that use the principles of evolution to identify the optimal solution.
The method involves creating a population of potential solutions and
using selection, mutation, and crossover to evolve the population
toward the optimal solution.
• In conclusion, Response Surface Methodology (RSM) provides various
optimization techniques for finding the optimal set of input variables
that result in the desired output response. The choice of optimization
technique depends on the complexity of the problem, the number of
input variables, and the desired level of precision.

• The following designs may be used during the optimization
phase:
• a) Central Composite Design
• b) Box-Behnken Design

Unit 5. Design and Analysis of experiments: Factorial Design: Definition, 22, 23design. Advantage of factorial design Response Surface methodology: Central composite design, Historical Design, and Optimization Techniques

More Related Content

What's hot (20)

Similar to Unit 5. Design and Analysis of experiments: Factorial Design: Definition, 22, 23design. Advantage of factorial design Response Surface methodology: Central composite design, Historical Design, and Optimization Techniques (20)

More from Ravinandan A P (20)

Recently uploaded (20)

Unit 5. Design and Analysis of experiments: Factorial Design: Definition, 22, 23design. Advantage of factorial design Response Surface methodology: Central composite design, Historical Design, and Optimization Techniques

Editor's Notes