Transcript Optimization of Sample Prep by using factorial design

Simplifying sample prep optimization by
using factorial design
Wan Raihana Wan Aasim
Universiti Sains Malaysia
Sample prep : Everyone does it!
Sample prep is a integral part of any analytical method
Introduction
Factorial
design basics
The goal of sample prep is enrichment, cleanup and signal
enhancement
Analysis of
factorial
design
Some commonly used sample prep methods for
chromatography applications are:
7 Steps to
factorial
design
Solid Phase
Microextraction
Liquid-liquid extraction
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Solid Phase Extraction
QuEChERS
Why optimize sample prep?
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
The performance of a sample prep method depends on
several variables e.g. pH, temperature, solvent type etc.
Optimization of
sample prep is
essential to ensure
optimum recovery,
selectivity and
sensitivity
Most times, optimization is performed by sequential
analysis of experimental variables
A simpler and more efficient alternative is the use of a
statistical approach called factorial design
Tutorial objectives
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
In this tutorial, you will learn :
 Why factorial design is an excellent
tool for sample prep optimization.
 Basic principles of factorial design.
 Key terminology and concepts
 How factorial designs are analyzed
 How to set up your own factorial design for sample prep
optimization in seven easy steps
Once you have completed the tutorial, there is
a short quiz to help you assess if you have
mastered the information contained in this
tutorial
How is optimization USUALLY done?
Introduction
The most common approach to sample prep
optimization is known as :
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
 The classic approach to sample prep optimization
 A factor = an experimental variable
 OFAT involves sequential experiments where one
factor is varied and the others are held constant
 This process is repeated until an optimal
combination of factors is found which gives the
best results
A simple optimization example
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
To understand the OFAT approach, consider the following
sample prep method as an example:
A liquid-liquid extraction (LLE) method for isolation of
amphetamine (AM) from human urine samples
Objective of optimization
Maximize recovery of the sample prep method mentioned
above by optimizing the following experimental variables
at the two levels specified below:
Variable/Factor to Optimize
Levels/values to be tested
Extraction Solvent [ExtSolv]
Hexane or ethyl acetate
Urine pH [pH]
pH 8 or pH 10
Extraction time [ExtTime]
30 mins or 60 mins
Optimizing with OFAT
Introduction
Factorial
design basics
Analysis of
factorial
design
Using an OFAT approach, the following experiments
would have been performed:
Experiment
sets
ExtSolv
varied
pH varied
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
ExtTime
varied
Conclusion :
Run
Factors/Variables Tested
ExtSolv
pH
ExtTime
1
Hexane
pH 8
30 min
2
EtOAc
pH 8
30 min
3
EtOAc
pH 8
30 min
4
EtOAc
pH 10
30 min
5
EtOAc
pH 10
30 min
6
EtOAc
pH 10
60 min
Highest Recovery
when :
ExtSolv = Ethyl
acetate
pH = 10
ExtTime = 60 min
Recovery is highest when :
 Extraction solvent : ethyl acetate
 Urine pH = 10
 Extraction time = 60 min
Optimizing with OFAT
Introduction
Experiment
sets
Factorial
design basics
ExtSolv
Varied
Analysis of
factorial
design
7 Steps to
factorial
design
pH varied
ExtTime
varied
© 2010 Wan Raihana W.A
Factors/Variables Tested
ExtSolv
pH
ExtTime
1
Hexane
pH 8
30 min
2
EtOAc
pH 8
30 min
3
EtOAc
pH 8
30 min
4
EtOAc
pH 10
30 min
5
EtOAc
pH 10
30 min
6
EtOAc
pH 10
60 min
Highest Recovery
when
ExtSolv = Ethyl
acetate
pH = 10
ExtTime = 60 min
Disadvantages of approach :
 Not all combinations of variables are tested
i.e. what about ExtSolv = hexane; pH = 10; ExtTime = 60 min?
Conclusion
SelfAssessment
Run

Unable to detect factor interactions
i.e. what if the extraction time depended on the type of
extraction solvent used?
What are factor interactions ?
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Factor interactions occur when the
effect of one factor depends on the
level of another factor
A simple example of a factor interaction
Baking a chocolate cake
2 factors : oven temperature, oven
time. Every baker knows that...
High temperature, low oven time
Low temperature, high oven time
The selection of oven time depends on
the oven temperature used
Why use a factorial design approach?
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Using a classic OFAT approach, important information
regarding potential interactions is left out.
However, by using a factorial design approach, sample
prep methods can be optimized quickly, efficiently and
with greater statistical confidence in the results
Advantages of factorial design:
 All factor-level combinations can be tested
 Factor interactions can be detected
 Higher statistical power
 Easy to implement
 Efficient design – can obtain more information
compared to OFAT
What is Factorial Design?
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Factorial design is an experimental design which
simultaneously studies multiple experimental
factors/variables at multiple levels
Pioneering work in this field was by
Sir Ronald A. Fisher at Rothamsted
Agricultural Field Research Station,
London, England in the early 1920s
Can be used for
 Process optimization
 To determine effects of
variables in a process
 Modelling of a process
 Determination of robustness
Sir Ronald A. Fisher
(1890 – 1962)
What is Factorial Design?
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Simultaneous analysis of all possible
factor & level combinations
 Most common designs are 2-level factorial designs
where each factor is studied at two discrete levels.
 Represented by the formula 2x where x represents the
number of factors studied
 The formula also indicates the number of experiments
required for a specific design
Number of Factors
Experiments needed
Conclusion
2
22 = 4
SelfAssessment
3
23 = 8
4
24 = 16
© 2010 Wan Raihana W.A
But first, understand some terms
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
The most important terms to know are :
 Factors
 Levels
 Trials/Runs
 Response
In order to understand these concepts, the previous LLE
sample prep described will be used as an example.
A liquid-liquid extraction (LLE) method for
isolation of amphetamine (AM) from
human urine samples
DoE Lingo : Factors
Introduction
Factors refer to the experimental variables that are to be
optimized
Factorial
design basics
Factors can either be qualitative or quantitative
Analysis of
factorial
design
7 Steps to
factorial
design
Variable/Factor to Optimize Levels/values to be tested
Extraction Solvent [ExtSolv]
Hexane or
ethyl acetate
Qualitative
Factor
Urine pH [pH]
pH 8 or pH
10
Quantitative
Factor
Extraction time [ExtTime]
30 mins Quantitative
or 60 mins
Factor
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Factors
DoE Lingo : Levels
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Levels are the specific and discrete values or settings
assigned to each factor
Levels are either qualitative or quantitative depending on
the factor
Variable/Factor to Optimize Levels/values to be tested
Extraction Solvent
Qualitative
Factor[ExtSolv]
Urine pH [pH]
Quantitative
Factor
Hexane or ethyl acetate
Extraction time
[ExtTime]
Quantitative
Factor
30 mins or 60 mins
pH 8 or pH 10
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Levels
DoE Lingo : Runs
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Runs refer to the specific number of experiments required
to perform a factorial design experiment
Runs are also referred to as trials
Number of Factors
Experiments needed for
a factorial design
2
4
3
8
4
16
Runs or Trials
From the above table, it can be seen that the number of
runs or trials required for a 3 factor, 2-level factorial design
is 8 runs or trials
DoE Lingo : Response
Response is the output of the experiment performed.
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
For example, in the LLE optimization previously described,
the output of the experiment would be the percentage
recovery of amphetamine from urine
A factorial design may have more than one response
For example, if the LLE method was expanded to
include another two drugs, the factorial design
should have three responses to reflect each drug.
Standard 2-level Factorial Design
Matrix
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Standard factorial designs can be obtained from reference
books and statistical software packages
Below is a standard 2-level factorial design matrix for
three factors (number of runs = 8)
Experiment
Factor A
Factor B
Factor C
Run 1
-1
-1
-1
Run 2
1
-1
-1
Run 3
-1
1
-1
Run 4
1
1
-1
Run 5
-1
-1
1
Run 6
1
-1
1
Run 7
-1
1
1
Run 8
1
1
1
-1 & 1 are symbols representing different levels in factorial design notation
From OFAT to Factorial
Introduction
Factorial
design basics
Analysis of
factorial
design
For our previous
OFAT example, the
equivalent factorial
design would be:
ExtSolv
-1
1
Hexane
Ethyl Acetate
pH 8
pH 10
30 min
60 min
pH
ExtTime
Factor
ExtSolvA
Factor
pH B
Factor C
ExtTime
Run 1
-1
Hexane
-18
pH
30-1
min
7 Steps to
factorial
design
Run 2
1
Ethyl Acetate
-18
pH
30-1
min
Run 3
-1
Hexane
pH110
30-1
min
Run 4
1
Ethyl Acetate
pH110
30-1
min
Conclusion
Run 5
-1
Hexane
-18
pH
1
60 min
Run 6
1
Ethyl Acetate
-18
pH
60 1min
Run 7
-1
Hexane
pH110
1
60 min
Run 8
1
Ethyl Acetate
pH110
60 1min
SelfAssessment
© 2010 Wan Raihana W.A
Experiment
Levels
Factor
Characteristics of a Factorial Design
Experiment
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
ExtSolv
pH
ExtTime
Run 1
Hexane
pH 8
30 min
Run 2
Ethyl Acetate
pH 8
30 min
Run 3
Hexane
pH 10
30 min
Run 4
Ethyl Acetate
pH 10
30 min
Run 5
Hexane
pH 8
60 min
Run 6
Ethyl Acetate
pH 8
60 min
Run 7
Hexane
pH 10
60 min
Run 8
Ethyl Acetate
pH 10
60 min
All possible factor-level combinations are represented in
the factorial experiment
Running a Factorial Design
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Experiment
ExtSolv
pH
ExtTime
Response
Run 1
Hexane
pH 8
30 min
65.3
Run 2
Ethyl Acetate
pH 8
30 min
81.3
Run 3
Hexane
pH 10
30 min
53.3
Run 4
Ethyl Acetate
pH 10
30 min
69.9
Run 5
Hexane
pH 8
60 min
61.8
Run 6
Ethyl Acetate
pH 8
60 min
77.4
Run 7
Hexane
pH 10
60 min
73.9
Run 8
Ethyl Acetate
pH 10
60 min
89.9
Each run is performed according to the factor settings
specified in the design matrix
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
The response (result) for each run should be recorded
In this example, the response is the percent recovery for
amphetamine (AM)
Analyzing Factorial Designs
Most statistical packages can analyze factorial designs
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
In this tutorial, all analyses were
performed with Minitab 15
Major analytical tools
 ANOVA – to identify significant factors and factor
interactions
 Normal plot of Effects
 Visual approach
 Pareto Chart
 Easiest to
 Main Effects Plot
understand and
 Interaction Plots
interpret
Analysis : Effect Size and ANOVA
Introduction
Factorial
design basics
Analysis of
factorial
design
Effect Size:
The measure of the
strength of the effect
of a variable on the
response
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Model Fit
The value of R-Sq represents the
represent the proportion of variation in
the response data explained by the
terms in the model.
p-values
Values below a specific
chosen significance level
represent statistically
significant factors
Analysis : Normal Plot of Effects
Significance
level
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
pH
Extraction Solvent
Normal
line & nonsignificant
effects
Extraction Time –Solvent
Interaction
 Non-significant factors and interactions fall
near the normal line (indicated in blue)
 The further away the factor/interaction
normal
line, theand
larger
the effect
A comparison offrom
the the
relative
magnitude
statistical
size and
significance
significance of factor
effects
and factor interactions
Analysis : Pareto Plot
Introduction
Factorial
design basics
Nonsignificant
pH
Extraction Time – Solvent Interaction
Analysis of
factorial
design
Extraction Solvent
Significance Cut-Off Line
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
 Factors and interactions that exceed the
significance cut-off line are significant at α
= 0.05
 representation
The magnitudeof
ofrelative
each effect
can be seen
Another visual
magnitude
and
by the of
length
of effects
the representative
bar
statistical significance
factor
and interactions
Analysis : Main Effect Plot
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
% Recovery
increases when pH
changes from the low
level (-1, pH 8) to the
high level (1, pH 10)
% Recovery
% Recovery does not change
increases when the
when extraction time
extraction solvent
changes from the low level (changes from hexane
1, 30 min) to the high level
(level -1) to ethyl
(1, 60 min)
acetate (level 1)
A main effect plot shows the magnitude and “direction”
of the factors being studied
Analysis : Interaction Plots
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
The interaction plot for
ExtTime vs ExtSolv
indicates that :
 When ExtSolv is
Hexane, the optimum
recovery is when
ExtTime is 30 min
ExtTime –
ExtSolv
Interaction
 When ExtSolv is Ethyl
Acetate, optimum
recovery
is whenare detected by crossed lines in
Factor
interactions
ExtTime is
60 min
interaction
plots
Analysis : Pieces of the Puzzle
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
What we know so far in our optimization experiment:
 Statistically significant factors are pH and extraction
solvent
 The extraction solvent and extraction time factor
interaction is statistically significant
 % Recovery increases when pH changes from pH 8 to
10 and extraction solvent changes from hexane to
ethyl acetate
 A change in extraction time does not increase percent
recovery
 When ExtSolv is Hexane, the optimum recovery is
when ExtTime is 30 min
 When ExtSolv is Ethyl Acetate, optimum recovery is
when ExtTime is 60 min
Analysis :
Putting the Pieces Together
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Based on the results from the main effects plot, the
highest recovery for AM is obtained when
 Urine pH is pH 10
 Extraction solvent is ethyl acetate
 Extraction time on its own does not have any effect on
recovery
But taking into account the factor interaction results :
 When ethyl acetate is used, the highest recovery is
when extraction time is 60 minutes
Optimized factor settings :
pH 10;
Extraction solvent : ethyl acetate;
Extraction time : 60 minutes
7 steps to experimental design
Setting up your own factorial design optimization
Step 1 – Identify response
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Based on the sample prep to be optimized, identify the
response that characterizes the process
For a single method, multiple responses may be selected,
depending on what needs to be optimized
Examples of responses:
Percent recovery, peak areas,
reproducibility, % yield
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Factorial designs work best with
quantifiable responses
Step 2 – Identify factors
Select the factors that need to be optimized
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Select factors that are easily controlled i.e. pH, incubation
temperature rather than factors that are uncontrollable
i.e. ambient temperature.
Several factors may influence a sample prep method, but
the number of runs increases greatly with the number of
factors, therefore limit factors to those that are most
important.
3 – 5 factors are usual. More than 5 factors is impractical
as it results in a large number of runs
Step 3 – Determine levels
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Determine the two levels for each of the factors to be
optimized.
For quantitative factors, the levels chosen should span a
logical range
The range should
not be too wide
or too narrow
Step 4 – Identify the design
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Based on the number of factors to optimize, identify the
appropriate design matrix
Factorial design matrices can be obtained from:
 Statistical software – Minitab has built in designs to
choose from
 Design of experiments books
Step 4 – Identify the design
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Using the standard design matrix, fill in the variables and
factor levels in order to obtain the respective factor-level
combinations for each experimental run
Filled
Standard
in design
Design
matrix
Matrix
with selected
from statistical
factorsbook
& levels
Experiment
Factor
ExtSolvA
Factor
pH B
ExtTime
Factor C
Run 1 Run 1
Hexane
-1
pH
-18
30-1
min
Run 2 Run 2
Ethyl Acetate
1
pH
-18
30-1
min
Run 3 Run 3
Hexane
-1
pH110
30-1
min
Run 4 Run 4
Ethyl Acetate
1
pH110
30-1
min
Run 5 Run 5
Hexane
-1
pH
-18
60 min
1
Run 6 Run 6
Ethyl Acetate
1
pH
-18
60 1min
Run 7 Run 7
Hexane
-1
pH110
60 min
1
Run 8 Run 8
Ethyl Acetate
1
pH110
60 1min
Step 5 – Perform the experiments
Introduction
Using the design matrix to identify factor-level
combinations for each run, conduct the experiment
Factorial
design basics
Experiments should randomized and replicated
Analysis of
factorial
design
More replicates = more statistical power
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
If replicates are performed, the mean of the replicates for
each run is taken as the response.
Step 6 – Analyze the experiments
For each response, analyze using:
Introduction
Factorial
design basics
 ANOVA, to identify model fit and statistical
significance of experiment
Analysis of
factorial
design
 Normal plot or pareto chart, to visually identify
significant factors and interactions
7 Steps to
factorial
design
 Main effects plot, to identify the optimum levels for
each significant factor
Conclusion
 Interaction plot, to identify the optimum levels for
each significant factor interaction
SelfAssessment
© 2010 Wan Raihana W.A
Step 7: Confirmatory runs &
Next Steps
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
Using the optimized levels for each factor, perform
confirmation runs in order to check results
Non-significant factors need no further optimization and
can be set to any convenient level
Next steps:
 If optimized method is acceptable, can proceed to
validation etc.
 If further optimization is required, consider other
more advanced experimental designs e.g. response
surface methodology or central composite design
Conclusion
Introduction
Factorial
design basics
Analysis of
factorial
design
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
 Factorial designs provide a
simple but efficient approach
for optimization of sample
prep methods
 Factorial designs provide
additional information
regarding factor interactions
which may have a large impact
of sample prep methods
 Factorial designs provide
higher statistical power and
increase confidence in
optimization
Recommended reading
1.
Introduction
Factorial
design basics
2.
Analysis of
factorial
design
7 Steps to
factorial
design
3.
Conclusion
4.
SelfAssessment
© 2010 Wan Raihana W.A
Bayne, C. K. and I. B. Rubin (1986).
Practical Experimental Designs and
Optimization Methods for
Chemists. Weinheim, VCH.
Mason, R. L., R. F. Gunst, et al.
(2003). Statistical Design and
Analysis of Experiments With
Applications to Engineering and
Science. Hoboken, New Jersey, John
Wiley & Sons.
Wu, J. C. F. and M. Hamada (2000).
Experiments : Planning, Analysis
and Parameter Design
Optimization. New York, Wiley
Araujo, P. W. and R. G. Brereton
(1996). "Experimental design I.
Screening." TrAC Trends in
Analytical Chemistry 15(1): 26-31.
Self-Assessment
Introduction
Factorial
design basics
Analysis of
factorial
design
Congratulations! You have reached the end of this
tutorial. As a final step, use the quiz below to assess if
you’ve mastered the main concepts in this tutorial
Use the right
and left
arrows
(below the
title bar of
the quiz) to
navigate the
questions
7 Steps to
factorial
design
Conclusion
SelfAssessment
© 2010 Wan Raihana W.A
If you have
finished, click
HERE to end
the tutorial
Simplifying sample prep optimization by
using factorial design
Wan Raihana Wan Aasim
Universiti Sains Malaysia
Thanks for using this tutorial and
good luck with your sample prep optimization!
Copyright © 2010. Wan Raihana Wan Aasim. All rights reserved
Contact the author : [email protected]