Simplifying sample prep optimization by using factorial design Wan Raihana Wan Aasim Universiti Sains Malaysia Sample prep : Everyone does it! Introduction Factorial design basics Analysis of factorial design 7 Steps to factorial design Sample prep is a integral part of any analytical method The goal of sample prep is enrichment, cleanup and signal enhancement Some commonly used sample prep methods for chromatography applications are: 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 Factorial design basics Analysis of factorial design 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A The most common approach to sample prep optimization is known as : OFAT One-Factor-At-a-Time 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 To understand the OFAT approach, consider the following sample prep method as an example: Factorial design basics Analysis of factorial design 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A 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 Variable/Factor to Optimize Levels/values to be tested below: 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 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A Using an OFAT approach, the following experiments would have been performed: Factors/Variables Tested Experiment sets Run ExtSolv varied 1 2 3 4 5 6 pH varied ExtTime varied Conclusion : ExtSolv

pH ExtTime Hexane EtOAc EtOAc EtOAc EtOAc EtOAc pH 8 pH 8 pH 8 pH 10 pH 10 pH 10 30 min 30 min 30 min 30 min 30 min 60 min Highest Recovery when : ExtSolv = Ethyl acetate pH = 10 ExtTime = 60 min Recovery is highest when : Extraction solvent : ethyl acetate Urine pH = 10 Optimizing with OFAT Factors/Variables Tested

Introduction Experiment sets Run Factorial design basics ExtSolv Varied 1 2 3 4 5 6 Analysis of factorial design 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A pH varied ExtTime varied ExtSolv pH ExtTime

Hexane EtOAc EtOAc EtOAc EtOAc EtOAc pH 8 pH 8 pH 8 pH 10 pH 10 pH 10 30 min 30 min 30 min 30 min 30 min 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? 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 Conclusion SelfAssessment 2010 Wan Raihana W.A 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 2 22 = 4 3 23 = 8 4 24 = 16 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

Variable/Factor to Optimize Levels/values to be tested 7 Steps to factorial design 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]Factor Quantitative 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 2 3 4 Experiments needed for a factorial design 4 8 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 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 Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Factor A -1 1 -1 1 -1 1 -1 1

Factor B -1 -1 1 1 -1 -1 1 1 Factor C -1 -1 -1 -1 1 1 1 1 SelfAssessment 2010 Wan Raihana W.A -1 & 1 are symbols representing different levels in factorial design notation From OFAT to Factorial Introduction Factorial design basics Analysis of factorial design 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A For our previous

OFAT example, the equivalent factorial design would be: Experiment Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Factor ExtSolv pH ExtTime Factor ExtSolvA -1 Hexane 1 Ethyl Acetate -1 Hexane 1 Ethyl Acetate -1 Hexane 1 Ethyl Acetate -1 Hexane 1 Ethyl Acetate Levels -1 Hexane

pH 8 30 min Factor pH B -1 8 pH -18 pH pH110 pH110 -18 pH -18 pH pH110 pH110 1 Ethyl Acetate pH 10 60 min Factor C ExtTime 30-1 min 30-1 min 30-1 min 30-1 min 1 60 min 60 1min 1 60 min 60 1min Characteristics of a Factorial

Design Introduction Factorial design basics Analysis of factorial design 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A Experiment Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 ExtSolv Hexane Ethyl Acetate Hexane Ethyl Acetate Hexane Ethyl Acetate Hexane Ethyl Acetate pH pH 8 pH 8 pH 10 pH 10 pH 8

pH 8 pH 10 pH 10 ExtTime 30 min 30 min 30 min 30 min 60 min 60 min 60 min 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 = 0.05 The magnitude of each effect can be seen Another visual representation of relative 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 Recovery increases increases when when pH pH changes changes from from the the low low level level (-1, (-1, pH pH 8) 8) to to the the high high level level (1, (1, pH pH 10) 10) % % Recovery Recovery % % Recovery Recovery does does not not change change

increases when the increases when the when when extraction extraction time time extraction solvent extraction solvent(changes changes from from the the low low level level (changes from hexane changes from hexane 1, 1, 30 30 min) min) to to the the high high level level (level -1) to ethyl (level -1) to ethyl (1,

(1, 60 60 min) min) acetate acetate (level (level 1) 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 When ExtSolv is Ethyl ExtSolv Interaction 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 Run 1 Run 1 Run 2 Run 2 Run 3 Run 3 Run 4 Run 4 Run 5 Run 5 Run 6 Run 6 Run 7 Run 7 Run 8

Factor ExtSolvA -1 Hexane 1 Ethyl Acetate -1 Hexane 1 Ethyl Acetate -1 Hexane 1 Ethyl Acetate -1 1 Hexane Factor pH B -1 8 pH -18 pH 1 pH 10 1 pH 10 -1 pH -18 pH1 8 pH110 Factor C ExtTime 30-1 min 30-1 min

-1 30 min -1 30 min 1 60 min 1 60 1min 1 60 min Run 8 Ethyl Acetate pH 10 60 min 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 7 Steps to factorial design Conclusion SelfAssessment 2010 Wan Raihana W.A

More replicates = more statistical power 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 youve 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]