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Center for Biofilm Engineering CBE workshop – July 2009 Al Parker Statistician and Research Engineer Montana State University Ruggedness Assessment and Experimental Design in the Biofilm Laboratory
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Acknowledgments Colleagues in the CBE; esp., the SBML team Funding US EPA Montana Board of Research, Commercialization and Technology Industrial Associates of the CBE Big Sky Statistical Analysts LLC
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Statistical thinking Data Ruggedness Testing 2 p Factorial versus One-at-a-time design Uncertainty assessment
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Statistical thinking Data Ruggedness Testing 2 p Factorial versus One-at-a-time design Uncertainty assessment
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Grow: CDC biofilm reactor
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Sampling 1. Rod is removed from reactor 2. Coupon is removed from the rod 3. Rinse
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Treat: disinfecting an established biofilm
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Sample: harvest from coupon, disaggregate harvest biofilm by scraping with a wooden applicator stick K. Moll 2008 homogenize to disaggregate clumps K. Moll 2008
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Sampling and analysis Biofilm is scraped & rinsed into the dilution tube; the suspension is disaggregated Dilution series; plate in duplicate or triplicate Treated coupon A. Hilyard, 2008 Drop plate: Viable cell density (cfu/cm 2 )
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Statistical thinking Data Ruggedness Testing 2 p Factorial versus One-at-a-time design Uncertainty assessment
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A standard laboratory method is said to be rugged if the outcome is unaffected by slight departures from the protocol. Ruggedness
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Disaggregation: sonicated or homogenized Nutrient (TSB, continuous flow): 50, 100, 200 mg/l Rotation (stir plate): 125, 225, 325 rpm Temperature: 20, 23, 26 o C Time in batch mode: 3, 18, 24 hr Parameters in the protocol
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Is efficacy testing using the CDC reactor rugged with respect to changes in the batch time over which the biofilm was grown? Ruggedness
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Ruggedness with respect to batch time > 18 hours Time (h) Viable cell density (log scale) 0 10 7 10 5 18 10 3 © 2002 CBE
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1. Conduct a minimal number of experiments to: Identify unimportant parameters: Is the biofilm significantly influenced by all 5 parameters? Check for interactions among parameters 2. Conduct another series of experiments using only the influential parameters and interactions. Performing a ruggedness test
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Is efficacy testing using the CDC reactor rugged with respect to changes in stir plate rotation and temperature? Ruggedness
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Full factorial design: 2 factors, each at 3 levels © 2002 CBE
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Statistical thinking Data Ruggedness Testing 2 p Factorial versus One-at-a-time design Uncertainty assessment
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One-at-a-time: Study temperature © 2002 CBE
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One-at-a-time: Study rpm © 2002 CBE
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One-at-a-time design for 2 factors © 2002 CBE
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2 2 factorial design © 2002 CBE
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A factorial design is superior to a one-at-a- time design: Factorial design can detect an important interaction between the two factors; the one-at-a-time design can’t Factorial design has greater precision when estimating the main effects of each factor than the one-at-a-time design
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True mean log(density) increases with temperature; slope depends on RPM © 2002 CBE
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One-at-a-time design can estimate these four points only © 2002 CBE
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One-at-a-time design cannot detect the fact that the slope depends on RPM © 2002 CBE
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Factorial design can estimate these four points only © 2002 CBE
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Factorial design can detect the fact that the slope depends on RPM © 2002 CBE
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Temperature Batch time RPM One-at-a-time However … the factorial approach requires more experimental effort © 2002 CBE
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Temperature Batch time RPM One-at-a-time Factorial However … the factorial approach requires more experimental effort © 2002 CBE
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Temperature Batch time RPM 2 3 Factorial ½ Fraction of Can use fewer factorial runs; however, can’t estimate all interactions © 2002 CBE
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2 5 factorial design: 2 5 = 32 One-at-a-time design: 2*5 = 10 ¼ fraction of the 2 5 factorial design: 32* ¼ = 8 For Five factors, instead of three: how many experimental runs?
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Statistical thinking Data Ruggedness Testing 2 p Factorial versus One-at-a-time design Uncertainty assessment
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Differences among experiments is the major source of variation 67% attributable to between experiments 33% attributable to within experiments
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S n c m c 2 + Formula for the SE of the mean LR, averaged over experiments S c = within-experiment variance of control coupon LD S d = within-experiment variance of disinfected coupon LD S E = between-experiments variance of LR n c = number of control coupons n d = number of disinfected coupons m = number of experiments 2 2 2 S n d m d 2 + S m E 2 SE of mean LR =
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Where to invest effort to get the most precision? 2 experiments; 6 coupons each; SE of mean log density (12 coupons) = 0.24 4 experiments; 2 coupons each; SE of mean log density (8 coupons) = 0.19 The precision is increased by running more experiments with less effort per experiment
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Summary It is important to do an arm-chair experiment first Use 2 p (fractional) factorial design to determine ruggedness of the protocol to changes in parameters Rely on multiple, independent experiments, each with few samples, in contrast to one experiment with many samples
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Fin
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Reliable laboratory methods
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