Center for Biofilm Engineering Al Parker, Biostatistician Standardized Biofilm Methods Research Team Montana State University The Importance of Statistical Design and Analysis in the Laboratory Feb, 2011

Standardized Biofilm Methods Laboratory Darla Goeres Al Parker Marty Hamilton Diane Walker Lindsey Lorenz Paul Sturman Kelli Buckingham- Meyer

What is statistical thinking?  Data  Experimental Design  Uncertainty and variability assessment

What is statistical thinking?  Data (pixel intensity in an image? log(cfu) from viable plate counts?)  Experimental Design - controls - randomization - replication (How many coupons? experiments? technicians? labs?)  Uncertainty and variability assessment

Why statistical thinking?  Anticipate criticism (design method and experiments accordingly)  Provide convincing results (establish statistical properties)  Increase efficiency (conduct the least number of experiments)  Improve communication

Why statistical thinking? Standardized Methods

Attributes of a standard method: Seven R’s  Relevance  Reasonableness  Resemblance  Repeatability (intra-laboratory)  Ruggedness  Responsiveness  Reproducibility (inter-laboratory)

Attributes of a standard method: Seven R’s  Relevance  Reasonableness  Resemblance  Repeatability (intra-laboratory)  Ruggedness  Responsiveness  Reproducibility (inter-laboratory)

Resemblance of Controls Independent repeats of the same experiment in the same laboratory produce nearly the same control data, as indicated by a small repeatability standard deviation. Statistical tool: nested analysis of variance (ANOVA)

86 mm x 128 mm plastic plate with 96 wells Lid has 96 pegs Resemblance Example: MBEC

A100 50:NNGCSC B50 50:NNGCSC C25 50:NNGCSC D :NNGC E :NNGC F :NNGC G :NNGC H :NNGC MBEC Challenge Plate disinfectant neutralizer test control

Resemblance Example: MBEC Mean LD= 5.55 Control Data: log 10 (cfu/mm 2 ) from viable plate counts rowcfu/mm 2 log(cfu/mm 2 ) A 5.15 x B 9.01 x C 6.00 x D 3.00 x E 3.86 x F 2.14 x G 8.58 x H 4.29 x

ExpRow Control LD Mean LDSD 1A B5.95 1C5.78 1D5.48 1E5.59 1F5.33 1G4.93 1H5.63 2A B5.71 2C5.54 2D5.33 2E5.11 2F5.48 2G5.33 2H5.41 Resemblance Example: MBEC

Resemblance from experiment to experiment Mean LD = 5.48 S r = 0.26 the typical distance between a control well LD from an experiment and the true mean LD

Resemblance from experiment to experiment The variance S r 2 can be partitioned: 2% due to between experiment sources 98% due to within experiment sources

S n c m c 2 + Formula for the SE of the mean control LD, averaged over experiments S c = within-experiment variance of control LDs S E = among-experiment variance of control LDs n c = number of control replicates per experiment m = number of experiments 2 2 S m E 2 SE of mean control LD = CI for the true mean control LD = mean LD ± t m-1 x SE

8 2 Formula for the SE of the mean control LD, averaged over experiments S c = 0.98 x (0.26) 2 = S E = 0.02 x (0.26) 2 = n c = 8 m = SE of mean control LD = = % CI for the true mean control LD = 5.48 ± 12.7 x = (3.20, 7.76)

Resemblance from technician to technician Mean LD = 5.44 S r = 0.36 the typical distance between a control well LD and the true mean LD

The variance S r 2 can be partitioned: 0% due to technician sources 24% due to between experiment sources 76% due to within experiment sources Resemblance from technician to technician

Repeatability Independent repeats of the same experiment in the same laboratory produce nearly the same data, as indicated by a small repeatability standard deviation. Statistical tool: nested ANOVA

Repeatability Example Data: log reduction (LR) LR = mean(control LDs) – mean(disinfected LDs)

ExpRow Control LD Mean LDSD 1A B5.95 1C5.78 1D5.48 1E5.59 1F5.33 1G4.93 1H5.63 2A B5.71 2C5.54 2D5.33 2E5.11 2F5.48 2G5.33 2H5.41 Repeatability Example: MBEC A :NNGCSC B 50 50:NNGCSC C 25 50:NNGCSC D :NNGC E :NNGC F :NNGC G :NNGC H :NNGC

Repeatability Example: MBEC Mean LR = 1.63 ExpRow Control LD Control Mean LDCol Disinfected 6.25% LD Disinfected Mean LDLR 1A B C D E F G4.93 1H5.63 2A B C D E F G5.33 2H5.41

Repeatability Example Mean LR = 1.63 S r = 0.83 the typical distance between a LR for an experiment and the true mean LR

S n c m c 2 + Formula for the SE of the mean LR, averaged over experiments S c = within-experiment variance of control LDs S d = within-experiment variance of disinfected LDs S E = among-experiment variance of LRs n c = number of control replicates per experiment n d = number of disinfected replicates per experiment m = number of experiments S n d m d 2 + S m E 2 SE of mean LR =

Formula for the SE of the mean LR, averaged over experiments S c = within-experiment variance of control LDs S d = within-experiment variance of disinfected LDs S E = among-experiment variance of LRs n c = number of control replicates per experiment n d = number of disinfected replicates per experiment m = number of experiments CI for the true mean LR = mean LR ± t m-1 x SE

Formula for the SE of the mean LR, averaged over experiments S c 2 = S d 2 = S E 2 = n c = 8, n d = 5, m = 2 SE of mean LR = = % CI for the true mean LR= 1.63 ± 12.7 x = 1.63 ± 7.46 = (0.00, 9.09)

How many coupons? experiments? n c m m n d m margin of error= t m-1 x no. control coupons (n c ): no. disinfected coupons (n d ): no. experiments (m)

A method should be sensitive enough that it can detect important changes in parameters of interest. Statistical tool: regression and t-tests Responsiveness

disinfectant neutralizer test control Responsiveness Example: MBEC A: High Efficacy H: Low Efficacy A100 50:NNGCSC B50 50:NNGCSC C25 50:NNGCSC D :NNGC E :NNGC F :NNGC G :NNGC H :NNGC

Responsiveness Example: MBEC This response curve indicates responsiveness to decreasing efficacy between rows C, D, E and F

Responsiveness Example: MBEC Responsiveness can be quantified with a regression line: LR = row For each step in the decrease of disinfectant efficacy, the LR decreases on average by 0.97.

Summary  Even though biofilms are complicated, it is feasible to develop biofilm methods that meet the “Seven R” criteria.  Good experiments use control data!  Assess uncertainty by SEs and CIs.  When designing experiments, invest effort in more experiments versus more replicates (coupons or wells) within an experiment.

Any questions?