Center for Biofilm Engineering Importance of Statistical Design

Center for Biofilm Engineering Importance of Statistical Design

Center for Biofilm Engineering Importance of Statistical Design and Analysis Al Parker Standardized Biofilm Methods Research Team Montana State University July, 2010 Standardized Biofilm Methods Laboratory Darla Goeres Al Parker Marty Hamilton Lindsey Lorenz Paul Sturman Diane Walker Kelli BuckinghamMeyer What is statistical thinking? Data Design Uncertainty assessment

What is statistical thinking? Data (pixel intensity in an image? log(cfu) from viable plate counts?) Design - controls - randomization - replication (How many coupons? experiments? technicians? Labs?) Uncertainty and variability assessment Why statistical thinking? Provide convincing results Anticipate criticism Increase efficiency Improve communication Attributes of a standard method: Seven Rs Relevance Reasonableness Resemblance Repeatability (intra-laboratory reproducibility) Ruggedness Responsiveness Reproducibility (inter-laboratory) Attributes of a standard method: Seven Rs

Relevance Reasonableness Resemblance Repeatability (intra-laboratory reproducibility) Ruggedness Responsiveness Reproducibility (inter-laboratory) Resemblance 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) Resemblance Example Resemblance Example Data: log10(cfu) from viable plate counts Coupon 1 2 3 Density cfu / cm2 5.5 x 106 6.6 x 106 8.7 x 106 LD

log(cfu/cm2) 6.74 6.82 6.94 Mean LD= 6.83 Resemblance Example Exp control LD 1 6.73849 1 6.82056 1 6.93816 2 6.66276 2 6.73957

2 6.74086 3 6.91564 3 6.74557 3 6.89758 Mean LD SD 6.83240 0.10036 6.71440 0.04473 6.85293 0.09341

Resemblance from experiment to experiment 6.95 Mean LD = 6.77 6.90 2 loglog(cfu) 10 (cfu/cm ) 6.85 Sr = 0.15 6.80 6.75 6.70 6.65 6.60 6.55 1 2 experiment 3 the typical distance between a control coupon

LD from an experiment and the true mean LD Resemblance from experiment to experiment 6.95 The variance Sr2 can be partitioned: 6.90 2 loglog(cfu) 10 (cfu/cm ) 6.85 69% due to between experiment sources 6.80 6.75 6.70 6.65 31% due to within experiment sources 6.60 6.55

1 2 experiment 3 Formula for the SE of the mean control LD, averaged over experiments 2 Sc = within-experiment variance of control coupon LD SE2 = between-experiments variance of control coupon LD nc = number of control coupons per experiment m = number of experiments SE of mean control LD = 2 Sc nc m + 2 SE m Formula for the SE of the mean control LD, averaged over experiments

6.95 2 Sc = 0.31 x (.15)2 = 0.006975 2 6.90 6.85 6.80 SE = 0.69 x (.15) = 0.015525 log(cfu) 2 nc = 3 6.75 6.70 6.65 6.60 6.55 1 m=3 SE of mean control LD = 2 3

experiment .006975 33 95% CI for mean control LD + .015525 3 = 0.0771 = 6.77 t6 x 0.0771 = (6.58, 6.96) Resemblance from technician to technician 8.7 Mean LD = 8.42 log10log(cfu) (cfu/cm2) 8.6 8.5 Sr = 0.17

8.4 the typical distance between a coupon LD and the true mean LD 8.3 8.2 8.1 experiment Tech 1 2 1 3 1 2 2 3 Resemblance from technician to technician The variance Sr2 can be partitioned:

8.7 log10log(cfu) (cfu/cm2) 8.6 39% due to technician sources 8.5 8.4 43% due to between experiment sources 8.3 8.2 8.1 experiment Tech 1 2 1 3

1 2 2 3 18% due to within experiment sources 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) Repeatability Example Exp control LD 1 6.73849

1 6.82056 1 6.93816 2 6.66276 2 6.73957 2 6.74086 3 6.91564 3 6.74557 3 6.89758

Mean LD SD 6.83240 0.10036 6.71440 0.04473 6.85293 0.09341 Repeatability Example Exp 1 1 1 log density control disinfected 6.73849 3.08115 6.82056 3.29326 6.93816 3.03196 mean log density

control disinfected log reduction 6.83240 3.13546 3.69695 2 2 2 6.66276 6.73957 6.74086 2.92334 3.03488 3.21146 6.71440 3.05656 3.65784 3 3 3 6.91564 6.74557 6.89758

2.73748 2.66018 2.72651 6.85293 2.70805 4.14488 Mean LR = 3.83 Repeatability Example 4.2 Mean LR = 3.83 4.1 4.0 Sr = 0.27 LR 3.9 3.8 3.7 3.6 3.5 1 2

experiment 3 the typical distance between a LR for an experiment and the true mean LR Formula for the SE of the mean LR, averaged over experiments 2 Sc = within-experiment variance of control coupon LD Sd2 = within-experiment variance of disinfected coupon LD 2 SE = between-experiments variance of LR nc = number of control coupons nd = number of disinfected coupons m = number of experiments SE of mean LR = nc m 2 2 2

Sc + Sd nd m + SE m Formula for the SE of the mean LR, averaged over experiments 4.2 Sc2 = 0.006975 4.1 4.0 3.9 Sd = 0.014045 LR 2 3.8 3.7 SE2 = 0.066234

3.6 3.5 1 nc = 3, nd = 3, m = 3 SE of mean LR = .006975 33 2 3 experiment + .014045 33 + .066234 3 95% CI for mean LR = 3.83 t2 x 0.156 = (3.16, 4.50) = 0.156 How many coupons? experiments?

SE of mean LR = .006975 + nc m .014045 .066234 + m nd m no. control coupons (nc): no. disinfected coupons (nd): 2 2 3 3 6 6 12 12

no. experiments (m) 1 2 3 4 6 10 100 0.277 0.196 0.160 0.138 0.113 0.088 0.028 0.271 0.191 0.156 0.135 0.110 0.086 0.027 0.264 0.187 0.152 0.132 0.108 0.084 0.026

0.261 0.184 0.151 0.130 0.106 0.082 0.026 Reproducibility Repeats of the same experiment run independently by different researchers in different laboratories produce nearly the same result as indicated by a small reproducibility standard deviation. Requires a collaborative (multi-lab) study. Statistical tool: nested ANOVA Reproducibility Example Mean LR = 2.61 4.0 log reduction 3.5 SR = 1.07 3.0 2.5

2.0 1.5 experiment lab 1 3 1 4 3 4 2 5 the typical distance between a LR for an experiment at a lab and the true mean LR Reproducibility Example The variance SR2 can be partitioned: 4.0

log reduction 3.5 62% due to between lab sources 3.0 2.5 2.0 1.5 experiment lab 1 3 1 4 3 4 2 5

38% due to between experiment sources Formula for the SE of the mean LR, averaged over labratories Sc2= within-experiment variance of control coupon LD Sd2= within-experiment variance of disinfected coupon LD SE2= between-experiments variance of LR SL2= between-lab variance of LR nc = number of control coupons nd = number of disinfected coupons m = number of experiments L = number of labs SE of mean LR = 2 Sc ncmL + S 2 d ndmL +

S 2 E mL + 2 SL L Formula for the SE of the mean LR, averaged over labratories 4.0 Sc = 0.007569 2 log reduction 3.5 Sd2= 0.64 SE2= .2171 3.0 2.5 2.0

1.5 SL = 0.707668 2 experiment lab 1 3 1 4 3 4 2 5 nc = 3, nd = 3, m = 3, L = 2 SE of mean LR = .007569 332 + .64

332 + .707668 .2171 3 2 + 2 95% CI for mean LR = 2.61 t4 x 0.653 = (0.80, 4.42) = 0.653 How many coupons? experiments? labs? .007569 SE of mean LR = + ncmL no. of labs (L) no. control/dis coupons (nc and nd): .64 ndmL

+ .707668 .2171 + mL L 1 1 1 2 2 2 3 3 3 4 4

4 5 5 5 6 6 6 2 3 5 2 3 5 2 3 5

2 3 5 2 3 5 2 3 5 no. experiments (m) 1 1.117 1.068 1.027 0.790 0.755 0.726 0.645 0.617 0.593 0.559 0.534 0.513 0.500 0.478 0.459 0.456 0.436 0.419 2 0.989 0.961 0.939 0.699 0.680 0.664 0.571 0.555 0.542 0.494 0.481 0.469 0.442 0.430 0.420 0.404 0.392 0.383 3 0.942 0.923 0.907 0.666 0.653 0.642 0.544 0.533 0.524 0.471 0.462 0.454 0.421 0.413 0.406 0.385 0.377 0.370 4

0.918 0.903 0.891 0.649 0.639 0.630 0.530 0.522 0.515 0.459 0.452 0.446 0.411 0.404 0.399 0.375 0.369 0.364 6 0.893 0.883 0.875 0.632 0.624 0.619 0.516 0.510 0.505 0.447 0.442 0.437 0.399 0.395 0.391 0.365 0.361 0.357 10 0.873 0.867 0.862 0.617 0.613 0.609 0.504 0.500 0.497 0.436 0.433 0.431 0.390 0.388 0.385 0.356 0.354 0.352 100 0.844 0.844 0.843 0.597 0.597 0.596 0.488 0.487 0.487 0.422 0.422 0.422 0.378 0.377 0.377 0.345 0.344 0.344 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 numbers of experiments versus more coupons in an experiment). Any questions?

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