Statistical thinking in antibiofilm research
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Statistical thinking in antibiofilm research
Cord HamiltonAl Parker
Marty Hamilton
MBL and SBML: 23 October 20081
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Topics (presenter)
Calculating LR and the within-experiment standard error of LR (Cord)
Using data from repeated experiments to find more reliable LR values in the future (Al)
Analysis of dilution series counts (Marty)
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Log Reduction (LR) fora Quantitative Assay
Vc = viable cell density of biofilm grown in the absence of antimicrobial treatment
Vd = viable cell density of biofilm grown in the presence of the disinfectant
Log Reduction = log10(Vc) - log10(Vd)
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Numerical Example
Vc = 107 & Vd = 10
Log Reduction = log10(107) - log10(10) LR = 7 - 1 LR = 6
Interpretation: disinfectant killed 99.9999% of the bacteria
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Calculating LR whenthere are multiple coupons
= mean of control log10 densities
= mean of disinfected log10 densities
Log Reduction =
C
D
C - D
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Example: Mean of logsfor 3 disinfected coupons
Coupon Density log10Density (i) cfu / cm2 (Di) 1 9.6·104 4.982 2 1.7·104 4.230 3 9.7·103 3.987
Mean= 4.400 =
mean density = 4.09 10∙ 4
log of mean density = 4.61
D
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Example: Control coupons
Coupon log10Density (i) (Ci)
1 7.499 2 7.013 3 7.863
C = 7.458
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Calculating LR whenthere are multiple coupons
= 7.458 & = 4.400
Log Reduction =
C D
C - D
= 7.458 - 4.400
LR = 3.058
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Within-experiment standard error (SE) of the LR
Sc = variance of control log10 densities
Sd = variance of disinfected log10 densities
nc = number of control coupons
nd = number of disinfected coupons
SE of LR = (within-experiment)
Snc
Snd
c2
d2
2
2
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Example: Calculating SEfor single reactor experiment
Sc = 0.181865 and nc = 3
Sd = 0.269272 and nd = 3
SE = 0.181865
30.269272
3
2
2
= 0.3878
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Uncertainty in LR Estimate
LR ± SE = 3.058 ± 0.388
or 3.06 ± 0.39
or 3.1 ± 0.4
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3
2
1
0Log
Redu
ction
± S
E
Experiment1 2
RDR biofilm: 5 ppm chlorine for 10 minutes
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3 4 5
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Experiment repeated 3 times, each using three control and 3 disinfected coupons
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Statistical summary for data from 3 experiments, with 3 control and 3 disinfected coupons per experiment
log density mean log density SD log density Standard error ofExp control disinfected control disinfected log reduction control disinfected log reduction
1 6.73849 3.081151 6.82056 3.29326 6.83240 3.13546 3.69695 0.10036 0.13886 0.098921 6.93816 3.03196
2 6.66276 2.923342 6.73957 3.03488 6.71440 3.05656 3.65784 0.04473 0.14528 0.087762 6.74086 3.21146
3 6.91564 2.737483 6.74557 2.66018 6.85293 2.70805 4.14488 0.09341 0.04183 0.059093 6.89758 2.72651
Pooled within-experiment SD of the control log density: 0.08326Pooled within-experiment SD of the disinfected log density: 0.11851
Between-experiment SD of the log reduction: 0.25736
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S
nc • m
c2
+
Formula for the SE of the mean LR, averaged over experiments
Sc = within-experiment variance of control coupon LD
Sd = within-experiment variance of disinfected coupon LD
SE = between-experiments variance of LR
nc = number of control coupons
nd = number of disinfected coupons
m = number of experiments
2
2
2
S
nd • m
d2
+S
m
E2
SE of mean LR =
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Formula for the SE of the mean LR, using estimated standard deviations
0.0833
nc • m+
0.1185
nd • m
2
+0.2574
m
2
SE of mean LR =
2
Pooled within-experiment SD of the control log density: 0.0833Pooled within-experiment SD of the disinfected log density: 0.1185
Between-experiment SD of the log reduction: 0.2574
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Choosing the numbers of coupons and the number of experiments. Table cell is the the SE of the mean LR. Shaded SE values are designs requiring 24 coupons.
no. control coupons (nc): 2 3 6 12no. disinfected coupons (nd): 2 3 6 12
no. experiments (m) 1 0.277 0.271 0.264 0.2612 0.196 0.191 0.187 0.1843 0.160 0.156 0.152 0.1514 0.138 0.135 0.132 0.1306 0.113 0.110 0.108 0.106
10 0.088 0.086 0.084 0.082100 0.028 0.027 0.026 0.026
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Dilution series and drop plate technique
Source: BiofilmsOnline
Counted dilution32 colonies
10
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Find the fraction of initial beaker volume in each of the dilution tubes
Source: BiofilmsOnline
Beaker: containedall cells fromcoupon
0.1 0.01 0.001 0.0001
fraction of beaker volume in tube
10
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Estimated number of cells in beaker = cfu count divided by the volume fraction plated
Beaker: containsall cells fromcoupon
10-4 fraction in tube
Plated 50 μl from tube;plate contains a fraction50/10000 = 5 x 10-3 of the volume in the tube.
f = (5 x 10-3) 10-4 = 5 x 10-7
Estimate:32/(5 x 10-7) = 6.4 x 107
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Dilution series and filter technique: pooling data from two tubes
9 mlfiltered
10 ml filtered
Count 20 fields on each filter;corresponds to 0.02 of filter area
f = 0.001 x 0.9 x 0.02 = 1.8 x 10-5
f = 0.0001 x 1.0 x 0.02 = 2.0 x 10-6
421cfu
39cfu
The 460 cfu corresponds to this fraction of the beaker volume:f = 1.8x10-5 + 2.0x10-6
= 2.0 x 10-5
Estimate for beaker = 460/(2.0x10-5)= 2.3 x 107
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