Center for Biofilm Engineering
Experimental design
and statistical analysis
of in vitro models of
oral biofilms
Al Parker, Biostatistician
July, 2012
What is statistical thinking?
 Data/Response
 Experimental Design
 Uncertainty assessment
What is statistical thinking?
 Data/Response
(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
 Increase efficiency
(establish statistical properties)
(conduct the least number of experiments)
 Improve communication
Why statistical thinking?
in vitro testing
Attributes of an in vitro method: Seven R’s
 Relevance
 Reasonableness
 Ruggedness
 Responsiveness
 Reproducibility (inter-laboratory)
 Resemblance
 Repeatability (intra-laboratory reproducibility)
http://www.biofilm.montana.edu/content/ksa-sm-03
Attributes of an in vitro method: Seven R’s
 Relevance
 Reasonableness
 Ruggedness
 Responsiveness
 Reproducibility (inter-laboratory)
 Resemblance
 Repeatability (intra-laboratory reproducibility)
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,
CSr = STDEV(Mean Controls for each experiment)
http://www.biofilm.montana.edu/content/ksa-sm-10
Resemblance Example
ASTM E2647
Drip Flow Reactor
• Low shear
• Plug flow
Resemblance Example
4 slides or coupons
Experimental Design:
• saliva collected from volunteers
• 4 day old supragingival biofilms
• Both saline and treatment
applied for 1 minute
• 5 independent experimental runs
control
(sterile saline)
treated
(Chlorhexidine digluconate 0.12%)
Resemblance Example
Data: log10(cfu/cm2) from viable plate counts
Coupon
1
2
Density
LD
cfu/cm2 log(cfu/cm2)
2.3 x 108
8.36
1.7 x 108
8.23
ControlLD= 8.29
Resemblance Example
Exp
coupon
LD
1
8.36
1
8.23
2
7.62
2
7.49
3
7.59
3
7.78
4
7.84
4
8.08
5
7.77
5
7.33
Control
LD
Control
SD
8.29
0.0871
7.55
0.0910
7.68
0.1376
7.96
0.1660
7.55
0.315
Resemblance from experiment to experiment
Summary Statistics:
log10 (cfu/cm2)
1. Mean ControlLD = 7.81
the best guess for the
true mean control LD
2.
CSr=STDEV(ControlLDs)
=0.32
the typical distance
between
the ControlLD for a
single experiment and the
true mean control LD
CSr is not STDEV(LDs)
Resemblance from experiment to experiment
log10 (cfu/cm2)
The variance CSr2
can be partitioned:
84% due to among
experiment sources
16% due to within
experiment sources
Estimating the true mean control LD
with confidence
1. Start with your best guess: Mean ControlLD
2. Calculate the SE of Mean ControlLD, using:
CS2c = within-experiment variance of control coupon LD
CS2E = among-experiments variance of control coupon LD
nc = number of control coupons per experiment
m = number of experiments
SE of Mean ControlLD = CSr / m =
2
CS c
nc • m
+
2
CS E
m
3. CI for the true mean control LD = Mean ControlLD ± tm-1 x SE
Estimating the true mean control LD
with confidence
1. Mean ControlLD = 7.81
2. Calculate the SE of Mean ControlLD:
CS2c = 0.16 x (.32)2 = 0.03211
CS2E = 0.84 x (.32)2 = 0.08544
nc = 2
m=5
SE of Mean ControlLD =
0.03211
2•5
3. A 95% CI for true mean control LD
+
0.08544
5
= 0.1425
= 7.81 ± 2.78 x 0.1425
= 7.81 ± 0.33
= (7.41, 8.20)
log10 (cfu/cm2)
Estimating the true mean control LD
with confidence
We are 95%
confident that the
true mean of the
control LDs is in
this interval
Attributes of an in vitro method: Seven R’s
 Relevance
 Reasonableness
 Ruggedness
 Responsiveness
 Reproducibility (inter-laboratory)
 Resemblance
 Repeatability (intra-laboratory reproducibility)
Repeatability
Independent repeats of the same
experiment in the same laboratory produce
nearly the same response, as indicated by
a small
repeatability standard deviation
Sr = STDEV(Mean response for each experiment)
http://www.biofilm.montana.edu/content/ksa-sm-10
Repeatability Example
4 slides or coupons
control
(saline)
treated
(Chlorhexidine digluconate 0.12%)
Repeatability Example
Data/Response: log reduction (LR)
LR = mean(control LDs) – mean(treated LDs)
Repeatability Example
Exp
coupon
LD
1
8.36
1
8.23
2
7.62
2
7.49
3
7.59
3
7.78
4
7.84
4
8.08
5
7.77
5
7.33
Control
LD
Control
SD
8.29
0.0871
7.55
0.0910
7.68
0.1376
7.96
0.1660
7.55
0.315
Repeatability Example
Exp
control
coupon
LD
1
8.36
1
8.23
2
7.62
2
7.49
3
7.59
3
7.78
4
7.84
4
8.08
5
7.77
5
7.33
Control
LD
treated
coupon Treated
LD
LD
LR
6.60
8.29
4.97
5.79
2.51
5.54
2.08
5.22
2.46
6.50
1.46
6.66
0.89
5.61
7.55
5.47
5.25
7.68
5.20
7.37
7.96
5.63
7.46
7.55
5.87
Mean LR = 1.87
Since there is no
obvious pairing
between the
controls and
treated coupons
in each
experiment, get
1 LR for each
experiment
Repeatability Example
Summary Statistics:
1. Mean LR = 1.87
the best guess for the
true mean LR
2. Sr = STDEV(LRs)
= 0.69
the typical distance
between
the LR for a
single experiment
and the true mean LR
Estimating the true mean LR
with confidence
1. Start with your best guess: Mean LR
2. Calculate the SE of Mean LR, using:
S2c = within-experiment variance of control coupon LD
S2d = within-experiment variance of treated coupon LD
S2E = among-experiment variance of LR
nc = number of control coupons per experiment
nd = number of treated coupons per experiment
m = number of experiments
SE of mean LR = Sr /
m
=
2
Sc
nc • m
+
2
Sd
nd • m
3. CI for the true mean LR = Mean LR ± tm-1 x SE
+
2
SE
m
Estimating the true mean LR
with confidence
1. Mean LR = 1.87
2. Sc2 = 0.03211
Sd2 = 0.82092
SE2 = 0.06219
nc = 2, nd = 2, m = 5
SE of mean LR =
0.03211
2•5
+
3. 95% CI for true mean LR
0.82092
2•5
+
0.06219
= 0.309
5
= 1.87 ± 2.78 x 0.309
= 1.87 ± 0.8580
= (1.01, 2.73)
Estimating the true mean LR
with confidence
We are 95%
confident that the
true mean LR is in
this interval
How many coupons? experiments?
margin of error= tm-1 x
no. control coupons (nc):
no. treated coupons (nd):
no. experiments (m)
2
3
4
5
10
100
0.03211
nc • m
+
0.82092
nd • m
+
0.06219
m
1
1
1
2
2
2
1
3
4
4
1
7
8.49
6.31
6.21
5.39
4.67
4.10
2.35
1.75
1.72
1.49
1.29
1.13
1.50
1.12
1.10
0.96
0.83
0.73
1.17
0.87
0.86
0.75
0.64
0.57
0.68
0.50
0.49
0.43
0.37
0.33
0.19
0.14
0.14
0.12
0.10
0.09
Summary

Even though biofilms are complicated, it is feasible to develop
in vitro methods that meet the “Seven R” criteria.
 Good experiments use controls, randomization where possible, and
sufficient replication.
 Assess uncertainty by reporting CIs.
 To reduce uncertainty, invest effort in conducting more experiments
instead of using more coupons in a single experiment.
 For additional statistical resources for biofilm methods, check out:
http://www.biofilm.montana.edu/category/documents/ksa-sm
Any questions?