Description
Escherichia coli (ETEC O111 (in paper as “E. coli 111, B4”)) in the human model data 
Dose Slight to severe illness No slight to severe illness Total
7E+06 7 4 11
5.31E+08 8 4 12
6.5E+09 11 0 11
9E+09 12 0 12

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 39.8 33.4 3 3.84 
7.5e-09 		7.81 
1.19e-08
Beta Poisson 6.38 2 5.99 
0.0412
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 2.63E-01 9.92E-04 7.95E-02 1.00E-01 4.71E-01 5.53E-01 1.48E+01
N50 3.56E+06 6.89E-01 1.15E+03 2.08E+03 1.85E+07 2.49E+07 4.18E+07
beta Poisson model plot, with confidence bounds around optimized model
beta Poisson model plot, with confidence bounds around optimized model

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

 

 

# of Doses
4.00
Μodel
beta-Poisson
N50
3.56E+06
LD50/ID50
3.56E+06
Dose Units
CFU
Response
slight to severe illness
Exposure Route
oral
Contains Preferred Model
a
2.63E-01
Agent Strain
ETEC O111 (in paper as "E. coli 111, B4")
Experiment ID
43
Host type
human
Experiment Dataset
Description
Escherichia coli (ETEC O55 (in paper as “type 55, B5”)) in the human model data 
Dose Slight to severe illness No slight to severe illness Total
1.43E+08 6 2 8
1.73E+09 5 2 7
5.33E+09 6 2 8
1.6E+10 7 1 8

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 35 34.5 3 3.84 
4.2e-09 		7.81 
1.21e-07
Beta Poisson 0.486 2 5.99 
0.784
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 8.7E-02 9.87E-04 1.02E-03 1.67E-02 3.57E-01 4.67E-01 7.83E-01
N50 2.05E+05 3.40E-09 4.31E-06 2.31E-04 1.30E+08 2.09E+08 5.13E+08
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
beta Poisson model plot, with confidence bounds around optimized model
# of Doses
4.00
Μodel
beta-Poisson
N50
2.05E+05
LD50/ID50
2.05E+05
Dose Units
CFU
Response
slight to severe illness
Exposure Route
oral
Contains Preferred Model
a
8.7E-02
Agent Strain
ETEC O55 (in paper as “type 55, B5”)
Experiment ID
42
Host type
human
Experiment Dataset
Description
Escherichia coli (EIEC 1624) in the human model data 
Dose Mild to severe diarrhea No mild to severe diarrhea Total
1E+04 0 5 5
1E+06 1 8 9
1E+08 3 2 5

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 2.99 2.98 2 3.84 
0.0845 		5.99 
0.224
Beta Poisson 0.0156 1 3.84 
0.901
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.22E-08 1.97E-09 2.19E-09 4.40E-09 4.03E-08 1.17E-07 2.50E-07
ID50/LD50/ETC* 5.7E+07 2.77E+06 5.92E+06 1.72E+07 1.58E+08 3.17E+08 3.52E+08
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)
Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model
# of Doses
3.00
Μodel
exponential
LD50/ID50
5.7E+07
Dose Units
CFU
Response
mild to severe diarrhea
Exposure Route
oral (in milk)
Contains Preferred Model
k
1.22E-08
Agent Strain
EIEC 1624
Experiment ID
40
Host type
human
Experiment Dataset
Description
EIEC disease, unbuffered, in the human model data
Dose Mild to severe diarrhea No mild to severe diarrhea Total
1E+04 0 5 5
1E+04 0 5 5
1E+06 0 5 5
1E+06 1 8 9
1E+08 5 3 8
1E+08 3 2 5

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 3.19 2.24 5 3.84 
0.134 		11.1 
0.67
Beta Poisson 0.951 4 9.49 
0.917
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.07E-08 3.63E-09 4.79E-09 5.77E-09 2.04E-08 2.28E-08 3.21E-08
ID50/LD50/ETC* 6.5E+07 2.16E+07 3.04E+07 3.40E+07 1.20E+08 1.45E+08 1.91E+08
*Not a parameter of the exponential model; however, it facilitates comparison with other models.
Parameter histogram for exponential model (uncertainty of the parameter)
Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model
# of Doses
6.00
Μodel
exponential
LD50/ID50
6.5E+07
Dose Units
CFU
Response
mild to severe diarrhea
Exposure Route
oral (in milk)
Contains Preferred Model
k
1.07E-08
Agent Strain
EIEC 4608
Experiment ID
39, 40
Host type
human
Experiment Dataset
Description
Escherichia coli (EIEC 4608) in the human model data
Dose Mild to severe diarrhea No mild to severe diarrhea Total
1E+04 0 5 5
1E+06 0 5 5
1E+08 5 3 8

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 0.0986 -0.00188 2 3.84 
1 		5.99 
0.952
Beta Poisson 0.1 1 3.84 
0.751
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.
Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 9.7E-09 2.85E-09 2.86E-09 4.66E-09 2.04E-08 2.04E-08 5.07E-08
ID50/LD50/ETC* 7.14E+07 1.37E+07 3.40E+07 3.40E+07 1.49E+08 2.43E+08 2.44E+08
*Not a parameter of the exponential model; however, it facilitates comparison with other models.
Parameter histogram for exponential model (uncertainty of the parameter)
Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model
# of Doses
3.00
Μodel
exponential
LD50/ID50
7.14E+07
Dose Units
CFU
Response
mild to severe diarrhea
Exposure Route
oral (in milk)
Contains Preferred Model
k
9.7E-09
Agent Strain
EIEC 4608
Experiment ID
39
Host type
human
Experiment Dataset
Description
ETEC disease, unbuffered, in the human model data
Dose Mild to severe diarrhea No mild to severe diarrhea Total
1E+06 0 4 4
1E+08 1 4 5
1E+08 2 3 5
1E+08 3 2 5
1.43E+08 6 2 8
1.73E+09 5 2 7
5.33E+09 6 2 8
1E+10 4 1 5
1E+10 3 2 5
1E+10 4 1 5
1.6E+10 7 1 8

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 68.4 62.9 10 3.84 
2.22e-15 		18.3 
8.97e-11
Beta Poisson 5.53 9 16.9 
0.786
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 2.06E-01 1.75E-02 1.17E-01 1.32E-01 3.79E-01 4.29E-01 5.57E-01
N50 1.28E+08 3.53E+05 3.17E+07 4.09E+07 3.83E+08 4.65E+08 6.86E+08

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
beta Poisson model plot, with confidence bounds around optimized model
# of Doses
11.00
Μodel
beta-Poisson
N50
1.28E+08
LD50/ID50
1.28E+08
Dose Units
CFU
Response
mild to severe diarrhea
Exposure Route
oral (in milk)
Contains Preferred Model
a
2.06E-01
Agent Strain
ETEC B7A
Experiment ID
38, 42, 99, 165
Host type
human
Experiment Dataset
Description
E. coli disease (ETEC, EPEC, EIEC) in the human model data
Dose Mild to severe diarrhea No mild to severe diarrhea Total
1E+04 0 5 5
1E+04 0 5 5
1E+06 0 5 5
1E+06 1 8 9
1E+08 1 4 5
1E+08 5 3 8
1E+08 3 2 5
1E+08 2 3 5
1.43E+08 6 2 8
2.7E+08 9 7 16
1.73E+09 5 2 7
5.33E+09 6 2 8
1E+10 4 1 5
1E+10 3 2 5
1.6E+10 7 1 8

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 119 113 14 3.84 
0 		23.7 
0
Beta Poisson 6.56 13 22.4 
0.924
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.78E-01 9.39E-02 1.09E-01 1.19E-01 3.21E-01 3.63E-01 4.77E-01
N50 8.6E+07 1.75E+07 2.62E+07 3.25E+07 2.63E+08 3.23E+08 5.21E+08
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
beta Poisson model plot, with confidence bounds around optimized model
# of Doses
15.00
Μodel
beta-Poisson
N50
8.6E+07
LD50/ID50
8.6E+07
Dose Units
CFU
Response
mild to severe diarrhea
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.78E-01
Agent Strain
ETEC B7A
Experiment ID
38, 39, 40, 42, 99, 144
Host type
human
Experiment Dataset
Description

Please Note

The results from this experiment are not recommended for use, rather they are present for reference purposes. The confidence intervals are not complete for this experiment since the data is not allowing for a stable bootstrap outcome. It is recommended to use the recommended model as this data is likely just capable of passing the test of trend, but still likely suboptimal for dose response modeling purposes.

 

Human Inaba Strain 569B 
Dose Diarrhea or culture positive No diarrhea or culture positive Total
1E+04 0 2 2
1E+06 0 4 4
1E+07 0 4 4
1E+08 2 2 4
1E+09 1 1 2
1E+10 0 1 1
1E+11 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 15.1 10.4 6 3.84 
0.00126 		12.6 
0.0193
Beta Poisson 4.72 5 11.1 
0.451
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.98E-01 9.92E-04 9.92E-04 1.04E-03 3.20E-01 3.65E-01 4.07E-01
N50 6.36E+08 8.26E+05 8.26E+05 1.18E+08 5.33E+207 5.33E+207 8.87E+254

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

# of Doses
7.00
Μodel
beta-Poisson
N50
6.36E+08
LD50/ID50
6.36E+08
Dose Units
CFU
Response
diarrhea or culture positive
Exposure Route
oral (no NaHCO3)
Contains Preferred Model
a
1.98E-01
Agent Strain
Inaba 569B
Experiment ID
35
Host type
human
Description
Human data( Rickettsia rickettsii) 
Dose CLINICAL SIGNS NOT CLINICAL SIGNS Total
13 2 4 6
126 6 1 7
1260 17 1 18

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 13.5 13.2 2 3.84 
0.000277		 5.99 
0.00119
Beta Poisson 0.248 1 3.84 
0.618
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 6.75E-01 1.17E-01 2.44E-01 3.31E-01 1.21E+03 3.74E+03 4.98E+03
N50 2.36E+01 2.56E-02 3.35E+00 7.30E+00 6.41E+01 8.91E+01 1.28E+02

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

# of Doses
3.00
Μodel
beta-Poisson
N50
2.36E+01
LD50/ID50
2.36E+01
Dose Units
CFU
Response
clinical signs
Exposure Route
intradermal
Contains Preferred Model
a
6.75E-01
Agent Strain
Sheila Smith
Experiment ID
301
Host type
human
Description
Pooled data (experiment no. 300 and 301) 
Dose MORBIDITY NOT MORBIDITY Total
13 2 4 6
25 1 3 4
66 2 0 2
83 2 0 2
99 2 0 2
126 6 1 7
182 7 0 7
1110 1 1 2
1260 17 1 18
1770 2 0 2
2290 2 0 2
2590 2 0 2
3170 2 0 2
5060 7 0 7
5520 2 0 2
5650 2 0 2
5670 1 0 1
7460 2 0 2
9200 2 0 2
10800 2 0 2
16800 2 0 2
41000 2 0 2
45500 3 0 3
53200 2 0 2
55200 2 0 2
132000 2 0 2
149000 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 42.2 30.5 26 3.84 
3.41e-08		 38.9 
0.0235
Beta Poisson 11.7 25 37.7 
0.989
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 7.77E-01 3.82E-01 4.41E-01 4.90E-01 4.24E+00 3.59E+03 3.25E+04
N50 2.13E+01 5.70E+00 8.34E+00 1.01E+01 4.00E+01 4.16E+01 5.10E+01

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

# of Doses
27.00
Μodel
beta-Poisson
N50
2.13E+01
LD50/ID50
2.13E+01
Dose Units
CFU
Response
morbidity
Contains Preferred Model
a
7.77E-01
Agent Strain
R1 and Sheila Smith
Experiment ID
300 and 301
Host type
pooled
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