Description
EPEC disease in the human model data
Dose Diarrhea No diarrhea Total
1E+06 0 4 4
1E+06 1 4 5
1E+08 1 4 5
5E+08 3 2 5
2.5E+09 6 0 6
1E+10 3 2 5
1E+10 5 0 5
2E+10 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 31.8 20.6 7 3.84 
5.69e-06 		14.1 
4.37e-05
Beta Poisson 11.2 6 12.6 
0.0813
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 2.21E-01 9.31E-02 1.18E-01 1.27E-01 1.25E+00 7.41E+02 1.29E+04
N50 6.85E+07 6.14E+06 1.11E+07 1.52E+07 6.32E+08 7.69E+08 1.09E+09
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
8.00
Μodel
beta-Poisson
N50
6.85E+07
LD50/ID50
6.85E+07
Dose Units
CFU
Response
diarrhea
Exposure Route
oral (with NaHCO3)
Contains Preferred Model
a
2.21E-01
Agent Strain
EPEC B171-8 (serotype O11:NM)
Experiment ID
214, 216, 217
Host type
human
Experiment Dataset
Description
Moredunn isolate data 
Dose Infected Non-infected Total
100 2 2 4
300 2 3 5
1000 1 2 3
3000 3 1 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 7.37 6.16 3 3.84 
0.0131 		7.81 
0.0611
Beta Poisson 1.21 2 5.99 
0.546
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 1.14E-01 9.79E-04 9.81E-04 9.82E-04 1.17E+03 2.25E+03 5.52E+03
N50 4.55E+02 2.13E-09 2.19E-06 1.55E-05 5.62E+05 3.59E+09 1.43E+16

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
4.00
Μodel
beta-Poisson
N50
4.55E+02
LD50/ID50
4.55E+02
Dose Units
oocysts
Response
infection
Exposure Route
oral
Contains Preferred Model
a
1.14E-01
Agent Strain
Moredun isolate
Experiment ID
183
Host type
human
Description
TU502 data 
Dose Diarrhea Not diarrhea Total
10 2 3 5
30 3 2 5
100 5 2 7
500 3 1 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 11.6 11.5 3 3.84 
0.000708 		7.81 
0.00894
Beta Poisson 0.119 2 5.99 
0.942
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 2.7E-01 9.83E-04 9.85E-04 2.03E-03 6.60E+00 6.70E+02 3.19E+03
N50 1.68E+01 3.41E-16 9.86E-09 1.68E-06 7.15E+01 9.76E+01 6.59E+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
4.00
Μodel
beta-Poisson
N50
1.68E+01
LD50/ID50
1.68E+01
Dose Units
oocysts
Response
diarrhea
Exposure Route
oral
Contains Preferred Model
a
2.7E-01
Agent Strain
*C. hominis*, TU502
Experiment ID
181
Host type
human
Description
Human Inaba 569B 
Dose Diarrhea and culture positive No diarrhea and 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 0 2 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 14.9 7.58 6 3.84 
0.00589 		12.6 
0.0207
Beta Poisson 7.36 5 11.1 
0.195
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 1.31E-01 1.04E-03 1.04E-03 1.04E-03 1.67E-01 1.67E-01 1.67E-01
N50 2.91E+09 3.23E+08 3.23E+08 3.23E+08 8.87E+254 8.87E+254 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
2.91E+09
LD50/ID50
2.91E+09
Dose Units
CFU
Response
diarrhea and culture positive
Exposure Route
oral (no NaHCO3)
Contains Preferred Model
a
1.31E-01
Agent Strain
Inaba 569B (classical)
Experiment ID
167
Host type
human
Description
Escherichia coli (ETEC 214-4 (ST)) in the human model data 
Dose Diarrhea or vomiting No diarrhea or vomiting Total
1E+06 0 4 4
1E+08 3 2 5
1E+10 4 1 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 15.9 15.3 2 3.84 
9e-05 		5.99 
0.000359
Beta Poisson 0.531 1 3.84 
0.466
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 2.5E-01 9.94E-04 9.94E-04 9.94E-04 1.76E+02 7.32E+02 7.32E+02
N50 9.1E+07 3.05E+04 4.09E+04 5.00E+04 3.20E+08 6.91E+08 6.91E+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
3.00
Μodel
beta-Poisson
N50
9.1E+07
LD50/ID50
9.1E+07
Dose Units
CFU
Response
diarrhea or vomiting
Exposure Route
oral (in milk)
Contains Preferred Model
a
2.5E-01
Agent Strain
ETEC 214-4 (ST)
Experiment ID
165
Host type
human
Experiment Dataset
Description
EPEC, infection, buffered, in the human model data
Dose Shedding in feces No shedding in feces Total
1E+06 3 1 4
1E+06 5 0 5
1E+06 4 1 5
1E+08 5 0 5
1E+08 5 0 5
9E+08 8 0 8
1E+10 10 0 10
1E+10 9 0 9
1E+10 14 0 14
1E+10 5 0 5
1E+10 5 0 5
1E+10 5 0 5
2.3E+10 19 0 19

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 1.98 2.71e-06 12 3.84 
0.999 		21 
0.999
Beta Poisson 1.98 11 19.7 
0.999
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 1.95E-06 8.47E-07 1.03E-06 1.25E-06 2.64E-06 2.64E-06 2.64E-06
ID50/LD50/ETC* 3.56E+05 2.63E+05 2.63E+05 2.63E+05 5.53E+05 6.73E+05 8.18E+05
*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
13.00
Μodel
exponential
LD50/ID50
3.56E+05
Dose Units
CFU
Response
shedding in feces
Exposure Route
oral (w. 2g NaHCO3)
Contains Preferred Model
k
1.95E-06
Agent Strain
EPEC E2348/69 (O127:H6)
Experiment ID
154, 156, 158, 160, 219, 220, 221
Host type
human
Experiment Dataset
Description
ETEC infection, unbuffered, in the human model data
Dose Diarrhea No diarrhea Total
1E+06 0 4 4
1E+06 1 4 5
1E+08 1 4 5
5E+08 3 2 5
2.5E+09 6 0 6
1E+10 9 1 10
1E+10 9 5 14
1E+10 3 2 5
1E+10 5 0 5
2E+10 2 0 2
2.3E+10 14 5 19

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 57.8 43.4 10 3.84 
4.51e-11 		18.3 
9.36e-09
Beta Poisson 14.4 9 16.9 
0.108
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 1.62E-01 8.23E-02 9.98E-02 1.08E-01 3.69E-01 4.21E-01 5.36E-01
N50 9.98E+07 7.29E+06 1.55E+07 2.20E+07 8.50E+08 1.06E+09 1.57E+09
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
9.98E+07
LD50/ID50
9.98E+07
Dose Units
CFU
Response
diarrhea
Exposure Route
oral (w. 2g NaHCO3)
Contains Preferred Model
a
1.62E-01
Agent Strain
EPEC E2348/69 (O127:H6)
Experiment ID
153, 157, 159, 214, 216, 217
Host type
human
Experiment Dataset
Description
EPEC disease in the human model data
Dose Diarrhea No diarrhea Total
1E+06 3 3 6
1E+07 6 9 15
1E+08 6 1 7
1E+08 7 4 11
1E+08 7 5 12
1E+08 9 3 12
1E+08 6 3 9
1E+08 4 2 6
1E+08 3 1 4
1E+08 4 0 4
2.7E+08 9 7 16
5E+08 19 8 27
1E+09 5 3 8
1E+09 7 1 8
1E+09 5 5 10
1E+10 8 0 8
1E+10 5 4 9
1E+10 9 3 12
1E+10 9 5 14

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 412 393 18 3.84 
0 		28.9 
0
Beta Poisson 19.1 17 27.6 
0.322
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 7.54E-02 8.28E-03 1.11E-02 1.51E-02 1.46E-01 1.59E-01 1.84E-01
N50 1.7E+06 2.80E-11 1.91E-06 1.44E-03 2.34E+07 3.09E+07 4.67E+07
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
19.00
Μodel
beta-Poisson
N50
1.7E+06
LD50/ID50
1.7E+06
Dose Units
CFU
Response
diarrhea
Exposure Route
oral (with NaHCO3)
Contains Preferred Model
a
7.54E-02
Agent Strain
ETEC B7A
Experiment ID
142, 143, 144, 145, 147, 151, 161, 162, 163, 164, 168, 169, 170, 172
Host type
human
Experiment Dataset
Description
UCP isolate 
Dose Infected Non-infected Total
500 3 2 5
1000 2 1 3
5000 2 3 5
1E+04 4 0 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 11.5 6.99 3 3.84 
0.0082 		7.81 
0.00945
Beta Poisson 4.48 2 5.99 
0.107
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 1.45E-01 9.81E-04 4.63E-03 9.53E-03 1.27E+00 1.46E+02 9.10E+02
N50 1.79E+02 2.74E-13 7.60E-10 4.54E-09 2.62E+03 3.22E+03 6.10E+03

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
4.00
Μodel
beta-Poisson
N50
1.79E+02
LD50/ID50
1.79E+02
Dose Units
oocysts
Response
infection
Exposure Route
oral
Contains Preferred Model
a
1.45E-01
Agent Strain
UCP isolate
Experiment ID
141
Host type
human
Description
TAMU data 
Dose Infected Non-infected Total
10 2 1 3
30 2 1 3
100 3 0 3
500 5 0 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 1.07 0.21 3 3.84 
0.647 		7.81 
0.783
Beta Poisson 0.864 2 5.99 
0.649
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 5.72E-02 1.80E-02 1.92E-02 2.46E-02 2.65E+00 2.65E+00 2.65E+00
ID50/LD50/ETC* 1.21E+01 2.61E-01 2.61E-01 2.61E-01 2.82E+01 3.61E+01 3.84E+01
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

Exponential model plot, with confidence bounds around optimized model

Parameter histogram for exponential model (uncertainty of the parameter)

 

 

# of Doses
4.00
Μodel
exponential
LD50/ID50
1.21E+01
Dose Units
oocysts
Response
infection
Exposure Route
oral
Contains Preferred Model
k
5.72E-02
Agent Strain
TAMU isolate
Experiment ID
140
Host type
human
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