Description
Model data for Shigella flexneri (2a, strain 2457T) in the human 
Dose Illness Not illness Total
180 9 27 36
5000 28 21 49
1E+04 1 3 4
1E+04 52 36 88
1E+05 3 1 4
1E+05 14 10 24
1E+06 7 1 8
1E+07 13 6 19
1E+08 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 677 671 8 3.84 
0 		15.5 
0
Beta Poisson 6.04 7 14.1 
0.535
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 1.17E-01 4.86E-02 6.43E-02 7.25E-02 1.68E-01 1.78E-01 2.02E-01
N50 3.64E+03 3.32E+02 8.92E+02 1.22E+03 9.16E+03 1.12E+04 1.73E+04

 

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
9.00
Μodel
beta-Poisson
N50
3.64E+03
LD50/ID50
3.64E+03
Dose Units
CFU
Response
illness
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.17E-01
Agent Strain
2a (strain 2457T)
Experiment ID
82, 223
Host type
human
Experiment Dataset
Description
Model data for Shigella flexneri (2a, strain 2457T) in the human 
Dose Illness Not illness Total
1E+04 1 3 4
1E+05 3 1 4
1E+06 7 1 8
1E+07 13 6 19
1E+08 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 73.6 70.2 4 3.84 
0 		9.49 
3.89e-15
Beta Poisson 3.44 3 7.81 
0.329
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 1.43E-01 1.32E-02 2.12E-02 2.63E-02 2.90E-01 3.32E-01 4.27E-01
N50 3.54E+04 1.29E-11 8.16E-07 3.11E-04 3.34E+05 4.65E+05 9.68E+05
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
5.00
Μodel
beta-Poisson
N50
3.54E+04
LD50/ID50
3.54E+04
Dose Units
CFU
Response
illness
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.43E-01
Agent Strain
2a (strain 2457T)
Experiment ID
82
Host type
human
Experiment Dataset
# of Doses
17.00
Μodel
beta-Poisson
N50
2.35E+03
LD50/ID50
2.35E+03
Dose Units
CFU
Response
illness
Exposure Route
oral (in milk)
Contains Preferred Model
Status
paired
a
1.1E-01
Agent Strain
M 131
Experiment ID
81, 215, 82, 223, 224, 225
Host type
human
Description
Model data for Shigella dysenteriae in the human
Dose Illness Not illness Total
10 1 9 10
200 2 2 4
200 1 3 4
2000 7 3 10
1E+04 5 1 6
1E+04 2 4 6

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 30.5 16.9 5 3.84 
3.94e-05 		11.1 
1.2e-05
Beta Poisson 13.6 4 9.49 
0.00887
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 4.93E-03 9.85E-04 9.87E-04 9.88E-04 3.61E-01 4.26E-01 5.85E-01
N50 3.64E-01 2.07E-02 5.54E-02 7.42E-02 2.05E+03 4.61E+03 1.09E+28
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
6.00
Μodel
beta-Poisson
N50
3.64E-01
LD50/ID50
3.64E-01
Dose Units
CFU
Response
illness
Exposure Route
oral (in milk)
Contains Preferred Model
a
4.93E-03
Agent Strain
M 131
Experiment ID
81, 215
Host type
human
Experiment Dataset
Description
Model data for Shigella dysenteriae (M 131) in the human 
Dose Illness Not illness Total
10 1 9 10
200 2 2 4
2000 7 3 10
1E+04 5 1 6

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 13.2 13.2 3 3.84 
0.000283 		7.81 
0.0042
Beta Poisson 0.0315 2 5.99 
0.984
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 2.77E-01 5.24E-03 1.10E-01 1.34E-01 1.63E+00 1.88E+01 1.72E+03
N50 2.38E+02 1.35E+01 4.73E+01 6.36E+01 1.42E+03 2.02E+03 5.89E+03

 

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
2.38E+02
LD50/ID50
2.38E+02
Dose Units
CFU
Response
illness
Exposure Route
oral (in milk)
Contains Preferred Model
a
2.77E-01
Agent Strain
M 131
Experiment ID
81
Host type
human
Experiment Dataset
Description
Model data for Shigella flexneri (2a, strain 2457T) in the human 
Dose Illness Not illness Total
180 9 27 36
5000 28 21 49
1E+04 52 36 88
1E+05 14 10 24

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 154 153 3 3.84 
0 		7.81 
0
Beta Poisson 1.69 2 5.99 
0.429
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 1.35E-01 9.86E-04 1.22E-02 6.85E-02 2.06E-01 2.22E-01 2.58E-01
N50 3.11E+03 5.09E+01 4.31E+02 9.64E+02 7.49E+03 9.14E+03 1.89E+04

 

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
3.11E+03
LD50/ID50
3.11E+03
Dose Units
CFU
Response
illness
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.35E-01
Agent Strain
2a (strain 2457T)
Experiment ID
223
Host type
human
Experiment Dataset
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