$$P(response)=1-[1+dose\frac{2^{\frac{1}{a}}-1}{N^{50}} ]^{-a}$$

Description
Model data for Shigella flexneri (2a, strain 2457T) in the human 
Dose Positive stool isolation No positive stool isolation Total
180 6 30 36
5000 33 16 49
1E+04 66 21 87
1E+05 15 9 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 169 160 3 3.84 
0 		7.81 
0
Beta Poisson 8.73 2 5.99 
0.0127
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 2.65E-01 1.47E-01 1.74E-01 1.87E-01 3.82E-01 4.09E-01 4.70E-01
N50 1.48E+03 5.60E+02 7.33E+02 8.26E+02 2.55E+03 2.78E+03 3.38E+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
1.48E+03
LD50/ID50
1.48E+03
Dose Units
CFU
Response
positive stool isolation
Exposure Route
oral (in milk)
Contains Preferred Model
a
2.65E-01
Agent Strain
2a (strain 2457T)
Experiment ID
83
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 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 S. Typhi (Quailes) in humans 
Dose Disease No disease Total
1000 0 14 14
1E+05 32 84 116
1E+07 16 16 32
1E+08 8 1 9
1E+09 40 2 42

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 293 284 4 3.84 
0 		9.49 
0
Beta Poisson 8.63 3 7.81 
0.0346
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 2.03E-01 1.33E-01 1.49E-01 1.57E-01 2.74E-01 2.89E-01 3.27E-01
N50 8.53E+05 3.38E+05 4.28E+05 4.80E+05 1.62E+06 1.85E+06 2.49E+06

 

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
5.00
Μodel
beta-Poisson
N50
8.53E+05
LD50/ID50
8.53E+05
Dose Units
CFU
Response
disease
Exposure Route
oral (in milk)
Contains Preferred Model
a
2.03E-01
Agent Strain
Quailes
Experiment ID
80
Host type
human
Description
Model data for S. Typhi (Quailes) in humans
Dose Disease No disease Total
1000 0 14 14
1E+05 28 76 104
1E+05 32 84 116
1E+07 15 15 30
1E+07 16 16 32
1E+08 8 1 9
1E+09 4 0 4
1E+09 40 2 42

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 419 406 7 3.84 
0 		14.1 
0
Beta Poisson 13.8 6 12.6 
0.0321
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 1.75E-01 1.21E-01 1.32E-01 1.39E-01 2.23E-01 2.34E-01 2.58E-01
N50 1.11E+06 5.13E+05 6.10E+05 6.72E+05 2.00E+06 2.28E+06 2.95E+06

 

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
8.00
Μodel
beta-Poisson
N50
1.11E+06
LD50/ID50
1.11E+06
Dose Units
CFU
Response
disease
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.75E-01
Agent Strain
Quailes
Experiment ID
79, 80
Host type
human
Description
Model data for S. Typhi (Quailes) in humans
Dose Disease No disease Total
1E+05 28 76 104
1E+07 15 15 30
1E+09 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 124 121 2 3.84 
0 		5.99 
0
Beta Poisson 2.87 1 3.84 
0.0905
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 1.11E-01 3.19E-02 4.80E-02 5.49E-02 1.96E-01 2.17E-01 2.59E-01
N50 3.45E+06 4.81E+05 6.95E+05 8.50E+05 9.53E+07 2.24E+08 4.19E+09

 

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
3.45E+06
LD50/ID50
3.45E+06"
Dose Units
CFU
Response
disease
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.11E-01
Agent Strain
Quailes
Experiment ID
79
Host type
human
Description
human/type 39 strain SF 299 model data 
Dose Infected Non-infected Total
0.05 0 11 11
0.15 2 7 9
0.5 8 16 24
5 5 11 16
50 47 15 62

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 50.3 44.3 4 3.84 
2.76e-11 		9.49 
3.06e-10
Beta Poisson 6.01 3 7.81 
0.111
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 2.24E-01 9.88E-04 1.40E-01 1.53E-01 3.71E-01 4.27E-01 7.63E-01
N50 3.29E+00 1.90E-02 1.34E+00 1.59E+00 7.67E+00 9.27E+00 1.59E+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
6.00
Μodel
beta-Poisson
N50
1.81E+00
LD50/ID50
1.81E+00
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
2.21E-01
Agent Strain
type 39
Experiment ID
65
Host type
human
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