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

Description
mice (10day old, day1) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 10 10
25 0 16 16
250 0 15 15
2500 0 13 13
25000 12 4 16
250000 14 3 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential

21.1

 13.8 5 3.84 
0.000207 		11.1 
0.000783
Beta Poisson

7.32

 4 9.49 
0.12
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 6.73E-01 3.02E-01 3.62E-01 3.80E-01 1.55E+00 6.30E+03 1.06E+04
N50 1.93E+04 9.62E+03 1.12E+04 1.18E+04 3.42E+04 4.01E+04 5.18E+04

 

 

 

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
1.93E+04
LD50/ID50
1.93E+04
Dose Units
CFU
Response
death(after day 1)
Exposure Route
injected in eyelids
Contains Preferred Model
a
6.73E-01
Agent Strain
ATCC 19660
Experiment ID
283
Host type
Swiss webster mice(10day old)
Description
Model data for rotavirus (CJN strain) in the human 
Dose Infected Non-infected Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 8 3 11
90 6 1 7
900 7 1 8
9000 5 2 7
9E+04 3 0 3

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 125 119 7 3.84 
0 		14.1 
0
Beta Poisson 6.2 6 12.6 
0.401
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 2.53E-01 1.28E-01 1.51E-01 1.64E-01 5.18E-01 6.58E-01 6.76E+02
N50 6.17E+00 1.46E+00 2.17E+00 2.49E+00 1.89E+01 2.49E+01 4.37E+01

 

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
LD50/ID50
6.17E+00
Dose Units
FFU
Exposure Route
oral
Contains Preferred Model
a
2.53E-02
k
6.17E+00
Experiment ID
70
Host type
human
Experiment Dataset
Description
White rabbit /  Pseudomonas aeruginosa 
Dose Severe Stromal Ulceration

Not Corneal Ulceration

 Total
63.2 0 5 5
2220 2 3 5
13200 1 4 5
78000 1 4 5
462000 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

13.2

 8.73 4 3.84 
0.00313  		9.49 
0.0105
Beta Poisson

4.43

 3 7.81 
0.219
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 1.09E-01 4.05E-02 5.23E-02 5.72E-02 9.05E+06 4.82E+07 2.53E+12
N50 1.52E+05 4.66E+03 1.13E+04 1.55E+04 1.55E+07 6.25E+07 1.96E+09

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
5.00
Μodel
beta-Poisson
N50
1.52E+05
LD50/ID50
1.52E+05
Dose Units
CFU
Response
Severe stromal ulceration
Exposure Route
contact lens
Contains Preferred Model
a
1.09E-01
Experiment ID
298
Host type
white rabbit
Description
White rabbit /  Pseudomonas aeruginosa 
Dose Corneal Ulceration

Not Corneal Ulceration

 Total
63.2 0 5 5
2220 2 3 5
13200 3 2 5
78000 3 2 5
462000 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

9.41

 7.02 4 3.84 
0.00807  		9.49 
0.0516
Beta Poisson

2.39

 3 7.81 
0.495
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 3.55E-01 1.53E-01 1.76E-01 1.91E-01 4.52E+00 1.73E+07 1.35E+11
N50 6.57E+03 7.71E+02 1.44E+03 1.70E+03 2.55E+04 4.30E+04 8.32E+04

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
5.00
Μodel
beta-Poisson
N50
6.57E+03
LD50/ID50
6.57E+03
Dose Units
CFU
Response
corneal ulceration
Exposure Route
contact lens
Contains Preferred Model
a
3.55E-01
Experiment ID
297
Host type
white rabbit
Description
Pooled data of White rabbit /  Pseudomonas aeruginosa 
Dose Corneal Ulceration

Not Corneal Ulceration

 Total
63.2 0 5 5
63.2 0 5 5
2220 2 3 5
2220 2 3 5
13200 3 2 5
13200 1 4 5
78000 3 2 5
78000 1 4 5
462000 5 0 5
462000 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

30.9

 20.8 9 3.84 
5.11e-06  		16.9 
0.000312
Beta Poisson

10.1

 8 15.5 
0.26
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 1.9E-01 9.63E-02 1.15E-01 1.24E-01 3.86E-01 5.51E-01 2.50E+00
N50 1.85E+04 3.18E+03 4.73E+03 6.01E+03 7.05E+04 8.98E+04 1.97E+05

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
10.00
Μodel
beta-Poisson
N50
1.85E+04
LD50/ID50
1.85E+04
Dose Units
CFU
Response
corneal ulceration
Exposure Route
contact lens
Contains Preferred Model
a
1.9E-01
Experiment ID
297 & 298
Host type
white rabbit
Description
Model data for rotavirus (CJN strain) in the human 
Dose Detectable shedding No detectable shedding Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 8 3 11
90 4 3 7
900 3 5 8
9000 4 3 7
9E+04 2 1 3

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 157 148 7 3.84 
0 		14.1 
0
Beta Poisson 9.42 6 12.6 
0.151
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 9.6E-02 9.94E-04 9.96E-04 9.98E-04 1.59E-01 1.74E-01 2.05E-01
N50 9.61E+01 2.95E-03 1.59E-02 4.56E-02 2.83E+03 1.46E+04 1.58E+80

 

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
96.1
LD50/ID50
96.1
Dose Units
FFU
Response
detectable shedding
Exposure Route
oral
Contains Preferred Model
a
9.6E-2
Agent Strain
CJN strain (unpassaged
Experiment ID
125
Host type
human
Experiment Dataset
Description
Model data for rotavirus (CJN strain) in the human 
Dose Symptoms and infection No symptoms and infection Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 5 6 11
90 2 5 7
900 4 4 8
9000 3 4 7
9E+04 2 1 3

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 103 99.5 7 3.84 
0 		14.1 
0
Beta Poisson 3.14 6 12.6 
0.791
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 7.28E-02 9.93E-04 9.95E-04 9.96E-04 1.32E-01 1.46E-01 1.83E-01
N50 1.47E+03 6.55E-03 1.85E-02 4.58E-02 5.47E+06 1.82E+31 6.68E+122

 

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
1.47E+03
LD50/ID50
1.47E+03
Dose Units
FFU
Response
infection
Exposure Route
oral
Contains Preferred Model
a
7.28E-02
Agent Strain
CJN strain (unpassaged)
Experiment ID
71
Host type
human
Description
Escherichia coli (EIEC 1624) in the human model data
Dose Positive stool isolation No positive stool isolation Total
1E+04 0 5 5
1E+06 5 4 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 28.6 27.2 2 3.84 
1.82e-07 		5.99 
6.18e-07
Beta Poisson 1.38 1 3.84 
0.24
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 1.55E-01 1.26E-03 1.26E-03 2.84E-02 1.84E+01 1.29E+02 1.90E+02
N50 2.11E+06 1.73E+05 2.95E+05 2.95E+05 7.85E+08 9.22E+140 9.22E+140
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 mode
beta Poisson model plot, with confidence bounds around optimized mode
# of Doses
3.00
Μodel
beta-Poisson
N50
2.11E+06
LD50/ID50
2.11E+06
Dose Units
CFU
Response
positive stool isolation
Exposure Route
oral (in milk)
Contains Preferred Model
a
1.55E-01
Agent Strain
EIEC 1624
Experiment ID
98
Host type
human
Experiment Dataset
Description
Dose response data
Dose Positive stool isolation No positive stool isolation Total
1E+06 3 1 4
1E+08 4 1 5
1E+08 5 0 5
1E+08 5 0 5
1E+10 5 0 5
1E+10 5 0 5
1E+10 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 64.1 61.4 6 3.84 
4.77e-15 		12.6 
6.67e-12
Beta Poisson 2.71 5 11.1 
0.745
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 3.75E-01 1.29E-01 1.34E-01 1.34E-01 9.97E+00 9.97E+00 1.07E+01
N50 1.78E+05 3.63E-01 3.63E-01 3.63E-01 2.46E+06 3.48E+06 6.09E+06
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
7.00
Μodel
beta-Poisson
N50
1.78E+05
LD50/ID50
1.78E+05
Dose Units
CFU
Response
positive stool isolation
Exposure Route
oral (in milk)
Contains Preferred Model
a
3.75E-01
Agent Strain
ETEC B7A
Experiment ID
96, 100, 166
Host type
human
Experiment Dataset
Description
Guinea pig/Vollum Strain model data 
Dose Dead Survived Total
200 0 4 4
2000 0 8 8
2E+04 6 6 12
2E+05 10 2 12
2E+06 7 1 8
2E+07 7 0 7

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 29.2 26.6 5 3.84 
2.46e-07 		11.1 
2.11e-05
Beta Poisson 2.58 4 9.49 
0.631
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 5.49E-01 2.55E-01 3.03E-01 3.32E-01 5.51E+00 2.45E+03 6.16E+03
N50 2.85E+04 1.00E+04 1.25E+04 1.43E+04 6.57E+04 7.85E+04 1.09E+05

 

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
2.85E+04
LD50/ID50
2.85E+04
Dose Units
spores
Response
death
Exposure Route
inhalation
Contains Preferred Model
a
5.49E-01
Agent Strain
Vollum
Experiment ID
84
Host type
guinea pig
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