Description
Rhesus monkey Data 
Dose MORBIDITY NOT MORBIDITY Total
25 1 3 4
66 2 0 2
83 2 0 2
99 2 0 2
182 7 0 7
1110 1 1 2
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 27.6 16.4 23 3.84 
5.12e-05		 35.2 
0.232
Beta Poisson 11.2 22 33.9 
0.972
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 8.58E-01 9.77E-04 9.77E-04 9.78E-04 5.70E+06 1.41E+08 1.62E+11
N50 1.88E+01 3.58E-01 1.81E+00 7.74E+00 1.02E+03 4.02E+03 3.71E+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
24.00
Μodel
beta-Poisson
N50
1.88E+01
LD50/ID50
1.88E+01
Dose Units
CFU
Response
morbidity
Exposure Route
aerosol
Contains Preferred Model
a
8.58E-01
Agent Strain
R1
Experiment ID
300
Host type
rhesus monkey
Description
Mouse/ CO92 model data 
Dose Dead Survived Total
2 0 20 20
8 5 15 20
26 13 7 20
74 9 1 10
257 10 0 10

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 3.12 -9.43e-05 4 3.84 
1 		9.49 
0.539
Beta Poisson 3.12 3 7.81 
0.374
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 3.45E-02 2.01E-02 2.28E-02 2.44E-02 4.89E-02 5.18E-02 5.79E-02
ID50/LD50/ETC* 2.01E+01 1.20E+01 1.34E+01 1.42E+01 2.84E+01 3.04E+01 3.44E+01
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
5.00
Μodel
exponential
LD50/ID50
2.01E+01
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
k
3.45E-02
Agent Strain
CO92
Experiment ID
3
Host type
mice
Description
Mice/ Aa strain model data
Dose Dead Survived Total
1E+04 0 22 22
1E+05 1 21 22
1E+06 1 10 11
1E+07 16 6 22
1E+08 22 0 22

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 1.27 0.0341 4 3.84 
0.854 		9.49 
0.867
Beta Poisson 1.23 3 7.81 
0.745
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 1.33E-07 6.86E-08 7.91E-08 8.83E-08 2.06E-07 2.24E-07 2.75E-07
ID50/LD50/ETC* 5.22E+06 2.52E+06 3.10E+06 3.37E+06 7.85E+06 8.76E+06 1.01E+07
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
5.00
Μodel
exponential
LD50/ID50
5.22E+06
Dose Units
CFU
Response
death
Exposure Route
oral
Contains Preferred Model
k
1.33E-07
Agent Strain
Aa strain
Experiment ID
275
Host type
mice
Description

Optimization Output for experiment 274

Monkeys / SCHU S-4 model data 
Dose Dead Survived Total
5 1 5 6
11 3 3 6
32 4 2 6
65 6 0 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 1.26 -0.000367 3 3.84 
1 		7.81 
0.738
Beta Poisson 1.26 2 5.99 
0.531
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 4.73E-02 2.28E-02 2.72E-02 2.98E-02 7.81E-02 9.03E-02 1.11E-01
ID50/LD50/ETC* 1.46E+01 6.27E+00 7.67E+00 8.88E+00 2.33E+01 2.55E+01 3.04E+01
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
4.00
Μodel
exponential
LD50/ID50
1.46E+01
Dose Units
CFU
Response
death
Exposure Route
inhalation
Contains Preferred Model
k
4.73E-02
Agent Strain
SCHU S-4
Experiment ID
274
Host type
monkey
Description
Dose response data
Dose Infected Non-infected Total
100 6 6 12
1E+05 6 6 12
1E+08 10 2 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 193 192 2 3.84 
0 		5.99 
0
Beta Poisson 1.43 1 3.84 
0.231
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 5.79E-02 9.94E-04 9.78E-03 1.25E-02 1.27E-01 1.42E-01 1.87E-01
N50 4.8E+02 3.44E-13 5.25E-08 1.89E-05 5.61E+04 1.50E+05 4.41E+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
3.00
Μodel
beta-Poisson
N50
4.8E+02
LD50/ID50
4.8E+02
Dose Units
CFU
Response
infection
Exposure Route
oral
Contains Preferred Model
a
5.79E-02
Agent Strain
sub sp. Paratuberculosis IOI strain
Experiment ID
263
Host type
cheviots
Description
Dose response data
Dose Infected Non-infected Total
1000 8 8 16
1E+07 16 0 16
1E+09 16 0 16

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 3.07e-05 7.15e-06 2 3.84 
0.998 		5.99 
1
Beta Poisson 2.36e-05 1 3.84 
0.996
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 6.93E-04 2.08E-04 2.88E-04 3.75E-04 1.16E-03 1.39E-03 1.67E-03
ID50/LD50/ETC* 1E+03 4.14E+02 5.00E+02 5.96E+02 1.85E+03 2.41E+03 3.34E+03
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for Exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

# of Doses
3.00
Μodel
exponential
LD50/ID50
1000
Dose Units
CFU
Response
infection
Exposure Route
oral
Contains Preferred Model
k
6.93E-04
Agent Strain
sub sp. Paratuberculosis Bovine
Experiment ID
262
Host type
deer
Description
Human Inaba Strain 569B  
Dose Infected Non-infected Total
10 0 2 2
1000 3 1 4
1E+04 11 2 13
1E+05 7 1 8
1E+06 21 2 23
1E+08 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 92.4 91.2 5 3.84 
0 		11.1 
0
Beta Poisson 1.16 4 9.49 
0.885
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 1.14E-01 1.48E-01 1.66E-01 5.44E-01 6.55E-01 2.91E+00
N50 2.43E+02 1.88E+01 4.82E+01 6.35E+01 1.52E+03 2.08E+03 3.60E+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
6.00
Μodel
beta-Poisson
N50
2.43E+02
LD50/ID50
2.43E+02
Dose Units
CFU
Response
infection
Exposure Route
oral (with NaHCO3)
Contains Preferred Model
a
2.50E-01
Agent Strain
Inaba 569B
Experiment ID
249
Host type
human
Description
Mice/ Salmonella strain 533 data 
Dose Dead Survived Total
1E+04 20 180 200
1E+05 17 153 170
1E+06 11 29 40
3160000 6 24 30
1E+07 12 8 20
3.16E+07 17 3 20
1E+08 19 1 20

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 214 165 6 3.84 
0 		12.6 
0
Beta Poisson 48.7 5 11.1 
2.56e-09
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 1.08E-01 6.19E-02 7.06E-02 7.52E-02 1.79E-01 1.98E-01 2.44E-01
N50 9.66E+06 1.93E+06 2.43E+06 2.82E+06 5.38E+07 8.11E+07 2.13E+08

 

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
9.66E+06
LD50/ID50
9.66E+06
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
a
1.08E-01
Agent Strain
strain 533
Experiment ID
248
Host type
mice
Description
Mice/ Salmonella strain 533 data 
Dose Dead Survived Total
603 6 36 42
1910 3 39 42
6030 7 35 42
19100 5 42 47
60300 6 34 40
191000 3 29 32
603000 6 20 26
1910000 7 7 14
6030000 7 5 12
1.91E+07 10 2 12
6.03E+07 13 0 13

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 193 146 10 3.84 
0 		18.3 
0
Beta Poisson 47.5 9 16.9 
3.22e-07
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 6.21E-02 3.53E-02 4.06E-02 4.32E-02 1.09E-01 1.25E-01 1.80E-01
N50 3.46E+07 9.76E+05 1.69E+06 2.40E+06 9.41E+08 2.13E+09 1.34E+10

 

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
11.00
Μodel
beta-Poisson
N50
3.46E+07
LD50/ID50
3.46E+07
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
a
6.21E-02
Agent Strain
strain 533
Experiment ID
247
Host type
mice
Description
Mice/Salmonella strain 216 and 219 data 
Dose Dead Survived Total
5 7 8 15
25 4 11 15
125 7 8 15
630 9 6 15
3160 8 7 15
16000 13 2 15
8E+04 15 0 15
4E+05 15 0 15
2E+06 15 0 15
1E+07 15 0 15

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 133 113 9 3.84 
0 		16.9 
0
Beta Poisson 20.5 8 15.5 
0.00846
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 2.1E-01 1.45E-01 1.58E-01 1.65E-01 2.92E-01 3.14E-01 3.63E-01
N50 4.98E+01 8.10E+00 1.40E+01 1.72E+01 1.31E+02 1.62E+02 2.34E+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
10.00
Μodel
beta-Poisson
N50
4.98E+01
LD50/ID50
4.98E+01
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
a
2.1E-01
Agent Strain
strain 216 and 219
Experiment ID
246
Host type
mice
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