Description
Human/ Salmonella anatum strain II data [4]
Dose Positive stool culture No positive stool culture Total
89000 5 1 6
448000 4 2 6
1040000 6 0 6
3.9E+06 4 2 6
1E+07 6 0 6
2.39E+07 5 1 6
4.45E+07 6 0 6
6.73E+07 8 0 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 62.8 54.2 7 3.84 
1.84e-13 		14.1 
4.22e-11
Beta Poisson 8.6 6 12.6 
0.198
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 2.3E-01 3.63E-02 5.29E-02 6.00E-02 5.51E-01 6.70E-01 1.40E+00
N50 4.91E+03 2.59E-10 2.73E-08 4.91E-06 8.72E+04 1.23E+05 2.29E+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
8.00
Μodel
beta-Poisson
N50
4.91E+03
LD50/ID50
4.91E+03
Dose Units
CFU
Response
positive stool culture
Exposure Route
oral (with eggnog)
Contains Preferred Model
a
2.3E-01
Agent Strain
strain II
Experiment ID
233
Host type
human
Description
Human/ Salmonella anatum strain I & II pooled data [4]
Dose Positive stool culture No positive stool culture Total
12000 2 3 5
24000 3 3 6
66000 4 2 6
89000 5 1 6
93000 1 5 6
141000 3 3 6
256000 5 1 6
448000 4 2 6
587000 4 2 6
860000 6 0 6
1040000 6 0 6
3.9E+06 4 2 6
1E+07 6 0 6
2.39E+07 5 1 6
4.45E+07 6 0 6
6.73E+07 8 0 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 138 119 15 3.84 
0 		25 
0
Beta Poisson 18.9 14 23.7 
0.168
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 3.18E-01 1.35E-01 1.71E-01 1.92E-01 5.70E-01 6.66E-01 9.56E-01
N50 3.71E+04 1.40E+03 5.50E+03 8.86E+03 8.82E+04 1.00E+05 1.30E+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
16.00
Μodel
beta-Poisson
N50
3.71E+04
LD50/ID50
3.71E+04
Dose Units
CFU
Response
positive stool culture
Exposure Route
oral (with eggnog)
Contains Preferred Model
a
3.18E-01
Agent Strain
strain I
Experiment ID
232, 233
Host type
human
Description
Human / Salmonella anatum strain I data
Dose Positive stool culture No positive stool culture Total
12000 2 3 5
24000 3 3 6
66000 4 2 6
93000 1 5 6
141000 3 3 6
256000 5 1 6
587000 4 2 6
860000 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 20.5 11 7 3.84 
0.000922 		14.1 
0.00457
Beta Poisson 9.53 6 12.6 
0.146
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 2.91E-01 9.77E-04 9.77E-04 4.11E-02 1.68E+00 5.36E+00 1.20E+03
N50 4.44E+04 6.74E-02 8.03E+02 4.15E+03 1.64E+05 6.89E+06 9.07E+07

 

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
4.44E+04
LD50/ID50
4.44E+04
Dose Units
CFU
Response
positive stool culture
Exposure Route
oral (with eggnog)
Contains Preferred Model
a
2.91E-01
Agent Strain
strain I
Experiment ID
232
Host type
human
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