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
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