ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
81 4 M 131 CFU human beta-Poisson a = 2.77E-01

LD50/ID50 = 2.38E+02
N50 = 2.38E+02
illness DuPont, H. L., et al. "The Response of Man to Virulent Shigella flexneri 2a." Journal of Infectious Diseases. 119 (1969): 3.
81, 215 6 M 131 CFU human beta-Poisson a = 4.93E-03

LD50/ID50 = 3.64E-01
N50 = 3.64E-01
illness Levine, M. M., et al. "Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery." Journal of Infectious Diseases. 127 (1973): 3.
Experiment ID:
81
# of Doses:
4
Agent Strain:
M 131
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 2.77E-01

LD50/ID50 = 2.38E+02
N50 = 2.38E+02
Reference:
Model data for Shigella dysenteriae (M 131) in the human [1]
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

beta Poisson model plot, with confidence bounds around optimized model


References

Experiment ID:
81, 215
# of Doses:
6
Agent Strain:
M 131
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 4.93E-03

LD50/ID50 = 3.64E-01
N50 = 3.64E-01
Reference:
Model data for Shigella dysenteriae in the human [1]
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.

beta Poisson model plot, with confidence bounds around optimized model


References