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ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
223 4 2a (strain 2457T) CFU human beta-Poisson a = 1.35E-01

LD50/ID50 = 3.11E+03
N50 = 3.11E+03
illness DuPont, H. L., et al. "Inoculum Size in Shigellosis and Implications for Expected Mode of Transmission." Journal of Infectious Diseases. 159 (1989): 6.
82 5 2a (strain 2457T) CFU human beta-Poisson a = 1.43E-01

LD50/ID50 = 3.54E+04
N50 = 3.54E+04
illness DuPont, H. L., et al. "Immunity in Shigellosis. I. Response of Man to Attenuated Strains of Shigella." Journal of Infectious Diseases. 125 (1972): 1.
82, 223 9 2a (strain 2457T) CFU human beta-Poisson a = 1.17E-01

LD50/ID50 = 3.64E+03
N50 = 3.64E+03
illness DuPont, H. L., et al. "The Response of Man to Virulent Shigella flexneri 2a." Journal of Infectious Diseases. 119 (1969): 3.
83 4 2a (strain 2457T) CFU human beta-Poisson a = 2.65E-01

LD50/ID50 = 1.48E+03
N50 = 1.48E+03
positive stool isolation Altboum, Z., et al. "Postexposure Prophylaxis against Anthrax: Evaluation of Various Treatment Regimens in Intranasally Infected Guinea Pigs." Infection and Immunity. 70 (2002): 11.
Experiment ID:
223
# of Doses:
4
Agent Strain:
2a (strain 2457T)
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.35E-01

LD50/ID50 = 3.11E+03
N50 = 3.11E+03
Reference:
Model data for Shigella flexneri (2a, strain 2457T) in the human [1]
Dose Illness Not illness Total
180 9 27 36
5000 28 21 49
1E+04 52 36 88
1E+05 14 10 24

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 154 153 3 3.84 
0		 7.81 
0
Beta Poisson 1.69 2 5.99 
0.429
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 1.35E-01 9.86E-04 1.22E-02 6.85E-02 2.06E-01 2.22E-01 2.58E-01
N50 3.11E+03 5.09E+01 4.31E+02 9.64E+02 7.49E+03 9.14E+03 1.89E+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

References

  1. Immunity in shigellosis. I. Response of man to attenuated strains of Shigella, DuPont, Herbert L., and , Journal of Infectious Diseases, Volume 125, Number 1, p.5-11, (1972)
Experiment ID:
82
# of Doses:
5
Agent Strain:
2a (strain 2457T)
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.43E-01

LD50/ID50 = 3.54E+04
N50 = 3.54E+04
Reference:
Model data for Shigella flexneri (2a, strain 2457T) in the human [1]
Dose Illness Not illness Total
1E+04 1 3 4
1E+05 3 1 4
1E+06 7 1 8
1E+07 13 6 19
1E+08 7 1 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 73.6 70.2 4 3.84 
0		 9.49 
3.89e-15
Beta Poisson 3.44 3 7.81 
0.329
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 1.43E-01 1.32E-02 2.12E-02 2.63E-02 2.90E-01 3.32E-01 4.27E-01
N50 3.54E+04 1.29E-11 8.16E-07 3.11E-04 3.34E+05 4.65E+05 9.68E+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

References

  1. The response of man to virulent Shigella flexneri 2a, DuPont, Herbert L., and , Journal of Infectious Diseases, Volume 119, Number 3, p.296-299, (1969)
Experiment ID:
82, 223
# of Doses:
9
Agent Strain:
2a (strain 2457T)
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.17E-01

LD50/ID50 = 3.64E+03
N50 = 3.64E+03
Reference:
Model data for Shigella flexneri (2a, strain 2457T) in the human 
Dose Illness Not illness Total
180 9 27 36
5000 28 21 49
1E+04 1 3 4
1E+04 52 36 88
1E+05 3 1 4
1E+05 14 10 24
1E+06 7 1 8
1E+07 13 6 19
1E+08 7 1 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 677 671 8 3.84 
0		 15.5 
0
Beta Poisson 6.04 7 14.1 
0.535
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 1.17E-01 4.86E-02 6.43E-02 7.25E-02 1.68E-01 1.78E-01 2.02E-01
N50 3.64E+03 3.32E+02 8.92E+02 1.22E+03 9.16E+03 1.12E+04 1.73E+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

Best Fit
Experiment ID:
83
# of Doses:
4
Agent Strain:
2a (strain 2457T)
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 2.65E-01

LD50/ID50 = 1.48E+03
N50 = 1.48E+03
Reference:
Model data for Shigella flexneri (2a, strain 2457T) in the human [1]
Dose Positive stool isolation No positive stool isolation Total
180 6 30 36
5000 33 16 49
1E+04 66 21 87
1E+05 15 9 24

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 169 160 3 3.84 
0		 7.81 
0
Beta Poisson 8.73 2 5.99 
0.0127
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 2.65E-01 1.47E-01 1.74E-01 1.87E-01 3.82E-01 4.09E-01 4.70E-01
N50 1.48E+03 5.60E+02 7.33E+02 8.26E+02 2.55E+03 2.78E+03 3.38E+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

  1. Immunity in shigellosis. I. Response of man to attenuated strains of Shigella, DuPont, Herbert L., and , Journal of Infectious Diseases, Volume 125, Number 1, p.5-11, (1972)