Description
Dose response data
Dose Dead Survived Total
200 0 10 10
4000 1 9 10
1E+04 1 4 5
15000 0 3 3
2E+04 5 2 7
5E+04 12 0 12
5E+04 3 0 3
1E+05 5 0 5
4E+05 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 8.92 -0.000282 8 3.84 
1 		15.5 
0.349
Beta Poisson 8.92 7 14.1 
0.258
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 4.99E-05 3.55E-05 3.87E-05 3.95E-05 6.48E-05 6.76E-05 7.46E-05
ID50/LD50/ETC* 1.39E+04 9.29E+03 1.03E+04 1.07E+04 1.75E+04 1.79E+04 1.95E+04
*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
9.00
Μodel
exponential
LD50/ID50
1.39E+04
Dose Units
CFU
Response
death
Exposure Route
inhalation
Contains Preferred Model
k
4.99E-05
Agent Strain
strain 74/81
Experiment ID
242, 243
Host type
mice
Description
mice/ Strain 74/81 data
Dose Dead Survived Total
200 0 10 10
4000 1 9 10
5E+04 12 0 12
4E+05 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 2.34 -0.00145 3 3.84 
1 		7.81 
0.506
Beta Poisson 2.34 2 5.99 
0.311
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 6.48E-05 5.45E-05 5.45E-05 5.45E-05 9.71E-05 9.71E-05 1.24E-04
ID50/LD50/ETC* 1.07E+04 5.57E+03 7.14E+03 7.14E+03 1.27E+04 1.27E+04 1.27E+04
*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
1.07E+04
Dose Units
CFU
Response
death
Exposure Route
inhalation
Contains Preferred Model
k
6.48E-05
Agent Strain
strain 74/81
Experiment ID
242
Host type
mice
Description
Guinea pigs/ Philadelphia 1 strain data 
Dose Infected Non-infected Total
1 0 4 4
5 4 10 14
50 17 1 18
100 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 0.582 0.000479 3 3.84 
0.983 		7.81 
0.9
Beta Poisson 0.582 2 5.99 
0.748
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 5.99E-02 3.26E-02 3.90E-02 4.18E-02 1.11E-01 1.31E-01 1.57E-01
ID50/LD50/ETC* 1.16E+01 4.42E+00 5.28E+00 6.25E+00 1.66E+01 1.78E+01 2.13E+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
1.16E+01
Dose Units
CFU
Response
infection
Exposure Route
inhalation
Contains Preferred Model
k
5.99E-02
Agent Strain
Philadelphia 1
Experiment ID
241
Host type
guinea pig
Description
Guinea pig/ Josiah strain model data 
Dose Dead Survived Total
5 1 7 8
48 1 7 8
724 3 5 8
5370 4 4 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 14.4 13.8 3 3.84 
0.000203 		7.81 
0.00237
Beta Poisson 0.633 2 5.99 
0.729
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 7.94E-02 9.77E-04 9.85E-04 9.87E-04 4.57E-01 1.19E+00 5.76E+02
N50 1.43E+04 2.13E-01 9.22E-01 2.90E+00 1.82E+13 3.06E+17 2.25E+34

 

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
4.00
Μodel
beta-Poisson
N50
1.43E+04
LD50/ID50
1.43E+04
Dose Units
PFU
Response
death
Exposure Route
inhalation
Contains Preferred Model
a
7.94E-02
Agent Strain
Josiah strain
Experiment ID
15
Host type
guinea pig
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