Description
Table 1: Goodness of fit
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 16.88 0.001 6 3.84 
0.98 		12.6
0.009
Beta Poisson 16.88 5 11.1
0.004
Neither model provides a good fit to the data

 

Table 2: Multi-hit dose response statistics
Model Deviance Δ DF χ20.95,df χ20.95,1 Good fit? Parameters LD50
Multi-hit 1.09 15.69 5 11.1 3.84 Yes k = 4.12 × 10−6 kmin=11 2,588,047

 

Figure 1. The multi-hit dose response model with 95% and 99% confidence bands
Figure 1. The multi-hit dose response model with 95% and 99% confidence bands

 

 

Figure 2. Histogram of the k parameter estimates after bootstrapping
Figure 2. Histogram of the k parameter estimates after bootstrapping

 

# of Doses
7.00
Μodel
exponential
Dose Units
CFU
Response
death
Exposure Route
intratracheal
Contains Preferred Model
Status
fitted
k
3.22E-7
Agent Strain
PA01
Experiment ID
Ojielo2003
Host type
C57BL/6 mice
Experiment Dataset
Dose (CFU) Positive Response Negative Response
80000 0 10
400000 0 10
900000 0 10
2000000 2 5
3000000 6 4
4500000 10 0
8000000 10 0
Description
Mice/Nine mile phase I model data 
Dose Dead Survived Total
0.05 0 10 10
0.5 0 10 10
5 0 10 10
50 0 10 10
501 0 10 10
5010 0 10 10
50100 0 10 10
501000 0 10 10
5010000 0 10 10
5.01E+07 0 10 10
5.01E+08 1 9 10
5.01E+09 3 7 10
5.01E+10 9 1 10

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 1.63 0.936 12 3.84 
0.333 		21 
1
Beta Poisson 0.693 11 19.7 
1
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 5.7E-11 2.31E-11 2.94E-11 3.33E-11 1.38E-10 1.61E-10 2.13E-10
ID50/LD50/ETC* 1.22E+10 3.25E+09 4.30E+09 5.02E+09 2.08E+10 2.36E+10 2.99E+10
*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
13.00
Μodel
exponential
LD50/ID50
1.22E+10
Dose Units
PFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
k
5.7E-11
Agent Strain
Nine mile phase I
Experiment ID
26
Host type
C57BL/6 mice
Description
C57BL/6 Mice KHW Strain Data
Dose Infected Non-infected Total
5 0 3 3
45 1 5 6
450 6 2 8
4500 7 0 7
45000 7 0 7

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 0.155 0.0201 4 3.84 
0.887		 9.49 
0.997
Beta Poisson 0.135 3 7.81 
0.987
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 3.18E-03 1.05E-03 1.41E-03 1.63E-03 7.50E-03 7.54E-03 1.46E-02
ID50/LD50/ETC* 2.18E+02 4.74E+01 9.19E+01 9.25E+01 4.25E+02 4.91E+02 6.63E+02
*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
5.00
Μodel
exponential
LD50/ID50
2.18E+02
Dose Units
CFU
Response
infection
Exposure Route
intravenous
Contains Preferred Model
k
3.18E-03
Agent Strain
KHW
Experiment ID
245
Host type
C57BL/6 mice
Description
C57BL/6 Mice KHW Strain Data 
Dose Infected Non-infected Total
150 0 6 6
450 1 5 6
1350 1 5 6
4050 3 3 6
12200 3 3 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 3.36 2.17 4 3.84 
0.141 		9.49 
0.499
Beta Poisson 1.19 3 7.81 
0.755
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized parameters for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1E-04 2.87E-05 4.15E-05 4.99E-05 1.89E-04 2.13E-04 2.70E-04
ID50/LD50/ETC* 6.92E+03 2.57E+03 3.26E+03 3.68E+03 1.39E+04 1.67E+04 2.41E+04
*Not a parameter of the exponential model; however, it facilitates comparison with other models.
Parameter histogram for exponential model (uncertainty of the parameter)
Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model
# of Doses
5.00
Μodel
exponential
LD50/ID50
6.92E+03
Dose Units
CFU
Response
infection
Exposure Route
intranasal
Contains Preferred Model
k
1.00E-04
Agent Strain
KHW
Experiment ID
18
Host type
C57BL/6 mice
Experiment Dataset
Subscribe to C57BL/6 mice