\[P(response)=1-exp(-k\times dose)\]

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
T1 Strain for serotype PEN 1 data 
Dose Infected Non-infected Total
1 0 5 5
100 0 5 5
1E+04 0 5 5
1E+06 3 2 5
1E+08 5 0 5

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 0.0918 -0.000599 4 3.84
1 		9.49
0.999
Beta Poisson 0.0924 3 7.81
0.993
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 9.01E-07 4.61E-08 2.21E-07 2.21E-07 4.61E-06 4.61E-06 4.61E-06
ID50/LD50/ETC* 7.69E+05 1.51E+05 1.51E+05 1.51E+05 3.14E+06 3.14E+06 1.51E+07
*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
7.69E+05
Dose Units
CFU
Response
infection
Exposure Route
intragastric
Contains Preferred Model
k
9.01E-07
Agent Strain
type strain for serotype PEN 1
Experiment ID
184
Host type
mice
Description

Badenoch et al. (1990) studied the combined effect of Acanthamoeba Ac118 (a group III isolate) and the bacterium Corynebacterium xerosis on the corneas of female Porton rats. A constant dose of 104 C. xerosis with increasing doses of Acanthamoeba spp. were injected into incisions in the rat corneas using a microsyringe (Badenoch et al. 1990).

The exponential model provided the best fit to the data. 

Figure 1: Plot of the exponential model fit to Experiment 1 with upper and lower 95% and 99% confidence
Figure 1: Plot of the exponential model fit to Experiment 1 with upper and lower 95% and 99% confidence

 

Figure 2: Histogram of the 10,000 bootstrap replicates of k for the best fitting exponential model fit to Experiment 1
Figure 2: Histogram of the 10,000 bootstrap replicates of k for the best fitting exponential model fit to Experiment 1

 

# of Doses
4.00
Μodel
exponential
LD50/ID50
6,886
Dose Units
no of trophozoites
Response
infection
Exposure Route
eyes-cornea
Contains Preferred Model
Status
fitted
Resampled Parameters
Exponential_Bootstrap.csv
k
1.01E-04
Agent Strain
Acanthamoeba Ac118
Experiment ID
Acanth_Cornea1
Host type
rat
Experiment Dataset
Dose (no. of organisms) Positive Responses Negative Responses Total Subjects/Responses
10 0 8 8
100 0 16 16
1000 2 16 18
10000 5 3 8
Description
mice (5day old) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 13 13
25 0 14 14
250 0 12 12
2500 4 13 17
25000 15 0 15
250000 17 0 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential

2.17

-0.000196 

 5 3.84 
1 		11.1 
0.825
Beta Poisson

2.17

 4 9.49 
0.704
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 1.39E-04 8.87E-05 9.90E-05 9.90E-05 2.05E-04 2.36E-04 2.73E-04
ID50/LD50/ETC* 4.98E+03 2.54E+03 2.94E+03 3.38E+03 7.00E+03 7.00E+03 7.82E+03
*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
6.00
Μodel
exponential
LD50/ID50
4.98E+03
Dose Units
CFU
Response
death(after day 21)
Exposure Route
injected in eyelids
Contains Preferred Model
k
1.39E-04
Agent Strain
ATCC 19660
Experiment ID
282
Host type
Swiss webster mice (5day old)
Description
mice (5day old) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 13 13
25 0 14 14
250 0 12 12
2500 4 13 17
25000 13 2 15
250000 17 0 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential

0.802

 0.0885 5 3.84 
0.766 		11.1 
0.977
Beta Poisson

0.713

 4 9.49 
0.95
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 8.52E-05 4.21E-05 4.99E-05 5.50E-05 1.53E-04 1.57E-04 2.05E-04
ID50/LD50/ETC* 8.13E+03 3.38E+03 4.40E+03 4.54E+03 1.26E+04 1.39E+04 1.65E+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
6.00
Μodel
exponential
LD50/ID50
8.13E+03
Dose Units
CFU
Response
death
Exposure Route
injected in eyelids
Contains Preferred Model
k
8.52E-05
Agent Strain
ATCC 19660
Experiment ID
281
Host type
Swiss webster mice (5day old)
Description

mice (5day old, day 1-21 pooled) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 13 13
2.5 0 13 13
25 0 14 14
25 0 14 14
250 0 12 12
250 0 12 12
2500 4 13 17
2500 4 13 17
25000 13 2 15
25000 15 0 15
250000 17 0 17
250000 17 0 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential

4.36 

 -0.000549

   3.84 
1 		19.7
0.958
Beta Poisson

4.36

 10 18.3 
0.93
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 500 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.05E-04 6.84E-05 7.49E-05 7.84E-05 1.48E-04 1.57E-04 1.73E-04
ID50/LD50/ETC* 6.61E+03 4.01E+03 4.40E+03 4.68E+03 8.84E+03 9.26E+03 1.01E+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
12.00
Μodel
exponential
LD50/ID50
6.61E+03
Dose Units
CFU
Response
death
Exposure Route
injected in eyelids
Contains Preferred Model
k
1.05E-04
Agent Strain
ATCC 19660
Experiment ID
281,282 (pooled)
Host type
Swiss webster mice (5day old)
Description
Swiss webster mice /  Pseudomonas aeruginosa 
Dose Infection (keratitis)

Not Infection (keratitis)

 Total
1E+04 0 8 8
1E+05 1 9 10
1E+06 1 7 8
1E+07 5 5 10
1E+08 10 0 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

3.6

 0.134 4 3.84 
0.715 		9.49 
0.464
Beta Poisson

3.46

 3 7.81 
0.326
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 8.8E-08 3.31E-08 3.89E-08 4.53E-08 1.58E-07 1.94E-07 2.47E-07
ID50/LD50/ETC* 7.88E+06 2.81E+06 3.57E+06 4.38E+06 1.53E+07 1.78E+07 2.09E+07
*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
7.88E+06
Dose Units
CFU
Response
infection (Keratitis)
Exposure Route
contact lens
Contains Preferred Model
k
8.8E-08
Agent Strain
ATCC 19660
Experiment ID
286
Host type
Swiss webster mice
Description
Model data for rotavirus (OSU (ATCC VR892)) in the pig 
Dose Infected Non-infected Total
0.9 0 3 3
9 0 3 3
90 5 1 6
900 3 0 3
2800 2 0 2
9000 3 0 3
56000 2 0 2
1.1E+07 2 0 2
2.2E+08 2 0 2
4.5E+09 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 1.1 -0.0019 9 3.84 
1 		16.9 
0.999
Beta Poisson 1.1 8 15.5 
0.998
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 1.73E-02 4.64E-03 7.21E-03 7.21E-03 3.28E-02 3.28E-02 3.28E-02
ID50/LD50/ETC* 4E+01 2.11E+01 2.11E+01 2.11E+01 9.61E+01 9.61E+01 1.49E+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
10.00
Μodel
exponential
LD50/ID50
4E+01
Dose Units
particles
Response
infection
Exposure Route
intragastric
Contains Preferred Model
k
1.73E-02
Agent Strain
OSU (ATCC VR892)
Experiment ID
68
Host type
pig
Description
Guinea pig/Vollum Strain model data 
Dose Dead Survived Total
19800 8 24 32
40800 18 14 32
76200 21 11 32
118000 28 4 32

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 1.43 -0.000184 3 3.84 
1 		7.81 
0.699
Beta Poisson 1.43 2 5.99 
0.49
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 1.65E-05 1.20E-05 1.30E-05 1.35E-05 2.03E-05 2.12E-05 2.28E-05
ID50/LD50/ETC* 4.2E+04 3.04E+04 3.27E+04 3.41E+04 5.14E+04 5.35E+04 5.80E+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

Bacillus Graph 2.png

# of Doses
4.00
Μodel
exponential
LD50/ID50
4.2E+04
Dose Units
spores
Response
death
Exposure Route
inhalation
Contains Preferred Model
k
1.65E-05
Agent Strain
Vollum
Experiment ID
87
Host type
guinea pig
Description
Rhesus Macaques/Vollum Strain model data
Dose Dead Survived Total
70300 1 7 8
77000 4 4 8
109000 5 3 8
138000 6 2 8
156000 5 3 8
161000 3 5 8
240000 8 0 8
3E+05 7 1 8
398000 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 11.3 -0.000503 8 3.84 
1 		15.5 
0.188
Beta Poisson 11.3 7 14.1 
0.128
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 7.16E-06 4.99E-06 5.47E-06 5.71E-06 9.09E-06 9.51E-06 1.05E-05
ID50/LD50/ETC* 9.69E+04 6.63E+04 7.29E+04 7.63E+04 1.21E+05 1.27E+05 1.39E+05
*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
9.69E+04
Dose Units
spores
Response
death
Exposure Route
inhalation
Contains Preferred Model
k
7.16E-06
Agent Strain
Vollum
Experiment ID
86
Host type
monkey
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