Description
intraperitoneal
Host
Spiny Frogs
# of Doses
4.00
Μodel
beta-Poisson
N50
4.23E+08 (β = 137,348)
LD50/ID50
4.23E+08
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
Status
fitted
a
0.72
Agent Strain
E. miricola
Experiment ID
ek_intraperitoneal
Experiment Dataset
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

The same exposure route and endpoint was evaluated for Experiments 3 and 4 (Cerva, 1967b; Culbertson et al. 1966)[6] [5]. A pooling analysis was attempted and successful. The beta-Poisson model provided a good fit to the pooled data and is shown below in Figure 1. Note: both the exact and approximate beta-Poisson models were fit to the data. The figures shown below and the csv file of bootstrapped parameter replicates are for the best fitting parameters of the exact beta-Poisson model. The successful pooling of multiple datasets generally increases the confidence in the estimated model parameters. 

Figure 1: Plot of the beta-Poisson model fit to the pooled Experiments 3 and 4 with upper and lower 95% and 99% confidence
Figure 1: Plot of the beta-Poisson model fit to the pooled Experiments 3 and 4 with upper and lower 95% and 99% confidence

 

Figure 2: Uncertainty plot of the 10,000 paired bootstrap replicates of alpha and beta for the pooled beta-Poisson model.
Figure 2: Uncertainty plot of the 10,000 paired bootstrap replicates of alpha and beta for the pooled beta-Poisson model.

 

 

[6] Cerva, L. (1967b). Intranasal, Intrapulmonary, and Intracardial Inoculation of Experimental Animals with Hartmanella castellanii. Folia Parasitologica (Praha), 14, 207–215.

[5] Culbertson, C. G., Ensminger, P. W., & Overton, W. M. (1966). Hartmannella (Acanthamoeba): Experimental Chronic, Granulomatous Brain Infections Produced by New Isolates of Low Virulence. The American Journal of Clinical Pathology, 46(3), 305–314.

# of Doses
9.00
Μodel
beta-Poisson
N50
19357
Dose Units
no of trophozoites
Response
death
Exposure Route
intranasal
Contains Preferred Model
Status
pooled
Resampled Parameters
Exact_BetaPoisson_Bootstrap.csv
a
0.245
Agent Strain
A. castellanii HN-3 and A culbertsoni A1
Experiment ID
Acanth_Intranasal_Pooled
Host type
mice
Experiment Dataset
Description
mice (10day old, day1-21) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 10 10
2.5 0 10 10
25 0 16 16
25 0 16 16
250 0 15 15
250 0 15 15
2500 0 13 13
2500 2 11 13
25000 12 4 16
25000 13 3 16
250000 14 3 17
250000 14 3 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

48.6 

 36.3 11 3.84 
 1.65e-09 		19.7
1.09e-06
Beta Poisson

12.3

 10 18.3 
0.265
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 500 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 6.01E-01 3.11E-01 3.69E-01 3.97E-01 1.04E+00 1.20E+00 2.01E+00
N50 1.48E+04 8.01E+03 9.07E+03 1.00E+04 2.29E+04 2.55E+04 2.83E+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

# of Doses
12.00
Μodel
beta-Poisson
N50
1.48E+04
LD50/ID50
1.48E+04
Dose Units
CFU
Response
death
Exposure Route
injected in eyelids
Contains Preferred Model
a
6.01E-01
Agent Strain
ATCC 19660
Experiment ID
283,284
Host type
Swiss webster mice(10day 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
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
Description
Guinea pig/ATCC 6605 Strain model data 
Dose Dead Survived Total
30 0 6 6
300 1 5 6
3000 0 10 10
3E+04 3 7 10
3E+05 8 2 10
3E+06 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 8.56 1.81 5 3.84 
0.178 		11.1 
0.128
Beta Poisson 6.75 4 9.49 
0.15
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 7.11E-06 2.60E-06 3.52E-06 3.87E-06 1.61E-05 1.97E-05 2.85E-05
ID50/LD50/ETC* 9.75E+04 2.43E+04 3.52E+04 4.30E+04 1.79E+05 1.97E+05 2.66E+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
6.00
Μodel
exponential
LD50/ID50
9.75E+04
Dose Units
spores
Response
death
Exposure Route
inhalation
Contains Preferred Model
k
7.11E-06
Agent Strain
ATCC 6605
Experiment ID
85
Host type
guinea pig
Description
Guinea pig/Vollum Strain model data 
Dose Dead Survived Total
200 0 4 4
2000 0 8 8
2E+04 6 6 12
2E+05 10 2 12
2E+06 7 1 8
2E+07 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 29.2 26.6 5 3.84 
2.46e-07 		11.1 
2.11e-05
Beta Poisson 2.58 4 9.49 
0.631
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 5.49E-01 2.55E-01 3.03E-01 3.32E-01 5.51E+00 2.45E+03 6.16E+03
N50 2.85E+04 1.00E+04 1.25E+04 1.43E+04 6.57E+04 7.85E+04 1.09E+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

# of Doses
6.00
Μodel
beta-Poisson
N50
2.85E+04
LD50/ID50
2.85E+04
Dose Units
spores
Response
death
Exposure Route
inhalation
Contains Preferred Model
a
5.49E-01
Agent Strain
Vollum
Experiment ID
84
Host type
guinea pig
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