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
Strain A3249 Data 
Dose Infected Non-infected Total
810 5 5 10
8100 6 4 10
91000 11 2 13
810000 8 3 11
1.1E+06 15 4 19
1.1E+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 110 108 5 3.84 
0		 11.1 
0
Beta Poisson 2.43 4 9.49 
0.658
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.44E-01 2.05E-02 3.61E-02 4.99E-02 2.66E-01 2.98E-01 3.71E-01
N50 8.9E+02 6.54E-10 1.47E-04 8.11E-02 6.69E+03 8.97E+03 1.53E+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
6.00
Μodel
beta-Poisson
N50
8.9E+02
LD50/ID50
8.9E+02
Dose Units
CFU
Response
infection
Exposure Route
oral
Contains Preferred Model
a
1.44E-01
Agent Strain
strain A3249
Experiment ID
106
Host type
human
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

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
Lead Editor: 
Yin Huang
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 (10day old, day2-21) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 10 10
25 0 16 16
250 0 15 15
2500 2 11 13
25000 13 3 16
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

27.3

 23.1 5 3.84 
 1.54e-06 		11.1
5.01e-05
Beta Poisson

4.19

 4 9.49 
0.381
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 2.38E-01 2.87E-01 3.17E-01 1.37E+00 1.13E+01 1.15E+04
N50 1.13E+04 4.53E+03 5.70E+03 6.34E+03 2.17E+04 2.46E+04 3.39E+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
6.00
Μodel
beta-Poisson
N50
1.13E+04
LD50/ID50
1.13E+04
Dose Units
CFU
Response
death(after day 2-21)
Exposure Route
injected in eyelids
Contains Preferred Model
a
5.49E-01
Agent Strain
ATCC 19660
Experiment ID
284
Host type
Swiss webster mice(10day old)
Description
mice (10day old, day1) /  Pseudomonas aeruginosa 
Dose Dead Survived Total
2.5 0 10 10
25 0 16 16
250 0 15 15
2500 0 13 13
25000 12 4 16
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

21.1

 13.8 5 3.84 
0.000207 		11.1 
0.000783
Beta Poisson

7.32

 4 9.49 
0.12
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 6.73E-01 3.02E-01 3.62E-01 3.80E-01 1.55E+00 6.30E+03 1.06E+04
N50 1.93E+04 9.62E+03 1.12E+04 1.18E+04 3.42E+04 4.01E+04 5.18E+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
6.00
Μodel
beta-Poisson
N50
1.93E+04
LD50/ID50
1.93E+04
Dose Units
CFU
Response
death(after day 1)
Exposure Route
injected in eyelids
Contains Preferred Model
a
6.73E-01
Agent Strain
ATCC 19660
Experiment ID
283
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 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
Model data for rotavirus (CJN strain) in the human 
Dose Infected Non-infected Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 8 3 11
90 6 1 7
900 7 1 8
9000 5 2 7
9E+04 3 0 3

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 125 119 7 3.84 
0 		14.1 
0
Beta Poisson 6.2 6 12.6 
0.401
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 2.53E-01 1.28E-01 1.51E-01 1.64E-01 5.18E-01 6.58E-01 6.76E+02
N50 6.17E+00 1.46E+00 2.17E+00 2.49E+00 1.89E+01 2.49E+01 4.37E+01

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters
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
beta Poisson model plot, with confidence bounds around optimized model
# of Doses
8.00
Μodel
beta-Poisson
LD50/ID50
6.17E+00
Dose Units
FFU
Exposure Route
oral
Contains Preferred Model
a
2.53E-02
k
6.17E+00
Experiment ID
70
Host type
human
Experiment Dataset
Subscribe to