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
Description
Mice/Naegleria fowleri LEE strain data 
Dose Dead Survived Total
1E+06 4 16 20
2.5E+06 12 8 20
5E+06 14 6 20
1E+07 20 0 20

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 3.47 -0.000862 3 3.84 
1 		7.81 
0.325
Beta Poisson 3.47 2 5.99 
0.177
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 3.07E-07 2.11E-07 2.31E-07 2.41E-07 3.98E-07 4.21E-07 4.68E-07
ID50/LD50/ETC* 2.26E+06 1.48E+06 1.65E+06 1.74E+06 2.88E+06 3.01E+06 3.28E+06
*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
2.26E+06
Dose Units
no of trophozoites
Response
death
Exposure Route
intravenous
Contains Preferred Model
k
3.07E-07
Agent Strain
LEE strain
Experiment ID
254
Host type
mice
Description
mice/ Naegleria fowleri LEE strain model data 
Dose Dead Survived Total
1E+06 4 16 20
2.5E+06 4 6 10
2.5E+06 12 8 20
5E+06 19 1 20
5E+06 14 6 20
1E+07 10 0 10
1E+07 20 0 20

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 8.85 -0.000501 6 3.84 
1 		12.6 
0.182
Beta Poisson 8.85 5 11.1 
0.115
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 3.42E-07 2.57E-07 2.75E-07 2.84E-07 4.15E-07 4.34E-07 4.67E-07
ID50/LD50/ETC* 2.03E+06 1.48E+06 1.60E+06 1.67E+06 2.44E+06 2.52E+06 2.70E+06
*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
7.00
Μodel
exponential
LD50/ID50
2.03E+06
Dose Units
no of trophozoites
Response
death
Exposure Route
intravenous
Contains Preferred Model
k
3.42E-07
Agent Strain
LEE strain
Experiment ID
253, 254
Host type
mice
Description
mice/Naegleria fowleri LEE strain data 
Dose Dead Survived Total
2.5E+06 4 6 10
5E+06 19 1 20
1E+07 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 4.11 -9.67 2 3.84 
1 		5.99 
0.128
Beta Poisson 13.8 1 3.84 
0.000206
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 4.21E-07 2.77E-07 3.04E-07 3.25E-07 5.95E-07 6.79E-07 8.02E-07
ID50/LD50/ETC* 1.64E+06 8.65E+05 1.02E+06 1.16E+06 2.13E+06 2.28E+06 2.50E+06
*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
3.00
Μodel
exponential
LD50/ID50
1.64E+06
Dose Units
no of trophozoites
Response
death
Exposure Route
intravenous
Contains Preferred Model
k
4.21E-07
Agent Strain
LEE strain
Experiment ID
253
Host type
mice
Subscribe to no of trophozoites