Description

Červa (1967a,b) studied white mice of the Czechoslovak H-strain weighing 13-15 grams inoculated intranasally by placing 0.02 mL of the A1 strain of Acanthamoeba over the nares of the ethyl-ether anesthetized mice (Cerva, 1967b).

The beta-Poisson model provided the best fit to the data. 

 

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

# of Doses
6.00
Μodel
beta-Poisson
N50
14,690 or 14,538
Dose Units
no of trophozoites
Response
death
Exposure Route
intranasal
Contains Preferred Model
Status
fitted
a
0.161
Agent Strain
A. culbertsoni (A1)
Experiment ID
Acanth_Intranasal1
Host type
mice
Experiment Dataset
Dose (no. of organisms) Positive Response Negative Response Total Subjects/Responses
3 0 20 20
30 2 18 20
300 1 19 20
3000 9 11 20
Description

Culbertson et al. (1966) studied the pathogenicity of the HN-3 strain of A. castellanii (Culbertson et al., 1966; Marciano-Cabral & Cabral, 2003) on ether-anesthetized-specific-pathogen-free (SPF) mice. Cultures of amebae were grown in trypticase soy broth and diluted so that 0.03 mL of a concentrated suspension could be instilled intranasally into the mice by placing fluid over the nares (Culbertson et al., 1966; Culbertson, Ensminger, & Overton, 1965a; Culbertson, Ensminger, & Overton, 1965b).

The exponential model provided the best fit to the data. 

Figure 1: Plot of exponential model fit to Experiment 6 with upper and lower 95% and 99% confidence
Figure 1: Plot of exponential model fit to Experiment 6 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 6
Figure 2: Histogram of the 10,000 bootstrap replicates of k for the best fitting exponential model fit to Experiment 6

 

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
3.00
Μodel
exponential
LD50/ID50
2.67E+03
Dose Units
no of trophozoites
Response
acute meningoencephalitis
Exposure Route
intranasal
Contains Preferred Model
Status
fitted
k
2.60E-04
Agent Strain
A. castellanii HN-3
Experiment ID
Acanth_Intranasal4
Host type
mice
Experiment Dataset
Dose (no. of organisms) Positive Response Negative Response Total Subjects/Responses
100 2 78 80
500 9 71 80
1000 21 59 80
Description

Culbertson et al. (1966) studied the pathogenicity of the HN-3 strain of A. castellanii (Culbertson et al., 1966; Marciano-Cabral & Cabral, 2003) on ether-anesthetized-specific-pathogen-free (SPF) mice. Cultures of amebae were grown in trypticase soy broth and diluted so that 0.03 mL of a concentrated suspension could be instilled intranasally into the mice by placing fluid over the nares (Culbertson et al., 1966; Culbertson, Ensminger, & Overton, 1965a; Culbertson, Ensminger, & Overton, 1965b).

The exponential model provided the best fit to the data. 

Figure 1: Plot of exponential model fit to Experiment 5 with upper and lower 95% and 99% confidence
Figure 1: Plot of exponential model fit to Experiment 5 with upper and lower 95% and 99% confidence

Culbertson, C. G., Holmes, D. H., & Overton, W. M. (1965b). Hartmanella castellani (Acanthamoeba sp.). The American Journal of Clinical Pathology, 43(4), 361–364.

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.

Figure 2: Histogram of the 10,000 bootstrap replicates of k for the best fitting exponential model fit to Experiment 5
Figure 2: Histogram of the 10,000 bootstrap replicates of k for the best fitting exponential model fit to Experiment 5
# of Doses
3.00
Μodel
exponential
LD50/ID50
749
Dose Units
no of trophozoites
Response
brain invasion
Exposure Route
intranasal
Contains Preferred Model
Status
fitted
k
9.26E-04
Agent Strain
A. castellanii HN-3
Experiment ID
Acanth_Intranasal3
Host type
mice
Experiment Dataset
Dose (no. of organisms) Positive Response Negative Response Total Subjects/Responses
100 7 73 80
500 31 49 80
1000 43 37 80
Description

Culbertson et al. (1966) studied the pathogenicity of the HN-3 strain of A. castellanii (Culbertson et al., 1966; Marciano-Cabral & Cabral, 2003) on ether-anesthetized-specific-pathogen-free (SPF) mice. Cultures of amebae were grown in trypticase soy broth and diluted so that 0.03 mL of a concentrated suspension could be instilled intranasally into the mice by placing fluid over the nares (Culbertson et al., 1966; Culbertson, Ensminger, & Overton, 1965a; Culbertson, Ensminger, & Overton, 1965b).

The exponential model provided the best fit to the data. 

 

Figure 1. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 1. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 2. Exponential model plot, with confidence bounds around optimized model
Figure 2. Exponential model plot, with confidence bounds around optimized model

Culbertson, C. G., Holmes, D. H., & Overton, W. M. (1965b). Hartmanella castellani (Acanthamoeba sp.). The American Journal of Clinical Pathology, 43(4), 361–364.

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
3.00
Μodel
exponential
LD50/ID50
5.28E+03
Dose Units
no of trophozoites
Response
death
Exposure Route
intranasal
Contains Preferred Model
Status
fitted
k
1.31E-04
Agent Strain
A. castellanii HN-3
Experiment ID
Acanth_Intranasal2
Host type
mice
Experiment Dataset
Dose (no. of organsims) Positive Responses Negative Responses Total Subjects/Responses
100 2 78 80
500 4 76 80
1000 10 70 80
Description
Mice/Naegleria fowleri LEE strain data
Dose Dead Survived Total
1E+03 7 3 10
1E+04 8 2 10
1E+05 10 0 10
1E+06 10 0 10

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom

χ20.95,1

 

 χ20.95,m-k 
 
Exponential 11.28 9.64 3 3.84 7.81 
0.325
Beta Poisson 1.64 2 5.99 
0.177
Beta-Poisson is preferred to Exponential;
Beta-Poisson model plot
Beta-Poisson model plot
# of Doses
4.00
Μodel
beta-Poisson
N50
422
LD50/ID50
422
Dose Units
no of trophozoites
Response
death
Exposure Route
intranasal
Contains Preferred Model
Status
fitted
a
0.536
Experiment ID
954
Host type
A/J mice
Experiment Dataset
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

SARS: Dose Response Experiments

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General Overview

Coronaviruses cause acute and chronic respiratory, enteric, and central nervous system (CNS) diseases in humans and many species of animals. Coronaviruses are divided into three groups based on the genome sequences, including SARS-CoV (a member of group II) as well as murine hepatitis virus (MHV), bovine coronavirus, porcine hemagglutinating encephalomyelitis virus (HEV), equine coronavirus, and human coronavirues OC43 and NL63, which also cause respiratory infections.

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
260 intranasal 4.00 rSARS-CoV PFU mice hACE-2 exponential 2.33E+02 k = 2.97E-03 death
Albuquerque, N. D., Baig, E. ., Ma, X. ., Zhang, J. ., He, W. ., Rowe, A. ., … Levy, G. A. (2006). Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice. Journal of Virology, 80, 21. https://doi.org/10.1128/JVI.00747-06
260, 261 intranasal 0.00 rSARS-CoV PFU mice hACE-2 and A/J exponential 2.82E+02 k = 2.46E-03 death
261 intranasal 4.00 MHV-1 PFU A/J mice exponential 3.24E+02 k = 2.14E-03 death
Albuquerque, N. D., Baig, E. ., Ma, X. ., Zhang, J. ., He, W. ., Rowe, A. ., … Levy, G. A. (2006). Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice. Journal of Virology, 80, 21. https://doi.org/10.1128/JVI.00747-06
Exposure Route:
intranasal
# of Doses:
4.00
Agent Strain:
rSARS-CoV
Dose Units:
PFU
Host type:
mice hACE-2
Μodel:
exponential
LD50/ID50:
2.33E+02
Optimized parameters: k = 2.97E-03
Response type:
death
Reference:
Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice
mice/rSARS-CoV strain model data [2]
Dose Dead Survived Total
240 1 2 3
800 3 0 3
2400 2 0 2
12000 6 0 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 0.968 -0.000923 3 3.84 
1 		7.81 
0.809
Beta Poisson 0.969 2 5.99 
0.616
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 2.97E-03 1.90E-03 1.90E-03 1.90E-03 2.97E-03 2.97E-03 2.97E-03
ID50/LD50/ETC* 2.33E+02 2.33E+02 2.33E+02 2.33E+02 3.64E+02 3.64E+02 3.64E+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

Highest quality
Exposure Route:
intranasal
# of Doses:
0.00
Agent Strain:
rSARS-CoV
Dose Units:
PFU
Host type:
mice hACE-2 and A/J
Μodel:
exponential
LD50/ID50:
2.82E+02
Optimized parameters: k = 2.46E-03
Response type:
death
Reference:
Pooled dose response model data [1]
Dose Dead Survived Total
5 0 5 5
50 1 4 5
240 1 2 3
500 3 2 5
800 3 0 3
2400 2 0 2
5000 5 0 5
12000 6 0 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 1.75 -0.00181 7 3.84 
1 		14.1 
0.972
Beta Poisson 1.75 6 12.6 
0.941
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 2.46E-03 1.07E-03 1.28E-03 1.35E-03 4.59E-03 5.27E-03 6.80E-03
ID50/LD50/ETC* 2.82E+02 1.02E+02 1.32E+02 1.51E+02 5.13E+02 5.43E+02 6.47E+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

Exposure Route:
intranasal
# of Doses:
4.00
Agent Strain:
MHV-1
Dose Units:
PFU
Host type:
A/J mice
Μodel:
exponential
LD50/ID50:
3.24E+02
Optimized parameters: k = 2.14E-03
Response type:
death
Reference:
Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice
Mice/MHV-1 strains model data [3]
Dose Dead Survived Total
5 0 5 5
50 1 4 5
500 3 2 5
5000 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 0.606 0.0689 3 3.84 
0.793 		7.81 
0.895
Beta Poisson 0.537 2 5.99 
0.765
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 2.14E-03 6.25E-04 6.55E-04 9.06E-04 6.58E-03 6.58E-03 9.86E-03
ID50/LD50/ETC* 3.24E+02 7.03E+01 1.05E+02 1.05E+02 7.65E+02 1.06E+03 1.11E+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

Adenovirus: Dose Response Experiments

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General Overview

Adenoviruses are medium-sized (90-100 nm), nonenveloped (naked) icosohedral viruses containing double-stranded DNA. According to the CDC, there are more than 52 immunologically distinct types that can cause infections in humans and animals.

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
31 inhalation 4.00 type 4 TCID50 human exponential 1.14E+00 k = 6.07E-01 infection
Couch, R. B., Cate, T. R., Douglas, R. G., Gerone, P. J., & . (1966). Effect of route of inoculation on experimental respiratory viral disease in volunteers and evidence for airborne transmission. Bacteriological Reviews, 30, 3.
Highest quality
Exposure Route:
inhalation
# of Doses:
4.00
Agent Strain:
type 4
Dose Units:
TCID50
Host type:
human
Μodel:
exponential
LD50/ID50:
1.14E+00
Optimized parameters: k = 6.07E-01
Response type:
infection
Reference:
Effect of route of inoculation on experimental respiratory viral disease in volunteers and evidence for airborne transmission
Humans/ type 4 Strain model data 
Dose Infected Non-infected Total
1 1 2 3
5 3 0 3
11 3 0 3
1000 6 0 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 0.487 -0.000723 3 3.84 
1 		7.81 
0.922
Beta Poisson 0.488 2 5.99 
0.784
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 6.07E-01 3.87E-01 3.87E-01 3.87E-01 1.13E+00 1.13E+00 1.13E+00
ID50/LD50/ETC* 1.14E+00 6.11E-01 6.11E-01 6.11E-01 1.79E+00 1.79E+00 1.79E+00
*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

Description
human/type 39 strain SF 299 model data 
Dose Infected Non-infected Total
0.05 0 11 11
0.15 2 7 9
0.5 8 16 24
5 5 11 16
50 47 15 62

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 50.3 44.3 4 3.84 
2.76e-11 		9.49 
3.06e-10
Beta Poisson 6.01 3 7.81 
0.111
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 2.24E-01 9.88E-04 1.40E-01 1.53E-01 3.71E-01 4.27E-01 7.63E-01
N50 3.29E+00 1.90E-02 1.34E+00 1.59E+00 7.67E+00 9.27E+00 1.59E+01

 

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
1.81E+00
LD50/ID50
1.81E+00
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
2.21E-01
Agent Strain
type 39
Experiment ID
65
Host type
human
Description
human/type 14 strain SF 765model data 
Dose Infected Non-infected Total
0.5 1 8 9
1.5 4 6 10
5 4 6 10
15 6 4 10
150 27 13 40
300 10 2 12

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 51.8 50.2 5 3.84 
1.42e-12 		11.1 
5.8e-10
Beta Poisson 1.68 4 9.49 
0.794
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 2.01E-01 7.76E-02 1.07E-01 1.22E-01 3.36E-01 3.69E-01 4.61E-01
N50 9.22E+00 1.41E+00 2.57E+00 3.40E+00 2.47E+01 3.14E+01 5.26E+01

 

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
9.22E+00
LD50/ID50
9.22E+00
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
2.01E-01
Agent Strain
type 14
Experiment ID
64
Host type
human
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