Description

 

Goodness of Fit and Model Selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 9.88 6.48 5 3.84 
0.011 		11.1
0.0788
beta Poisson 3.4 4 9.49
0.494
beta-Poisson fits better than exponential; can not reject good fit for beta-Poisson

 

 

 

 

 

 

 

Bootstrapped Parameter Estimates
Parameter MLE Estimate 0.5% 2.5% 5% 95% 97.5% 99.5%
α 6.95E-01 2.69E-01 3.39E-01 3.78E-01 2.56E+0 2.28E+01 1.18E+03
N50 3.39E+03 3.58E+01 2.47E+02 4.67E+02 1.09E+04 1.26E+04 1.85E+04

 

 

 

 

 

 

Host
C57Bl/6J mice
# of Doses
6.00
Μodel
beta-Poisson
N50
277
Dose Units
CFU
Response
infection
Exposure Route
oral
Contains Preferred Model
Status
fitted
a
0.253
Agent Strain
F5817
Experiment ID
292
Experiment Dataset
Dose (CFU) Infected Non-Infected Total
5500 7 3 10
32400 7 3 10
55000 9 1 10
251000 10 0 10
550000 10 0 10
2820000 10 0 10
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
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
Description
Model data for rotavirus (CJN strain) in the human 
Dose Detectable shedding No detectable shedding Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 8 3 11
90 4 3 7
900 3 5 8
9000 4 3 7
9E+04 2 1 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 157 148 7 3.84 
0 		14.1 
0
Beta Poisson 9.42 6 12.6 
0.151
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 9.6E-02 9.94E-04 9.96E-04 9.98E-04 1.59E-01 1.74E-01 2.05E-01
N50 9.61E+01 2.95E-03 1.59E-02 4.56E-02 2.83E+03 1.46E+04 1.58E+80

 

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
N50
96.1
LD50/ID50
96.1
Dose Units
FFU
Response
detectable shedding
Exposure Route
oral
Contains Preferred Model
a
9.6E-2
Agent Strain
CJN strain (unpassaged
Experiment ID
125
Host type
human
Experiment Dataset
Description
Model data for rotavirus (CJN strain) in the human 
Dose Symptoms and infection No symptoms and infection Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 5 6 11
90 2 5 7
900 4 4 8
9000 3 4 7
9E+04 2 1 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 103 99.5 7 3.84 
0 		14.1 
0
Beta Poisson 3.14 6 12.6 
0.791
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 7.28E-02 9.93E-04 9.95E-04 9.96E-04 1.32E-01 1.46E-01 1.83E-01
N50 1.47E+03 6.55E-03 1.85E-02 4.58E-02 5.47E+06 1.82E+31 6.68E+122

 

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
8.00
Μodel
beta-Poisson
N50
1.47E+03
LD50/ID50
1.47E+03
Dose Units
FFU
Response
infection
Exposure Route
oral
Contains Preferred Model
a
7.28E-02
Agent Strain
CJN strain (unpassaged)
Experiment ID
71
Host type
human

Listeria monocytogenes (Death as response): Dose Response Models

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General Overview

Listeria monocytogenes is a Gram-positive rod-shaped bacterium. It is the causative agent of listeriosis, a serious infection caused by eating food contaminated with the bacteria. The disease generally affects older adults, pregnant women, newborns, and adults with weakened immune systems.

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
292 oral 6.00 F5817 CFU beta-Poisson a = 0.253 N50 = 277 infection
Exposure Route:
oral
# of Doses:
6.00
Agent Strain:
F5817
Dose Units:
CFU
Host type:
Μodel:
beta-Poisson
LD50/ID50:
Optimized parameters: a = 0.253 N50 = 277
Response type:
infection
Reference:

 

Goodness of Fit and Model Selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 9.88 6.48 5 3.84 
0.011 		11.1
0.0788
beta Poisson 3.4 4 9.49
0.494
beta-Poisson fits better than exponential; can not reject good fit for beta-Poisson

 

 

 

 

 

 

 

Bootstrapped Parameter Estimates
Parameter MLE Estimate 0.5% 2.5% 5% 95% 97.5% 99.5%
α 6.95E-01 2.69E-01 3.39E-01 3.78E-01 2.56E+0 2.28E+01 1.18E+03
N50 3.39E+03 3.58E+01 2.47E+02 4.67E+02 1.09E+04 1.26E+04 1.85E+04

 

 

 

 

 

 

Giardia duodenalis: Dose Response Experiments

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Overview

Giardia is a flagellated protozoan parasite of vertebrates. It attaches noninvasively to the small intestinal wall and absorbs nutrients (Miliotis & Bier 2003). Cysts are intermittently excreted in the stools of infected people; they are infectious immediately.

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
46 oral 8.00 From an infected human Cysts human exponential 3.48E+01 k = 1.99E-02 infection
Rendtorff, R. C. (1954). The experimental transmission of human intestinal protozoan parasites. II. Giardia lamblia cysts given in capsules. American Journal of Hygiene, 59, 2. Retrieved from https://academic.oup.com/aje/article-abstract/59/2/196/89318?redirectedFrom=PDF
47 oral 4.00 From infected humans Cysts beaver beta-Poisson 1.46E+04 a = 1.37E-01 N50 = 1.46E+04 infection
Erlandsen, S. L., Sherlock, L. A., Januschka, M. ., Schupp, D. G., Schaefer, F. W., Jakubowski, W. ., & Bemrick, W. J. (1988). Cross-species transmission of Giardia spp.: inoculation of beavers and muskrats with cysts of human, beaver, mouse, and muskrat origin. Applied and Environmental Microbiology, 54, 11. Retrieved from http://aem.asm.org/content/54/11/2777.abstract
Highest quality
Exposure Route:
oral
# of Doses:
8.00
Agent Strain:
From an infected human
Dose Units:
Cysts
Host type:
human
Μodel:
exponential
LD50/ID50:
3.48E+01
Optimized parameters: k = 1.99E-02
Response type:
infection
Reference:
The experimental transmission of human intestinal protozoan parasites. II. Giardia lamblia cysts given in capsules
Dose response data 
Dose Infected Non-infected Total
1 0 5 5
10 2 0 2
25 6 14 20
100 2 0 2
1E+04 3 0 3
1E+05 3 0 3
3E+05 3 0 3
1E+06 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 8.37 -0.000469 7 3.84 
1 		14.1 
0.301
Beta Poisson 8.37 6 12.6 
0.212
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 1.99E-02 8.50E-03 1.05E-02 1.26E-02 2.92E-02 3.29E-02 3.71E-02
ID50/LD50/ETC* 3.48E+01 1.87E+01 2.11E+01 2.38E+01 5.49E+01 6.60E+01 8.15E+01
*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:
oral
# of Doses:
4.00
Agent Strain:
From infected humans
Dose Units:
Cysts
Host type:
beaver
Μodel:
beta-Poisson
LD50/ID50:
1.46E+04
Optimized parameters: a = 1.37E-01 N50 = 1.46E+04
Response type:
infection
Reference:
Cross-species transmission of Giardia spp.: inoculation of beavers and muskrats with cysts of human, beaver, mouse, and muskrat origin
Dose response data 
Dose Infected Non-infected Total
48 0 6 6
454 2 4 6
4460 1 2 3
550000 2 1 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 22.5 21.3 3 3.84 
3.97e-06 		7.81 
5.14e-05
Beta Poisson 1.22 2 5.99 
0.544
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 1.37E-01 1.34E-02 2.24E-02 4.22E-02 3.39E+00 2.21E+02 2.14E+03
N50 1.46E+04 5.09E+02 8.20E+02 1.06E+03 1.71E+08 8.25E+11 1.62E+18

 

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

Enterovirus: Dose Response Experiments

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General Overview

According to Stalkup and Chilukuri, enterovirus, a small (30 nm), nonenveloped, single-stranded RNA viruses, belongs to the family Picornaviridae.

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
62 oral 3.00 porcine, PE3-ECPO-6 PFU pig exponential 2.34E+03 k = 2.96E-04 infection
Cliver, D. O. (1981). Experimental infection by waterborne enteroviruses. Journal of Food Protection, 44, 861–865. Retrieved from http://www.jfoodprotection.org/doi/abs/10.4315/0362-028X-44.11.861?code=fopr-site
63 oral 3.00 porcine, PE7-05i PFU pig exponential 1.85E+02 k = 3.74E-03 infection
Cliver, D. O. (1981). Experimental infection by waterborne enteroviruses. Journal of Food Protection, 44, 861–865. Retrieved from http://www.jfoodprotection.org/doi/abs/10.4315/0362-028X-44.11.861?code=fopr-site
Exposure Route:
oral
# of Doses:
3.00
Agent Strain:
porcine, PE3-ECPO-6
Dose Units:
PFU
Host type:
pig
Μodel:
exponential
LD50/ID50:
2.34E+03
Optimized parameters: k = 2.96E-04
Response type:
infection
Reference:
Experimental infection by waterborne enteroviruses
Pigs/ Porcine enterovirus type 3 Strain model data 
Dose infected Non-infected Total
100 0 3 3
250 0 6 6
1000 2 4 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 1.24 -0.000314 2 3.84 
1 		5.99 
0.537
Beta Poisson 1.24 1 3.84 
0.265
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 2.96E-04 2.40E-17 2.40E-17 2.40E-17 7.19E-04 7.19E-04 1.02E-03
ID50/LD50/ETC* 2.34E+03 6.77E+02 9.64E+02 9.64E+02 2.89E+16 2.89E+16 2.89E+16
*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

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Exposure Route:
oral
# of Doses:
3.00
Agent Strain:
porcine, PE7-05i
Dose Units:
PFU
Host type:
pig
Μodel:
exponential
LD50/ID50:
1.85E+02
Optimized parameters: k = 3.74E-03
Response type:
infection
Reference:
Experimental infection by waterborne enteroviruses
pigs/ Porcine enterovirus type 7 
Dose infected Non-infected Total
250 4 2 6
250 3 3 6
1000 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 0.614 -5.49e-05 2 3.84 
1 		5.99 
0.736
Beta Poisson 0.614 1 3.84 
0.433
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 3.74E-03 1.83E-03 2.19E-03 2.19E-03 5.62E-03 5.62E-03 5.62E-03
ID50/LD50/ETC* 1.85E+02 1.23E+02 1.23E+02 1.23E+02 3.16E+02 3.16E+02 3.79E+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

Echovirus: Dose Response Experiments

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General Overview

Echoviruses, a member of the enterovirus genus, is a type of RNA virus that were shown to be a frequent cause of simple febrile illnesses and aseptic meningitis. Most infected persons experience no symptoms or have self-limited disease.

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
112 oral 6.00 strain 12 PFU human beta-Poisson 1.01E+03 a = 3.74E-01 N50 = 1.01E+03 infection
Suptel, E. A. (1963). Pathogenesis of experimental Coxsackie virus infection. Archive of Virology, 7, 61-66.
256 (excluding the outliers of exp 112) oral 4.00 strain 12 PFU human beta-Poisson 9.22E+02 a = 1.06E+00 N50 = 9.22E+02 infection
Schiff, G. M., Stefanović, G. M., Young, E. C., Sander, D. S., Pennekamp, J. K., & Ward, R. L. (1984). Studies of echovirus-12 in volunteers: determination of minimal infectious dose and the effect of previous infection on infectious dose. The Journal of Infectious Diseases, 150, 6. Retrieved from https://academic.oup.com/jid/article-abstract/150/6/858/880281
Exposure Route:
oral
# of Doses:
6.00
Agent Strain:
strain 12
Dose Units:
PFU
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
1.01E+03
Optimized parameters: a = 3.74E-01 N50 = 1.01E+03
Response type:
infection
Reference:
Pathogenesis of experimental Coxsackie virus infection
humans/ echovirus-12 strain 
Dose infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
1E+04 12 0 12
33000 2 2 4
330000 2 1 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 122 110 5 3.84 
0 		11.1 
0
Beta Poisson 11.7 4 9.49 
0.0196
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 3.74E-01 1.24E-01 1.81E-01 2.09E-01 7.79E-01 9.41E-01 2.01E+00
N50 1.01E+03 3.84E+02 5.32E+02 5.94E+02 1.75E+03 1.97E+03 2.54E+03

 

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

Highest quality
Exposure Route:
oral
# of Doses:
4.00
Agent Strain:
strain 12
Dose Units:
PFU
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
9.22E+02
Optimized parameters: a = 1.06E+00 N50 = 9.22E+02
Response type:
infection
Reference:
Studies of echovirus-12 in volunteers: determination of minimal infectious dose and the effect of previous infection on infectious dose
humans/ echovirus-12 strain 
Dose infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
1E+04 12 0 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 7.39 4.18 3 3.84 
0.041 		7.81 
0.0605
Beta Poisson 3.21 2 5.99 
0.201
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 1.06E+00 3.07E-01 4.04E-01 4.69E-01 1.23E+01 6.22E+02 3.74E+04
N50 9.22E+02 4.68E+02 5.59E+02 6.15E+02 1.37E+03 1.49E+03 1.73E+03

 

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

Cryptosporidium parvum: Dose Response Experiments

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General overview

Various species of Cryptosporidium infect most vertebrates. C. parvum infects cattle but can also infect humans; C. hominis appears to be restricted to humans, and began to be recognized in the early 2000s (Hunter 2005) .

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
108 oral 8.00 Iowa strain oocysts human exponential 1.65E+02 k = 4.19E-03 infection
DuPont, H. L., Chappell, C. L., Sterling, C. R., Okhuysen, P. C., Rose, J. B., & Jakubowski, W. . (1995). The infectivity of Cryptosporidium parvum in healthy volunteers. The New England Journal of Medicine, 332, 13. Retrieved from https://www.nejm.org/doi/full/10.1056/NEJM199503303321304
139 oral 8.00 Iowa isolate oocysts human exponential 1.32E+02 k = 5.26E-03 infection
Messner, M. J., Chappell, C. L., & Okhuysen, P. C. (2001). Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data. Water Research, 35, 16. Retrieved from https://www.sciencedirect.com/science/article/pii/S0043135401001191
140 oral 4.00 TAMU isolate oocysts human exponential 1.21E+01 k = 5.72E-02 infection
Messner, M. J., Chappell, C. L., & Okhuysen, P. C. (2001). Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data. Water Research, 35, 16. Retrieved from https://www.sciencedirect.com/science/article/pii/S0043135401001191
141 oral 4.00 UCP isolate oocysts human beta-Poisson 1.79E+02 a = 1.45E-01 N50 = 1.79E+02 infection
Coster, T. S., Wolf, M. K., Hall, E. R., Cassels, F. J., Taylor, D. N., Liu, C. T., … McQueen, C. E. (2007). Immune response, ciprofloxacin activity, and gender differences after human experimental challenge by two strains of enterotoxigenic Escherichia coli. Infection and Immunity, 75, 1.
181 oral 4.00 *C. hominis*, TU502 oocysts human beta-Poisson 1.68E+01 a = 2.7E-01 N50 = 1.68E+01 diarrhea
Okhuysen, P. C., Rich, S. M., Chappell, C. L., Grimes, K. A., Widmer, G. ., Feng, X. ., & Tzipori, S. . (2002). Infectivity of a Cryptosporidium parvum Isolate of Cervine Origin for Healthy Adults and Interferon-γ Knockout Mice. Journal of Infectious Diseases, 185, 9. Retrieved from https://academic.oup.com/jid/article/185/9/1320/937719
183 oral 4.00 Moredun isolate oocysts human beta-Poisson 4.55E+02 a = 1.14E-01 N50 = 4.55E+02 infection
Blaser, M. J., Duncan, D. J., Warren, G. H., & W-ll, W. . (1983). Experimental Campylobacter jejuni Infection of Adult Mice. Infection and Immunity, 39, 2.
Exposure Route:
oral
# of Doses:
8.00
Agent Strain:
Iowa strain
Dose Units:
oocysts
Host type:
human
Μodel:
exponential
LD50/ID50:
1.65E+02
Optimized parameters: k = 4.19E-03
Response type:
infection
Reference:
The infectivity of Cryptosporidium parvum in healthy volunteers
Iowa strain data 
Dose Infected Non-infected Total
30 1 4 5
100 3 5 8
300 2 1 3
500 5 1 6
1000 2 0 2
1E+04 3 0 3
1E+05 1 0 1
1E+06 1 0 1

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 0.503 0.131 7 3.84 
0.717 		14.1 
0.999
Beta Poisson 0.372 6 12.6 
0.999
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 4.19E-03 1.80E-03 2.22E-03 2.46E-03 7.52E-03 8.52E-03 1.12E-02
ID50/LD50/ETC* 1.65E+02 6.17E+01 8.14E+01 9.22E+01 2.82E+02 3.12E+02 3.84E+02
*Not a parameter of the exponential model; however, it facilitates comparison with other models.
Parameter histogram for exponential model (uncertainty of the parameter)
Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model
Exposure Route:
oral
# of Doses:
8.00
Agent Strain:
Iowa isolate
Dose Units:
oocysts
Host type:
human
Μodel:
exponential
LD50/ID50:
1.32E+02
Optimized parameters: k = 5.26E-03
Response type:
infection
Reference:
Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data
Iowa isolate data 
Dose Infected Not infected Total
30 2 3 5
100 4 4 8
300 2 1 3
500 5 1 6
1000 2 0 2
1E+04 3 0 3
1E+05 1 0 1
1E+06 1 0 1

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 3.07 2 7 3.84 
0.157 		14.1 
0.879
Beta Poisson 1.07 6 12.6 
0.983
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 5.26E-03 2.25E-03 2.75E-03 3.08E-03 1.03E-02 1.19E-02 1.60E-02
ID50/LD50/ETC* 1.32E+02 4.33E+01 5.80E+01 6.72E+01 2.25E+02 2.52E+02 3.08E+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:
oral
# of Doses:
4.00
Agent Strain:
TAMU isolate
Dose Units:
oocysts
Host type:
human
Μodel:
exponential
LD50/ID50:
1.21E+01
Optimized parameters: k = 5.72E-02
Response type:
infection
Reference:
Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data
TAMU data 
Dose Infected Non-infected Total
10 2 1 3
30 2 1 3
100 3 0 3
500 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 1.07 0.21 3 3.84 
0.647 		7.81 
0.783
Beta Poisson 0.864 2 5.99 
0.649
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 5.72E-02 1.80E-02 1.92E-02 2.46E-02 2.65E+00 2.65E+00 2.65E+00
ID50/LD50/ETC* 1.21E+01 2.61E-01 2.61E-01 2.61E-01 2.82E+01 3.61E+01 3.84E+01
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

Exponential model plot, with confidence bounds around optimized model

Parameter histogram for exponential model (uncertainty of the parameter)

 

 

Exposure Route:
oral
# of Doses:
4.00
Agent Strain:
UCP isolate
Dose Units:
oocysts
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
1.79E+02
Optimized parameters: a = 1.45E-01 N50 = 1.79E+02
Response type:
infection
Reference:
Immune response, ciprofloxacin activity, and gender differences after human experimental challenge by two strains of enterotoxigenic Escherichia coli
UCP isolate 
Dose Infected Non-infected Total
500 3 2 5
1000 2 1 3
5000 2 3 5
1E+04 4 0 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 11.5 6.99 3 3.84 
0.0082 		7.81 
0.00945
Beta Poisson 4.48 2 5.99 
0.107
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 1.45E-01 9.81E-04 4.63E-03 9.53E-03 1.27E+00 1.46E+02 9.10E+02
N50 1.79E+02 2.74E-13 7.60E-10 4.54E-09 2.62E+03 3.22E+03 6.10E+03

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

Exposure Route:
oral
# of Doses:
4.00
Agent Strain:
*C. hominis*, TU502
Dose Units:
oocysts
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
1.68E+01
Optimized parameters: a = 2.7E-01 N50 = 1.68E+01
Response type:
diarrhea
Reference:
Infectivity of a Cryptosporidium parvum Isolate of Cervine Origin for Healthy Adults and Interferon-γ Knockout Mice
TU502 data 
Dose Diarrhea Not diarrhea Total
10 2 3 5
30 3 2 5
100 5 2 7
500 3 1 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 11.6 11.5 3 3.84 
0.000708 		7.81 
0.00894
Beta Poisson 0.119 2 5.99 
0.942
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 2.7E-01 9.83E-04 9.85E-04 2.03E-03 6.60E+00 6.70E+02 3.19E+03
N50 1.68E+01 3.41E-16 9.86E-09 1.68E-06 7.15E+01 9.76E+01 6.59E+02

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.

Exposure Route:
oral
# of Doses:
4.00
Agent Strain:
Moredun isolate
Dose Units:
oocysts
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
4.55E+02
Optimized parameters: a = 1.14E-01 N50 = 4.55E+02
Response type:
infection
Reference:
Experimental Campylobacter jejuni Infection of Adult Mice
Moredunn isolate data 
Dose Infected Non-infected Total
100 2 2 4
300 2 3 5
1000 1 2 3
3000 3 1 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 7.37 6.16 3 3.84 
0.0131 		7.81 
0.0611
Beta Poisson 1.21 2 5.99 
0.546
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 1.14E-01 9.79E-04 9.81E-04 9.82E-04 1.17E+03 2.25E+03 5.52E+03
N50 4.55E+02 2.13E-09 2.19E-06 1.55E-05 5.62E+05 3.59E+09 1.43E+16

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.

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