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Experiment ID
139
Pathogen
Cryptosporidium hominis
Cryptosporidium parvum
Agent Strain
Iowa isolate
Contains Preferred Model
No
Reference
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
Exposure Route
oral
Response
infection
Host type
human
# of Doses
8.00
Dose Units
oocysts
Μodel
exponential
k
5.26E-03
LD50/ID50
1.32E+02
Description
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

References