Agent Strain: Iowa strain
Optimized parameters:
k = 4.19E-03
LD50/ID50 = 1.65E+02
Iowa strain data [1]
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)
Exponential model plot, with confidence bounds around optimized model
References
- The infectivity of Cryptosporidium parvum in healthy volunteers, DuPont, H. L., Chappell C. L., Sterling C. R., Okhuysen P. C., Rose J. B., and Jakubowski W. , The New England journal of medicine, Volume 332, p.13, (1995)
Agent Strain: Iowa isolate
Optimized parameters:
k = 5.26E-03
LD50/ID50 = 1.32E+02
Iowa isolate data [1]
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
Agent Strain: TAMU isolate
Optimized parameters:
k = 5.72E-02
LD50/ID50 = 1.21E+01
TAMU data [1]
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)
References
Agent Strain: UCP isolate
Optimized parameters: a = 1.45E-01
LD50/ID50 = 1.79E+02
N50 = 1.79E+02
UCP isolate [1]
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
References
Agent Strain: *C. hominis*, TU502
Optimized parameters: a = 2.7E-01
LD50/ID50 = 1.68E+01
N50 = 1.68E+01
TU502 data [1]
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.
References
- Cryptosporidium Hominis: Experimental Challenge of Healthy Adults, Chappell, C. L., Okhuysen P. C., Langer-Curry R., Widmer G., Akiyoshi D. E., Tanriverdi S., and Tzipori S. , The American Journal of Tropical Medicine and Hygiene, Volume 75, p.5, (2006)
Agent Strain: Moredun isolate
Optimized parameters: a = 1.14E-01
LD50/ID50 = 4.55E+02
N50 = 4.55E+02
Moredunn isolate data [1]
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.
References
- Infectivity of a Cryptosporidium parvum Isolate of Cervine Origin for Healthy Adults and Interferon-γ Knockout Mice, Okhuysen, P. C., Rich S. M., Chappell C. L., Grimes K. A., Widmer G., Feng X., and Tzipori S. , Journal of Infectious Diseases, Volume 185, p.9, (2002)