Optimization Output for Exp. 79

Basic information

Experiment ID	79
Pathogen	Salmonella typhi
Agent Strain	Quailes
Contains Preferred Model	No
Reference	Hornick, R. B., Greisman, S. ., Woodward, T. E., DuPont, H. L., Dawkins, A. T., & Snyder, M. J. (1970). Typhoid fever: pathogenesis and immunologic control. The New England Journal of Medicine, 283, 13.
Exposure Route	oral (in milk)
Response	disease

Detailed information

Host type	human
# of Doses	3.00
Dose Units	CFU
Μodel	beta-Poisson
a	1.11E-01
N50	3.45E+06
LD50/ID50	3.45E+06"

Description

**Model data for S. Typhi (Quailes) in humans**
Dose	Disease	No disease	Total
1E+05	28	76	104
1E+07	15	15	30
1E+09	4	0	4

**Goodness of fit and model selection**
Model	Deviance	Δ	Degrees of freedom	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	124	121	2	3.84 0	5.99 0
Beta Poisson	2.87	121	1	3.84 0	3.84 0.0905
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
Parameter	MLE estimate	0.5%	2.5%	5%	95%	97.5%	99.5%
α	1.11E-01	3.19E-02	4.80E-02	5.49E-02	1.96E-01	2.17E-01	2.59E-01
N₅₀	3.45E+06	4.81E+05	6.95E+05	8.50E+05	9.53E+07	2.24E+08	4.19E+09

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

Hornick, R. B., Woodward, T. E., McCrumb, F. R., Snyder, M. J., Dawkins, A. T., & Bulkeley, J. T. De la Macorra F and Corozza FA (1966) Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness. Transactions of the Association of American Physicians, 79, 361.