Optimization Output for Exp. 81, 215 | QMRA wiki

Basic information

Experiment ID	81, 215
Pathogen	Shigella dysenteriae
Agent Strain	M 131
Contains Preferred Model	No
Reference	Levine, M. M., DuPont, H. L., Formal, S. B., Hornick, R. B., Takeuchi, A. ., Gangarosa, E. J., … Libonati, J. P. (1973). Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery. Journal of Infectious Diseases, 127, 3.
Exposure Route	oral (in milk)
Response	illness

Detailed information

Host type

human

# of Doses

6.00

Dose Units

CFU

Μodel

beta-Poisson

a

4.93E-03

N50

3.64E-01

LD50/ID50

3.64E-01

Experiment Dataset

Description

**Model data for Shigella dysenteriae in the human**
Dose	Illness	Not illness	Total
10	1	9	10
200	2	2	4
200	1	3	4
2000	7	3	10
1E+04	5	1	6
1E+04	2	4	6

**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	30.5	16.9	5	3.84 3.94e-05	11.1 1.2e-05
Beta Poisson	13.6	16.9	4	3.84 3.94e-05	9.49 0.00887
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
Parameter	MLE estimate	0.5%	2.5%	5%	95%	97.5%	99.5%
α	4.93E-03	9.85E-04	9.87E-04	9.88E-04	3.61E-01	4.26E-01	5.85E-01
N₅₀	3.64E-01	2.07E-02	5.54E-02	7.42E-02	2.05E+03	4.61E+03	1.09E+28

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

Levine, M. M., DuPont, H. L., Formal, S. B., Hornick, R. B., Takeuchi, A. ., Gangarosa, E. J., … Libonati, J. P. (1973). Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery. Journal of Infectious Diseases, 127, 3.