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