Optimization Output for Exp. 81 | QMRA wiki

Basic information

Experiment ID	81
Pathogen	Shigella dysenteriae
Agent Strain	M 131
Contains Preferred Model	No
Reference	DuPont, H. L., Hornick, R. B., Dawkins, A. T., Snyder, M. J., & Formal, S. B. (1969). The Response of Man to Virulent Shigella flexneri 2a. Journal of Infectious Diseases, 119, 3.
Exposure Route	oral (in milk)
Response	illness

Detailed information

Host type

human

# of Doses

4.00

Dose Units

CFU

Μodel

beta-Poisson

a

2.77E-01

N50

2.38E+02

LD50/ID50

2.38E+02

Experiment Dataset

Description

**Model data for** **Shigella dysenteriae** **(M 131) in the human**
Dose	Illness	Not illness	Total
10	1	9	10
200	2	2	4
2000	7	3	10
1E+04	5	1	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	13.2	13.2	3	3.84 0.000283	7.81 0.0042
Beta Poisson	0.0315	13.2	2	3.84 0.000283	5.99 0.984
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	2.77E-01	5.24E-03	1.10E-01	1.34E-01	1.63E+00	1.88E+01	1.72E+03
N₅₀	2.38E+02	1.35E+01	4.73E+01	6.36E+01	1.42E+03	2.02E+03	5.89E+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

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.