Optimization Output for Exp. 40 | QMRA wiki

Basic information

Experiment ID	40
Pathogen	Escherichia coli
Agent Strain	EIEC 1624
Contains Preferred Model	No
Reference	DuPont, H. L., Formal, S. B., Hornick, R. B., Snyder, M. J., Libonati, J. P., Sheahan, D. G., … Kalas, J. P. (1971). Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine, 285, 1.
Exposure Route	oral (in milk)
Response	mild to severe diarrhea

Detailed information

Host type

human

# of Doses

3.00

Dose Units

CFU

Μodel

exponential

k

1.22E-08

LD50/ID50

5.7E+07

Experiment Dataset

Description

**Escherichia coli** **(EIEC 1624) in the human model data**
Dose	Mild to severe diarrhea	No mild to severe diarrhea	Total
1E+04	0	5	5
1E+06	1	8	9
1E+08	3	2	5

**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	2.99	2.98	2	3.84 0.0845	5.99 0.224
Beta Poisson	0.0156	2.98	1	3.84 0.0845	3.84 0.901
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
Parameter	MLE estimate	0.5%	2.5%	5%	95%	97.5%	99.5%
k	1.22E-08	1.97E-09	2.19E-09	4.40E-09	4.03E-08	1.17E-07	2.50E-07
ID50/LD50/ETC*	5.7E+07	2.77E+06	5.92E+06	1.72E+07	1.58E+08	3.17E+08	3.52E+08
*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

DuPont, H. L., Formal, S. B., Hornick, R. B., Snyder, M. J., Libonati, J. P., Sheahan, D. G., … Kalas, J. P. (1971). Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine, 285, 1.