Optimization Output for Exp. 87 | QMRA wiki

Basic information

Experiment ID	87
Pathogen	Bacillus anthracis
Agent Strain	Vollum
Contains Preferred Model	Yes
Reference	June, R. ., Ferguson, W. ., & Worfel, M. . (1953). Experiments in feeding adult volunteers with Escherichia coli 55, B5, a coliform organism associated with infant diarrhea. American Journal of Hygiene, 57(2). https://doi.org/10.1093/oxfordjournals.aje.a119570
Exposure Route	inhalation
Response	death

Detailed information

Host type	guinea pig
# of Doses	4.00
Dose Units	spores
Μodel	exponential
k	1.65E-05
LD50/ID50	4.2E+04

Description

**Guinea pig/Vollum Strain model data**
Dose	Dead	Survived	Total
19800	8	24	32
40800	18	14	32
76200	21	11	32
118000	28	4	32

**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	1.43	-0.000184	3	3.84 1	7.81 0.699
Beta Poisson	1.43	-0.000184	2	3.84 1	5.99 0.49
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

**Optimized parameters 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	1.65E-05	1.20E-05	1.30E-05	1.35E-05	2.03E-05	2.12E-05	2.28E-05
ID50/LD50/ETC*	4.2E+04	3.04E+04	3.27E+04	3.41E+04	5.14E+04	5.35E+04	5.80E+04
*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

Bacillus Graph 2.png

References

Druett, H. ., Henderson, D. ., Packman, L. ., & Peacock, S. . (1953). Studies on respiratory infection: I. The influence of particle size on respiratory infection with anthrax spores. Epidemiology & Infection, 51, 359–371.