Optimization Output for Exp. 86 | QMRA wiki

Basic information

Experiment ID	86
Pathogen	Bacillus anthracis
Agent Strain	Vollum
Contains Preferred Model	No
Reference	Druett, H. A., Henderson, D. W., Packman, L. ., & Peacock, S. . (1953). Studies on respiratory infection. The Journal of Hygiene, 51, 3.
Exposure Route	inhalation
Response	death

Detailed information

Host type	monkey
# of Doses	9.00
Dose Units	spores
Μodel	exponential
k	7.16E-06
LD50/ID50	9.69E+04

Description

**Rhesus Macaques/Vollum Strain model data**
Dose	Dead	Survived	Total
70300	1	7	8
77000	4	4	8
109000	5	3	8
138000	6	2	8
156000	5	3	8
161000	3	5	8
240000	8	0	8
3E+05	7	1	8
398000	8	0	8

**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	11.3	-0.000503	8	3.84 1	15.5 0.188
Beta Poisson	11.3	-0.000503	7	3.84 1	14.1 0.128
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	7.16E-06	4.99E-06	5.47E-06	5.71E-06	9.09E-06	9.51E-06	1.05E-05
ID50/LD50/ETC*	9.69E+04	6.63E+04	7.29E+04	7.63E+04	1.21E+05	1.27E+05	1.39E+05
*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

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.