Difference between revisions of "Coxiella burnetii: Dose Response Models"

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Williams, J. C. and J. L. Cantrell (1982). "[http://iai.asm.org/cgi/content/abstract/35/3/1091 Biological and immunological properties of Coxiella burnetii vaccines in C57BL/1OScN endotoxin-nonresponder mice]." Infection and Immunity '''35'''(3): 1091–1102.
 
Williams, J. C. and J. L. Cantrell (1982). "[http://iai.asm.org/cgi/content/abstract/35/3/1091 Biological and immunological properties of Coxiella burnetii vaccines in C57BL/1OScN endotoxin-nonresponder mice]." Infection and Immunity '''35'''(3): 1091–1102.
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[[Category:Dose Response Model]]

Revision as of 21:45, 11 November 2011

Coxiella burnetii

Author: Yin Huang
If you want to download this chapter in pdf format, please click here
If you want to download the excel spreadsheet of tables, please click the captions of tables. If you want to download a specific figure, just click on the figure


General overview of Coxiella burnetii and Q fever

Coxiella burnetii (C. burnetii), an obligate intracellular gram-negative bacterium, is the causative agent of Q fever. C. burnetii multiplies only within the phagolysosomal vacuoles, particularly the macrophages of the host. During natural infections, the organism grows to high numbers in placental tissues of animals such as goats, sheep, and cows. The Center for Disease Control and Prevention (CDC) has classified C. burnetii as a category B biological terrorist agent because it consistently causes disability, can be manufactured on a large scale, remains stable under production, storage, and transportation conditions, can be efficiently disseminated and remains viable for years after dissemination.

Q fever, a zoonotic disease found worldwide, may manifest as acute or chronic disease. The acute form is generally not fatal and manifests as self-controlled febrile illness. Chronic Q fever is usually characterized by endocarditis. Many animal models, including humans, have been studied for Q fever infection through various exposure routes.

Humans are infected primarily through inhalation of aerosolized C. burnetii with as few as 10 organisms causing disease. Aerosols, or airborne particles, easily cause infection even without contact with infected animals, whereas person-to-person infection is rare. Ingestion of contaminated dairy products or bites from infected ticks may also lead to infection but these modes of transmission are very rare. However, there have been some recorded cases of human Q fever caused by the consumption of unpasteurized goat milk products (Tamrakar et al. 2011).


Summary Data

Williams and Cantrell interperitoneally inoculated groups of C57BL/10ScN male mice with 11 different doses of C. burnetii phase I Ohio strain to develop a vaccine against Q fever.

Scott and Williams examined the susceptibility of inbred mice to infection by C. burnetii Nine mile phase I strain. As many as 47 strains of inbred mice were evaluated. Groups of resistant C57BL/6J mice were inoculated with mean doses ranging from 10−1.3 to 107 organisms. The mortalities at various doses were recorded.


Table 4.1. Summary of the Coxiella burnetii data and best fits

Experiment number Reference Host type/pathogen strain Route/number of doses Dose units Response Best-fit modela Best-fit parameters LD50
1* Williams et al., 1982 mice/ phase I Ohio strain interperitoneal/10 No. of organisms death Beta-Poisson α = 0.36, N50 = 4.93E+08 4.93E+08
2 Scott et al., 1987 mice/ Nine mile phase I strain interperitoneal/13 No. of organisms death Exponential K=5.70E-11 1.22E+10

*Recommended Model

It is recommended that experiment 1 should be used as the best dose-response model. A more virulent strain in experiment 1 can be more meaningful for emergency preparedness. Also, single host strain was used in experiment 1 instead of multiple strains as in experiment 2.

a:
Exponential and betapoisson model.jpg

Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 4.2. Mice/ phase I Ohio strain model data
Dose Dead Survived Total
7.00E+10 19 1 20
7.00E+09 23 7 30
7.00E+08 16 14 30
7.00E+07 6 24 30
7.00E+06 1 19 20
7.00E+05 0 30 30
7.00E+03 0 30 30
7.00E+01 0 30 30
7.00E+00 0 20 20
7.00E-01 0 30 30
Williams et al., 1982.


Table 4.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 73.87 72.76 9 3.84
0
16.92
0
Beta Poisson 1.11 8 15.51
0.998
Beta Poisson is best fitting model
Table 4.4 Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.36 -- -- -- -- -- --
N50 4.93E+08 -- -- -- -- -- --
LD50 4.93E+08 1.91E+08 2.41E+08 2.73E+08 9.37E+08 1.08E+09 1.39E+09


Figure 4.1 Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Figure 4.2 beta Poisson model plot, with confidence bounds around optimized model



Optimized Models and Fitting Analyses

Optimization Output for experiment 2

Table 8.5: Dose response data
Dose Dead Survived Total
5.01E+10 9 1 10
5.01E+09 3 7 10
5.01E+08 1 9 10
5.01E+07 0 10 10
5.01E+06 0 10 10
5.01E+05 0 10 10
5.01E+04 0 10 10
5.01E+03 0 10 10
5.01E+02 0 10 10
5.00E+01 0 10 10
5.00E+00 0 10 10
5.00E-01 0 10 10
5.00E-02 0 10 10
Scott et al., 1987.


Table 4.6: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 1.63 0.94 12 3.84
0.333
21.03
1
Beta Poisson 0.69 11 19.68
1
Exponential is best fitting model
Table 4.7 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 5.70E-11 2.30E-11 2.91E-11 3.31E-11 1.38E-10 1.56E-10 2.13E-10
LD50 1.22E+10 3.25E+9 4.45E+9 5.02E+9 2.09E+10 2.36E+10 3.02E+10


Figure 4.3 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 4.4 Exponential model plot, with confidence bounds around optimized model




Summary

Noting an apparent difference of LD50 between the experiment 1 (4.93x108) and experiment 2 (1.22 x1010) routes has been identified. This may reflect the difference of susceptibilities associated with different host and pathogen strains.



References

Scott, G. and J. C. Williams (1987). "Pathological responses of inbred mice to phase I Coxiella Burnetii." Journal of General Microbiology 133(3): 691–700.

Tamrakar, S. B., A. Haluska, C. N. Haas and T. A. Bartrand (2011). "Dose-Response Model of Coxiella burnetii (Q Fever)." Risk Analysis 31(1): 120-128.

Williams, J. C. and J. L. Cantrell (1982). "Biological and immunological properties of Coxiella burnetii vaccines in C57BL/1OScN endotoxin-nonresponder mice." Infection and Immunity 35(3): 1091–1102.