Mycobacterium avium: Dose Response Models

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Mycobacterium avium

Author: Sushil Tamrakar


General overview of Mycobacterium avium

Mycobacterium avium subsp. paratuberculosis (MAP) is an obligate pathogenic bacterium of the genus Mycobacterium which causes chronic inflammation of the intestine in domestic and wild ruminants as well as other animals, including primates. M. avium subsp.paratuberculosis can live in animals for years without necessarily causing clinical disease. Infection is widespread in domestic livestock in Europe and North America but can occur elsewhere. [1]



Summary Data

O’Brien et al.(1976) [2] exposed three groups of newly weaned 4-month-old red deer orally with M. avium subsp. paratuberculosis Bovine strain and necropsy was conducted 44 weeks post inoculation to determine the infection rate.

Brotherston et al. (1976)[3] inoculated South Country Cheviots at the age of three weeks orally with M. avium subsp. paratuberculosis IOI strain which was originally recovered from a clinical case of the disease in a sheep and VB/4 strain from an affected cow. The necropsy was done 1-9 months post inoculation.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
262* [2] deer sub sp. Paratuberculosis Bovine oral 3 CFU infection exponential k = 6.93E-04 1E+03
263 [3] cheviots sub sp. Paratuberculosis IOI strain oral 3 CFU infection beta-Poisson α = 5.79E-02 , N50 = 4.8E+02 4.8E+02
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.


*Recommended Model

Experiment number 262 model is the recommended model. The ID50 of the model has lower value than the other model.


Exponential and betapoisson model.jpg

Optimization Output for experiment 262

Dose response data [2]
Dose Infected Non-infected Total
1000 8 8 16
1E+07 16 0 16
1E+09 16 0 16


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 3.07e-05 7.15e-06 2 3.84
0.998
5.99
1
Beta Poisson 2.36e-05 1 3.84
0.996
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
0.5% 2.5% 5% 95% 97.5% 99.5%
k 6.93E-04 2.08E-04 2.88E-04 3.75E-04 1.16E-03 1.39E-03 1.67E-03
ID50/LD50/ETC* 1E+03 4.14E+02 5.00E+02 5.96E+02 1.85E+03 2.41E+03 3.34E+03
*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

Optimization Output for experiment 263

Dose response data [3]
Dose Infected Non-infected Total
100 6 6 12
1E+05 6 6 12
1E+08 10 2 12


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 193 192 2 3.84
0
5.99
0
Beta Poisson 1.43 1 3.84
0.231
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
0.5% 2.5% 5% 95% 97.5% 99.5%
α 5.79E-02 9.94E-04 9.78E-03 1.25E-02 1.27E-01 1.42E-01 1.87E-01
N50 4.8E+02 3.44E-13 5.25E-08 1.89E-05 5.61E+04 1.50E+05 4.41E+06


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

  1. [Ayele WY, Svastova P, et al. (2005) Mycobacterium avium Subspecies paratuberculosis Cultured from Locally and Commercially Pasteurized Cow's Milk in the Czech Republic. Applied and Environmental Microbiology 71(3): 1210-1214. Ayele]
  2. 2.0 2.1 2.2 O’Brien R, Mackintosh CG, Bakker D, Kopecna M, Pavlik I, Griffin JF, (2006) Immunological and molecular characterization of susceptibility in relationship to bacterial strain differences in Mycobacterium avium subsp. paratuberculosis infection in the red deer (Cervus elaphus). Infection and Immunity 74, 3530–3537. Full Text Cite error: Invalid <ref> tag; name "O.27Brien_et_al.281976.29" defined multiple times with different content Cite error: Invalid <ref> tag; name "O.27Brien_et_al.281976.29" defined multiple times with different content
  3. 3.0 3.1 3.2 Brotherston JG, Gilmour NJ, Samuel J, 1961. Quantitative studies of Mycobacterium johnei in the tissues of sheep. Journal of Comparative Pathology 71, 286–299. Full Text Cite error: Invalid <ref> tag; name "Brotherston_et_al_.281976.29" defined multiple times with different content Cite error: Invalid <ref> tag; name "Brotherston_et_al_.281976.29" defined multiple times with different content