Mycobacterium avium: Dose Response Models

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.

---

Summary Data

O’Brien et al.(1976) 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) 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* deer sub sp. Paratuberculosis Bovine oral 3 CFU infection exponential k = 6.93E-04 1E+03 263 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.

---

Optimization Output for experiment 262

Dose response data 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 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

Summary

Bovine strain is the most common strain of M.avium.

---

References

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.

Brotherston JG, Gilmour NJ, Samuel J, 1961. Quantitative studies of Mycobacterium johnei in the tissues of sheep. Journal of Comparative Pathology 71, 286–299.

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.

Ryan KJ and Ray CG (2010) Sherris Medical Microbiology, The McGraw-Hill Companies.