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General Overview

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.

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

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
262 3 sub sp. Paratuberculosis Bovine CFU deer exponential
k = 6.93E-04
LD50/ID50 = 1000

infection Nisbet, D. I., N. J. Gilmour, and J. G. Brotherston. "Quantitative studies of Mycobacterium johnei in tissues of sheep. III. Intestinal histopathology." Journal of comparative pathology. 72 (1962): 80.
263 3 sub sp. Paratuberculosis IOI strain CFU cheviots beta-Poisson a = 5.79E-02

LD50/ID50 = 4.8E+02
N50 = 4.8E+02
infection Badenoch, P. R., et al. "Pathogenicity of Acanthamoeba and a Corynebacterium in the Rat Cornea." Archives of Ophthalmology. 108 (1990): 1.
Best Fit
Experiment ID:
262
# of Doses:
3
Agent Strain:
sub sp. Paratuberculosis Bovine
Dose Units:
CFU
Host type:
deer
Μodel:
exponential
Optimized parameters:
k = 6.93E-04
LD50/ID50 = 1000

Reference:
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

Experiment ID:
263
# of Doses:
3
Agent Strain:
sub sp. Paratuberculosis IOI strain
Dose Units:
CFU
Host type:
cheviots
Μodel:
beta-Poisson
Optimized parameters: a = 5.79E-02

LD50/ID50 = 4.8E+02
N50 = 4.8E+02
Reference:
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