General Overview 

Salmonella is a genus of rod-shaped, gram-negative, non-spore forming, predominantly motile enterobacteria (Chalker and Blaser 1988). Many species of Salmonella have been isolated from eggs and egg products (McCullough and Eisele 1951). Salmonella meleagridis is one of the most common serotype of Salmonella (Zaidi, McDermott et al. 2006). Twenty human isolates of S. meleagridis had been identified in Canada so far during 1997.

http://www.cdc.gov/salmonella/

Summary Data

McCullough, and Eisele (1951) inoculated human volunteers orally with the S. Meleagridis strain I,II and III.[1]

Recommended Model

Eexperiment number 238 is the recommended one as the strain I was more virulent than strain III.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
238 11 strain I CFU human beta-Poisson a = 3.89E-01

LD50/ID50 = 1.68E+04
N50 = 1.68E+04
infection McCullough, N. B., and C. W. Elsele. "Experimental Human Salmonellosis: I." Pathogenicity of Strains of Salmonella meleagridis and Salmonella anatum Obtained from Spray-Dried Whole Egg. 88 (1951): 3.
240 4 strain III CFU human beta-Poisson a = 8.85E-01

LD50/ID50 = 5.24E+05
N50 = 5.24E+05
infection Muller, D., M. L. Edwards, and D. W. Smith. "Changes in Iron and Transferrin Levels and Body Temperature in Experimental Airborne Legionellosis." The Journal of Infectious Diseases. 147 (1983): 2.
Best Fit
Experiment ID:
238
# of Doses:
11
Agent Strain:
strain I
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 3.89E-01

LD50/ID50 = 1.68E+04
N50 = 1.68E+04
Reference:
Human / S. meleagridis strain I data [1]
Dose Infected Non-infected Total
12000 3 3 6
24000 4 2 6
52000 3 3 6
96000 3 3 6
155000 5 1 6
3E+05 6 0 6
720000 4 1 5
1150000 6 0 6
5.5E+06 5 1 6
2.4E+07 5 0 5
5E+07 6 0 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 71.8 63.8 10 3.84 
1.33e-15
18.3 
1.98e-11
Beta Poisson 7.99 9 16.9 
0.535
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 3.89E-01 1.23E-01 1.74E-01 2.01E-01 1.12E+00 1.91E+00 3.82E+02
N50 1.68E+04 7.98E+01 1.08E+03 2.27E+03 4.78E+04 5.71E+04 7.49E+04

 

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

Experiment ID:
240
# of Doses:
4
Agent Strain:
strain III
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 8.85E-01

LD50/ID50 = 5.24E+05
N50 = 5.24E+05
Reference:
Human/ S. meleagridis strain III data [1]
Dose Infected Non-infected Total
158000 1 5 6
1.5E+06 5 1 6
7680000 6 0 6
1E+07 5 1 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 7.81 5.51 3 3.84 
0.019
7.81 
0.0501
Beta Poisson 2.3 2 5.99 
0.316
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 8.85E-01 1.78E-01 2.91E-01 3.68E-01 1.40E+03 1.71E+03 8.24E+03
N50 5.24E+05 4.71E+04 1.20E+05 1.92E+05 1.19E+06 1.39E+06 1.90E+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