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General Overview

Salmonella, a genus of rod-shaped, gram-negative, non-spore forming, and predominantly motile enterobacteria, causes more than 104 cases of infections per year in United States. Salmonellosis is an important medical problem, as well as infection with non-typhi Salmonella which often causes mild self-limited illness, Severe sequelae including death may occur, particularly in immunocompromised hosts. It has been reported that the incidence of salmonellosis is higher in developing countries, where food handlers may be a reservoir for further transmission of infection. [1]

Salmonella anatum is a common cause of salmonellosis, an important infectious disease in humans and animals. [2] Additionally, unpasteurized fruit juices have been associated with outbreaks of gastrointestinal diseases caused by infection with Salmonella anatum [3]

Summary Data

McCullough, N. B. and C. W. Elsele (1951) inoculated human volunteers orally with the Salmonella anatum strain I,II and III.[4]

Recommended Model

The pooled model of experiment number 232 and 233 is the recommended model as more data points in the model result into improvement in fits.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
232 8 strain I CFU human beta-Poisson a = 2.91E-01

LD50/ID50 = 4.44E+04
N50 = 4.44E+04
positive stool culture 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.
232, 233 16 strain I CFU human beta-Poisson a = 3.18E-01

LD50/ID50 = 3.71E+04
N50 = 3.71E+04
positive stool culture McCullough, Norman B., and Wesley C Elsele. "Experimental human salmonellosis: I. Pathogenicity of strains of Salmonella meleagridis and Salmonella anatum obtained from spray-dried whole egg." The Journal of infectious diseases (1951): 278-289.
233 8 strain II CFU human beta-Poisson a = 2.3E-01

LD50/ID50 = 4.91E+03
N50 = 4.91E+03
positive stool culture 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.
Experiment ID:
232
# of Doses:
8
Agent Strain:
strain I
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 2.91E-01

LD50/ID50 = 4.44E+04
N50 = 4.44E+04
Reference:
Human / Salmonella anatum strain I data [4]
Dose Positive stool culture No positive stool culture Total
12000 2 3 5
24000 3 3 6
66000 4 2 6
93000 1 5 6
141000 3 3 6
256000 5 1 6
587000 4 2 6
860000 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 20.5 11 7 3.84 
0.000922
14.1 
0.00457
Beta Poisson 9.53 6 12.6 
0.146
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 2.91E-01 9.77E-04 9.77E-04 4.11E-02 1.68E+00 5.36E+00 1.20E+03
N50 4.44E+04 6.74E-02 8.03E+02 4.15E+03 1.64E+05 6.89E+06 9.07E+07

 

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

Best Fit
Experiment ID:
232, 233
# of Doses:
16
Agent Strain:
strain I
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 3.18E-01

LD50/ID50 = 3.71E+04
N50 = 3.71E+04
Reference:
Human/ Salmonella anatum strain I & II pooled data [4]
Dose Positive stool culture No positive stool culture Total
12000 2 3 5
24000 3 3 6
66000 4 2 6
89000 5 1 6
93000 1 5 6
141000 3 3 6
256000 5 1 6
448000 4 2 6
587000 4 2 6
860000 6 0 6
1040000 6 0 6
3.9E+06 4 2 6
1E+07 6 0 6
2.39E+07 5 1 6
4.45E+07 6 0 6
6.73E+07 8 0 8

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 138 119 15 3.84 
0
25 
0
Beta Poisson 18.9 14 23.7 
0.168
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 3.18E-01 1.35E-01 1.71E-01 1.92E-01 5.70E-01 6.66E-01 9.56E-01
N50 3.71E+04 1.40E+03 5.50E+03 8.86E+03 8.82E+04 1.00E+05 1.30E+05

 

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:
233
# of Doses:
8
Agent Strain:
strain II
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 2.3E-01

LD50/ID50 = 4.91E+03
N50 = 4.91E+03
Reference:
Human/ Salmonella anatum strain II data [4]
Dose Positive stool culture No positive stool culture Total
89000 5 1 6
448000 4 2 6
1040000 6 0 6
3.9E+06 4 2 6
1E+07 6 0 6
2.39E+07 5 1 6
4.45E+07 6 0 6
6.73E+07 8 0 8

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 62.8 54.2 7 3.84 
1.84e-13
14.1 
4.22e-11
Beta Poisson 8.6 6 12.6 
0.198
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 2.3E-01 3.63E-02 5.29E-02 6.00E-02 5.51E-01 6.70E-01 1.40E+00
N50 4.91E+03 2.59E-10 2.73E-08 4.91E-06 8.72E+04 1.23E+05 2.29E+05

 

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