Salmonella anatum
Author: Sushil Tamrakar
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General overview of Salmonella and Salmonellosis
Salmonella, a genus of rodshaped, Gramnegative, nonspore forming, and predominantly motile enterobacteria, causes more than 10^{4} cases of infections per year in United States. Salmonellosis is an important medical problem, as while infection with nontyphi Salmonella often causes mild selflimited 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; in these developing countries food handlers may be a reservoir for further transmission of infection (Chalker and Blaser 1988).
Salmonella anatum is a common cause of salmonellosis, an important infectious disease in humans and animals (Hartmann and West 1995). Unpasteurized fruit juices have been associated with outbreaks of gastrointestinal diseases caused by infection with Salmonella anatum (Krause, Terzagian et al. 2001).
Summary Data
McCullough, N. B. and C. W. Elsele (1951) inoculated human volunteers orally with the Salmonella anatum strain I,II and III.
Experiment serial number 
Reference 
Host type 
Agent strain 
Route 
# of doses 
Dose units 
Response 
Best fit model 
Optimized parameter(s) 
LD_{50}/ID_{50}

232, 233* 
^{[1]} 
human 
strain I 
oral, with eggnog 
16 
organisms 
positive stool culture 
betaPoisson 
α= 3.18E01 , N_{50} = 3.71E+04 
3.71E+04

232 
^{[1]} 
human 
strain I 
oral, with eggnog 
8 
organisms 
positive stool culture 
betaPoisson 
α = 2.91E01 , N_{50} = 4.44E+04 
4.44E+04

233 
^{[1]} 
human 
strain II 
oral, with eggnog 
8 
organisms 
positive stool culture 
betaPoisson 
α = 2.3E01 , N_{50} = 4.91E+03 
4.91E+03

*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.


a:
Optimization Output for experiment 232, 233
Human/ Salmonella anatum strain I & II pooled data ^{[1]}
Dose 
Positive stool culture 
Not 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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

138

119

15

3.84 0

25 0

Beta Poisson

18.9

14

23.7 0.168

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

3.18E01

1.35E01 
1.71E01 
1.92E01 
5.70E01 
6.66E01 
9.56E01

N_{50}

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
Optimization Output for experiment 232
Human / Salmonella anatum strain I data ^{[1]}
Dose 
Positive stool culture 
Not 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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

20.5

11

7

3.84 0.000922

14.1 0.00457

Beta Poisson

9.53

6

12.6 0.146

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

2.91E01

9.77E04 
9.77E04 
4.11E02 
1.68E+00 
5.36E+00 
1.20E+03

N_{50}

4.44E+04

6.74E02 
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
Optimization Output for experiment 233
Human/ Salmonella anatum strain II data ^{[1]}
Dose 
Positive stool culture 
Not 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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

62.8

54.2

7

3.84 1.84e13

14.1 4.22e11

Beta Poisson

8.6

6

12.6 0.198

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

2.3E01

3.63E02 
5.29E02 
6.00E02 
5.51E01 
6.70E01 
1.40E+00

N_{50}

4.91E+03

2.59E10 
2.73E08 
4.91E06 
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
Summary
The data set of Salmonella anatum strain III has only two points of response, hence it was not analyzed. As the data sets of strain I and II could be pooled, the pooled model is recommended model.
References
 ↑ ^{1.0} ^{1.1} ^{1.2} ^{1.3} ^{1.4} ^{1.5} McCullough, N. B. and C. W. Elsele (1951). "Experimental Human Salmonellosis: I. Pathogenicity of Strains of Salmonella meleagridis and Salmonella anatum Obtained from SprayDried Whole Egg." The Journal of Infectious Diseases 88(3): 278289.
Hartmann, F. A. and S. E. West (1995). "Antimicrobial susceptibility profiles of multidrugresistant Salmonella anatum isolated from horses." Journal of Veterinary Diagnostic Investigation 7: 159162.
Krause, G., R. Terzagian, et al. (2001). "Outbreak of Salmonella Serotype Anatum Infection Associated With Unpasteurized Orange Juice." Southern Medical Journal 94(12): 1168&hyhen;1172.
McCullough, N. B. and C. W. Elsele (1951). "Experimental Human Salmonellosis: I. Pathogenicity of Strains of Salmonella meleagridis and Salmonella anatum Obtained from SprayDried Whole Egg." The Journal of Infectious Diseases 88(3): 278289.