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General Overview

Salmonella, a genus of rod-shaped, gram-negative, non-spore forming, predominantly motile enterobacteria, causes more than 104 cases of infections per year in United States. (Chalker and Blaser 1988). Non-typhoidal salmonellae are important causes of many foodborne infections. Approximately 45,000 cases and 600 deaths have been reported annually to the Centers for Disease Control in the past decade. Salmonellae have a wide range of hosts and are strongly associated with agricultural products (Acheson and Hohmann 2001).

http://wwwnc.cdc.gov/eid/article/10/1/pdfs/03-0171.pdf

Summary Data

Meynell G.G. and Meynell E.W. (1958) inoculated albino (PGMS) mice intraperitoneally with the Salmonella typhimurium strains 216 and 219 and challenged albino (Tuck) mice with Salmonella typhimurium strain 533 via the intraperitoneal route. [1]

Recommended Model

Experiment number 246 is recommended model based on the least LD50 value. Although the strains were different and so the virulences, the estimated risk should be in conservative side.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
246 10 strain 216 and 219 CFU mice beta-Poisson a = 2.1E-01

LD50/ID50 = 4.98E+01
N50 = 4.98E+01
death Meynell, G. G., and E. W. Meynell. "The growth of micro-organisms in vivo with particular reference to the relation between dose and latent period." Epidemiology & Infection. 56 (1958).
247 11 strain 533 CFU mice beta-Poisson a = 6.21E-02

LD50/ID50 = 3.46E+07
N50 = 3.46E+07
death Meynell, G. G., and E. W. Meynell. "The growth of micro-organisms in vivo with particular reference to the relation between dose and latent period." Epidemiology & Infection. 56 (1958).
248 7 strain 533 CFU mice beta-Poisson a = 1.08E-01

LD50/ID50 = 9.66E+06
N50 = 9.66E+06
death Hornick, R. B., et al. "The Broad Street pump revisited: response of volunteers to ingested cholera vibrios." Bulletin of the New York Academy of Medicine. 47 (1971): 10.
Best Fit
Experiment ID:
246
# of Doses:
10
Agent Strain:
strain 216 and 219
Dose Units:
CFU
Host type:
mice
Μodel:
beta-Poisson
Optimized parameters: a = 2.1E-01

LD50/ID50 = 4.98E+01
N50 = 4.98E+01
Reference:
Mice/Salmonella strain 216 and 219 data [1]
Dose Dead Survived Total
5 7 8 15
25 4 11 15
125 7 8 15
630 9 6 15
3160 8 7 15
16000 13 2 15
8E+04 15 0 15
4E+05 15 0 15
2E+06 15 0 15
1E+07 15 0 15

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 133 113 9 3.84 
0
16.9 
0
Beta Poisson 20.5 8 15.5 
0.00846
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 2.1E-01 1.45E-01 1.58E-01 1.65E-01 2.92E-01 3.14E-01 3.63E-01
N50 4.98E+01 8.10E+00 1.40E+01 1.72E+01 1.31E+02 1.62E+02 2.34E+02

 

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:
247
# of Doses:
11
Agent Strain:
strain 533
Dose Units:
CFU
Host type:
mice
Μodel:
beta-Poisson
Optimized parameters: a = 6.21E-02

LD50/ID50 = 3.46E+07
N50 = 3.46E+07
Reference:
Mice/ Salmonella strain 533 data [1]
Dose Dead Survived Total
603 6 36 42
1910 3 39 42
6030 7 35 42
19100 5 42 47
60300 6 34 40
191000 3 29 32
603000 6 20 26
1910000 7 7 14
6030000 7 5 12
1.91E+07 10 2 12
6.03E+07 13 0 13

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 193 146 10 3.84 
0
18.3 
0
Beta Poisson 47.5 9 16.9 
3.22e-07
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 6.21E-02 3.53E-02 4.06E-02 4.32E-02 1.09E-01 1.25E-01 1.80E-01
N50 3.46E+07 9.76E+05 1.69E+06 2.40E+06 9.41E+08 2.13E+09 1.34E+10

 

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:
248
# of Doses:
7
Agent Strain:
strain 533
Dose Units:
CFU
Host type:
mice
Μodel:
beta-Poisson
Optimized parameters: a = 1.08E-01

LD50/ID50 = 9.66E+06
N50 = 9.66E+06
Reference:
Mice/ Salmonella strain 533 data [1]
Dose Dead Survived Total
1E+04 20 180 200
1E+05 17 153 170
1E+06 11 29 40
3160000 6 24 30
1E+07 12 8 20
3.16E+07 17 3 20
1E+08 19 1 20

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 214 165 6 3.84 
0
12.6 
0
Beta Poisson 48.7 5 11.1 
2.56e-09
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 1.08E-01 6.19E-02 7.06E-02 7.52E-02 1.79E-01 1.98E-01 2.44E-01
N50 9.66E+06 1.93E+06 2.43E+06 2.82E+06 5.38E+07 8.11E+07 2.13E+08

 

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