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General Overview

Salmonella enterica, serovar Typhi (S. Typhi for short, but formerly known as Salmonella typhi or Salmonella typhosa) causes typhoid fever.[1] Paratyphoid fever is a similar syndrome (but less common and less severe than typhoid fever) caused by Salmonella enterica, serovar Typhi (S. Paratyphi).[2] Typhoid and paratyphoid fevers are also jointly known as enteric fever.[1] Other Salmonella enterica serovars (e.g., Enteritidis, Typhimurium) cause a gastroenteritis known as salmonellosis. [2]

S. Typhi and S. Paratyphi only infect humans and are transmitted by the fecal-oral route (Miliotis and Bier 2003). Disease may include any combination of the following: cough, constipation, diarrhea, abdominal pain, anorexia, rose spots on the torso, or fever (Miliotis and Bier 2003). S. Typhi may also be shed asymptomatically for years in the feces of chronic carriers (Miliotis and Bier 2003).

http://www.cdc.gov/nczved/divisions/dfbmd/diseases/typhoid_fever/

Summary of data

There have been two feeding studies[3][4] in male prisoners of the Quailes strain of S. Typhi (which was named Salmonella typhosa at that time).

Other model fits to these data have been published (Haas, Rose, and Gerba 1999). However, these model fits exclude some of the experimental data for unclear reasons.

Recommended Model

The pooled model of experiment number 79 and 80 is the recommended model. Pooling is statistically accepted and it gives improvement in fits.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
79 3 Quailes CFU human beta-Poisson a = 1.11E-01

LD50/ID50 = 3.45E+06"
N50 = 3.45E+06
disease Hornick, R. B., et al. "Typhoid fever: pathogenesis and immunologic control." The New England journal of medicine. 283 (1970): 13.
79, 80 8 Quailes CFU human beta-Poisson a = 1.75E-01

LD50/ID50 = 1.11E+06
N50 = 1.11E+06
disease Hornick, R. B. al.. "Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness." Transactions of the Association of American Physicians. 79 (1966): 361-367.
80 5 Quailes CFU human beta-Poisson a = 2.03E-01

LD50/ID50 = 8.53E+05
N50 = 8.53E+05
disease Levine, M. M., et al. "Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery." Journal of Infectious Diseases. 127 (1973): 3.
Experiment ID:
79
# of Doses:
3
Agent Strain:
Quailes
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.11E-01

LD50/ID50 = 3.45E+06"
N50 = 3.45E+06
Reference:
Model data for S. Typhi (Quailes) in humans [3]
Dose Disease No disease Total
1E+05 28 76 104
1E+07 15 15 30
1E+09 4 0 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 124 121 2 3.84 
0
5.99 
0
Beta Poisson 2.87 1 3.84 
0.0905
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 1.11E-01 3.19E-02 4.80E-02 5.49E-02 1.96E-01 2.17E-01 2.59E-01
N50 3.45E+06 4.81E+05 6.95E+05 8.50E+05 9.53E+07 2.24E+08 4.19E+09

 

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:
79, 80
# of Doses:
8
Agent Strain:
Quailes
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.75E-01

LD50/ID50 = 1.11E+06
N50 = 1.11E+06
Reference:
Model data for S. Typhi (Quailes) in humans [3][4]
Dose Disease No disease Total
1000 0 14 14
1E+05 28 76 104
1E+05 32 84 116
1E+07 15 15 30
1E+07 16 16 32
1E+08 8 1 9
1E+09 4 0 4
1E+09 40 2 42

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 419 406 7 3.84 
0
14.1 
0
Beta Poisson 13.8 6 12.6 
0.0321
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 1.75E-01 1.21E-01 1.32E-01 1.39E-01 2.23E-01 2.34E-01 2.58E-01
N50 1.11E+06 5.13E+05 6.10E+05 6.72E+05 2.00E+06 2.28E+06 2.95E+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

Experiment ID:
80
# of Doses:
5
Agent Strain:
Quailes
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 2.03E-01

LD50/ID50 = 8.53E+05
N50 = 8.53E+05
Reference:
Model data for S. Typhi (Quailes) in humans [4]
Dose Disease No disease Total
1000 0 14 14
1E+05 32 84 116
1E+07 16 16 32
1E+08 8 1 9
1E+09 40 2 42

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 293 284 4 3.84 
0
9.49 
0
Beta Poisson 8.63 3 7.81 
0.0346
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 2.03E-01 1.33E-01 1.49E-01 1.57E-01 2.74E-01 2.89E-01 3.27E-01
N50 8.53E+05 3.38E+05 4.28E+05 4.80E+05 1.62E+06 1.85E+06 2.49E+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