Typhoid Salmonella
Kyle S. Enger, MPH
Overview
Salmonella enterica, serovar Typhi (S. Typhi for short, but formerly known as Salmonella typhi or Salmonella typhosa) causes typhoid fever (Crump and Mintz 2010). Paratyphoid fever is a similar syndrome (but less common and less severe than typhoid fever) caused by Salmonella enterica, serovar Typhi (S. Paratyphi) (Miliotis and Bier 2003). Typhoid and paratyphoid fevers are also jointly known as enteric fever (Crump and Mintz 2010). Other Salmonella enterica serovars (e.g., Enteritidis, Typhimurium) cause a gastroenteritis known as salmonellosis (Miliotis and Bier 2003).
S. Typhi and S. Paratyphi only infect humans and are transmitted by the fecaloral 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).
Summary of data
There have been two feeding studies (Hornick et al. 1966, Hornick et al. 1970) in male prisoners of the Quailes strain of S. Typhi (which was named Salmonella typhosa at that time). Data from these two studies can be pooled (P > 0.05), and the betaPoisson model is superior to the exponential model for all datasets. Although the pooled model fails the goodnessoffit test, it does not fail by much (P = 0.032), and therefore it is the preferred model.
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.
Experiment serial number 
Reference 
Host type 
Agent strain 
Route 
# of doses 
Dose units 
Response 
Best fit model 
Optimized parameter(s) 
LD_{50}/ID_{50}

79, 80* 
^{[1]}^{[2]} 
human 
Quailes 
oral, in milk 
8 
CFU 
disease 
betaPoisson 
α = 1.75E01 , N_{50} = 1.11E+06 
1.11E+06

79 
^{[1]} 
human 
Quailes 
oral, in milk 
3 
CFU 
disease 
betaPoisson 
α = 1.11E01 , N_{50} = 3.45E+06 
3.45E+06"

80 
^{[2]} 
human 
Quailes 
oral, in milk 
5 
CFU 
disease 
betaPoisson 
α = 2.03E01 , N_{50} = 8.53E+05 
8.53E+05

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


Optimization Output for experiment 79, 80
Model data for S. Typhi (Quailes) in humans ^{[1]}^{[2]}
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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

419

406

7

3.84 0

14.1 0

Beta Poisson

13.8

6

12.6 0.0321

Neither the exponential nor betaPoisson fits well; betaPoisson is less bad.


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

1.75E01

1.21E01 
1.32E01 
1.39E01 
2.23E01 
2.34E01 
2.58E01

N_{50}

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
Optimization Output for experiment 79
Model data for S. Typhi (Quailes) in humans ^{[1]}
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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

124

121

2

3.84 0

5.99 0

Beta Poisson

2.87

1

3.84 0.0905

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

1.11E01

3.19E02 
4.80E02 
5.49E02 
1.96E01 
2.17E01 
2.59E01

N_{50}

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
Optimization Output for experiment 80
Model data for S. Typhi (Quailes) in humans ^{[2]}
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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

293

284

4

3.84 0

9.49 0

Beta Poisson

8.63

3

7.81 0.0346

Neither the exponential nor betaPoisson fits well; betaPoisson is less bad.


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

2.03E01

1.33E01 
1.49E01 
1.57E01 
2.74E01 
2.89E01 
3.27E01

N_{50}

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
References
 ↑ ^{1.0} ^{1.1} ^{1.2} ^{1.3} Hornick, R.B. et al., 1966. Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness. Transactions of the Association of American Physicians, 79, pp.361367.
 ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} Hornick, R.B. et al., 1970. Typhoid fever: pathogenesis and immunologic control. The New England Journal of Medicine, 283(13), pp.686691. Abstract
Miliotis, M.D. & Bier, J. eds., 2003. International Handbook of Foodborne Pathogens, New York: M. Dekker.
Crump, J.A. & Mintz, E.D., 2010. Global trends in typhoid and paratyphoid Fever. Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 50(2), pp.241246. Full text