Salmonella Typhi: Dose Response Models

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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 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).



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 beta-Poisson model is superior to the exponential model for all datasets. Although the pooled model fails the goodness-of-fit 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) LD50/ID50
79, 80* [1][2] human Quailes oral, in milk 8 CFU disease beta-Poisson α = 1.75E-01 , N50 = 1.11E+06 1.11E+06
79 [1] human Quailes oral, in milk 3 CFU disease beta-Poisson α = 1.11E-01 , N50 = 3.45E+06 3.45E+06"
80 [2] human Quailes oral, in milk 5 CFU disease beta-Poisson α = 2.03E-01 , N50 = 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.


Exponential and betapoisson model.jpg

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
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


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
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


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
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



References

  1. 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.361-367.
  2. 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.686-691. Abstract

Miliotis MD, Bier J eds, 2003 International Handbook of Foodborne Pathogens, New York: M. Dekker.

Crump JA, Mintz ED, 2010 Global trends in typhoid and paratyphoid Fever. Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 50(2), pp.241-246. Full text