Salmonella Typhi: Dose Response Models

Typhoid Salmonella

Kyle S. Enger

Overview

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

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 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.

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50 79, 80* human Quailes oral, in milk 8 CFU disease beta-Poisson α = 1.75E-01 , N50 = 1.11E+06 1.11E+06 79 human Quailes oral, in milk 3 CFU disease beta-Poisson α = 1.11E-01 , N50 = 3.45E+06 3.45E+06" 80 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.

^*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.

---

Optimization Output for experiment 79, 80 (Salmonella Typhi)

Model data for S. Typhi (Quailes) in humans 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 (Salmonella Typhi)

Model data for S. Typhi (Quailes) in humans 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 (Salmonella Typhi)

Model data for S. Typhi (Quailes) in humans 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

---