Salmonella nontyphoid: Dose Response Models

Salmonella nontyphoid

Author: Yin Huang

General overview of Salmonella and Salmonellosis

Salmonella, a genus of rod-shaped, gram-negative, non-spore forming, predominantly motile enterobacteria, cause more than 10⁴ cases of infections per year in United States. Salmonellosis is an important medical problem. Infection with non-typhi Salmonella often causes mild self-limited illness; however, severe sequelae including death may occur, particularly in immunocompromised hosts. The incidence of salmonellosis is higher in developing than in developed countries and in developing countries food handlers may be a reservoir for further transmission of infection

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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.

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50 246* mice strain 216 and 219 intraperitoneal 10 CFU death beta-Poisson α= 2.1E-01 , N50 = 4.98E+01 4.98E+01 247 mice strain 533 intraperitoneal 11 CFU death beta-Poisson α = 6.21E-02 , N50 = 3.46E+07 3.46E+07 248 mice strain 533 intraperitoneal 7 CFU death beta-Poisson α= 1.08E-01 , N50 = 9.66E+06 9.66E+06 *This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

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Optimization Output for experiment 246

Mice/Salmonella strain 216 and 219 data 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

Optimization Output for experiment 247

Mice/ Salmonella strain 533 data 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

Optimization Output for experiment 248

Mice/ Salmonella strain 533 data 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

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Summary

Noting the very different LD₅₀ for different strains of host and pathogen, substantial variation of susceptibility is manifestly presented. Inconsistencies in the dose response pattern have been identified in the low-dose groups for all three experiments. The failure to successfully pool data from experiment 247 and 248 might be due to this variation and experimental errors. The mechanism behind this low dose variation is suggested for futher study.

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