Rickettsia rickettsi: Dose Response Models

Rickettsia rickettsii

(Rocky Mountain spotted Fever) Authors: Mark H. Weir and Sushil Tamrakar

Overview: Rickettsia rickettsi and Spotted Fever

Rocky Mountain spotted fever is a disease endemic to North America is caused by Rickettsia rickettsi. The bacterium is delivered to the victim by a tick bite, and is the most lethal disease of all Rickettsial illnesses, especially in the United States. While the main vector for the disease is via an insect (most typically a tick), there has been evidence cited in Saslaw and Carlisle (1966) that aerosol dissemination and infection can be possible as well. This form of exposure to the bacterium can still develop into the lethal form of the disease, therefore, aerosol animal models were needed.

Typically rocky mountain spotted fever (RMSF) can be a misnomer, as the disease neither originated from this area of America and Canada, nor is it isolated to just this region or these countries. As the bacterium has been known to cause RMSF in south and central America as well. RMSF presents with sudden onset of flu-like symptoms, followed by the onset of a spotty rash, similar to pox, yet not raised above the skin as a pox is. Patients often require hospitalization from infection and can be fatal is not treated immediately and aggressively.

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Summary Data

Saslaw and Carlisle in 1966 studied the aerosol infectivity of R. rickettsii in monkeys. Rhesus monkeys were challenged with aerosolized pathogens and morbidity as well as mortality was observed (Saslaw and Carlisle 1966). Dupont et al. carried out a study of R. rickettsii (Sheila Smith) in human volunteers via the intradermal route(Dupont, Hornick et al. 1973). Sammons et al. exposed Macaca mulatta (Rhesus monkey) to R. rickettsii (strain Sheila Smith) via different routes to find the changes in blood serum constituents(Sammons, Kenyon et al. 1976).

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50 300 and 301* Pooled data R1 and Sheila Smith NA 27 CFU morbidity beta-Poisson α= 7.77E-01 , N50 = 2.13E+01 2.13E+01 300 Rhesus monkeys R1 aerosol 24 CFU morbidity beta-Poisson α= 8.58E-01 , N50 = 1.88E+01 1.88E+01 301 Human Sheila Smith intradermal 3 CFU clinical signs beta-Poisson α= 6.75E-01 , N50 = 2.36E+01 2.36E+01 244 Rhesus monkey NA aerosol 24 CFU death beta-Poisson α= 1.45E-01 , N50 = 5.01E+01 5.01E+01 245 C57BL6 mice KHW intravenous 5 CFU infection exponential k = 3.18E-03 2.18E+02 *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 human exposed intradermally and aerosol exposed rhesus monkey is the recommended model. Intradermal route is the one of the natural routes of infection and aerosol route might be an accidental or intentional route. Moreover, the experiment 301 was conducted with human volunteers.

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Optimization Output for experiment 300 (Rickettsia rickettsi)

Rhesus monkey Data Dose MORBIDITY NOT MORBIDITY Total 25 1 3 4 66 2 0 2 83 2 0 2 99 2 0 2 182 7 0 7 1110 1 1 2 1770 2 0 2 2290 2 0 2 2590 2 0 2 3170 2 0 2 5060 7 0 7 5520 2 0 2 5650 2 0 2 5670 1 0 1 7460 2 0 2 9200 2 0 2 10800 2 0 2 16800 2 0 2 41000 2 0 2 45500 3 0 3 53200 2 0 2 55200 2 0 2 132000 2 0 2 149000 2 0 2

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 27.6 16.4 23 3.84 5.12e-05 35.2 0.232 Beta Poisson 11.2 22 33.9 0.972 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 8.58E-01 9.77E-04 9.77E-04 9.78E-04 5.70E+06 1.41E+08 1.62E+11 N50 1.88E+01 3.58E-01 1.81E+00 7.74E+00 1.02E+03 4.02E+03 3.71E+04

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 301 (Rickettsia rickettsi)

Human data( Rickettsia rickettsii) Dose CLINICAL SIGNS NOT CLINICAL SIGNS Total 13 2 4 6 126 6 1 7 1260 17 1 18

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 13.5 13.2 2 3.84 0.000277 5.99 0.00119 Beta Poisson 0.248 1 3.84 0.618 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 6.75E-01 1.17E-01 2.44E-01 3.31E-01 1.21E+03 3.74E+03 4.98E+03 N50 2.36E+01 2.56E-02 3.35E+00 7.30E+00 6.41E+01 8.91E+01 1.28E+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 300 and 3001 (Rickettsia rickettsi)

Pooled data (experiment no. 300 and 301) Dose MORBIDITY NOT MORBIDITY Total 13 2 4 6 25 1 3 4 66 2 0 2 83 2 0 2 99 2 0 2 126 6 1 7 182 7 0 7 1110 1 1 2 1260 17 1 18 1770 2 0 2 2290 2 0 2 2590 2 0 2 3170 2 0 2 5060 7 0 7 5520 2 0 2 5650 2 0 2 5670 1 0 1 7460 2 0 2 9200 2 0 2 10800 2 0 2 16800 2 0 2 41000 2 0 2 45500 3 0 3 53200 2 0 2 55200 2 0 2 132000 2 0 2 149000 2 0 2

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 42.2 30.5 26 3.84 3.41e-08 38.9 0.0235 Beta Poisson 11.7 25 37.7 0.989 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 7.77E-01 3.82E-01 4.41E-01 4.90E-01 4.24E+00 3.59E+03 3.25E+04 N50 2.13E+01 5.70E+00 8.34E+00 1.01E+01 4.00E+01 4.16E+01 5.10E+01

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 244 (Rickettsia rickettsi)

Rhesus monkey Data Dose Dead Survived Total 25 1 3 4 66 2 0 2 83 2 0 2 99 1 1 2 182 3 4 7 1111 1 1 2 1774 1 1 2 2287 1 1 2 2586 2 0 2 3166 1 1 2 5055 6 1 7 5519 2 0 2 5652 2 0 2 5669 1 0 1 7459 2 0 2 9199 1 1 2 10774 2 0 2 16790 1 1 2 41023 2 0 2 45498 1 2 3 53206 2 0 2 55195 2 0 2 131771 1 1 2 149175 2 0 2

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 137 113 23 3.84 0 35.2 0 Beta Poisson 24 22 33.9 0.345 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 1.45E-01 1.82E-02 2.72E-02 4.15E-02 2.59E-01 2.87E-01 3.49E-01 N50 5.01E+01 6.71E-12 6.31E-07 2.86E-03 2.62E+02 3.28E+02 4.87E+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 245

C57BL/6 Mice KHW Strain Data Dose Infected Non-infected Total 5 0 3 3 45 1 5 6 450 6 2 8 4500 7 0 7 45000 7 0 7

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 0.155 0.0201 4 3.84 0.887 9.49 0.997 Beta Poisson 0.135 3 7.81 0.987 Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

Optimized k parameter for the exponential model, from 10000 bootstrap iterations Parameter MLE estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% k 3.18E-03 1.05E-03 1.41E-03 1.63E-03 7.50E-03 7.54E-03 1.46E-02 ID50/LD50/ETC* 2.18E+02 4.74E+01 9.19E+01 9.25E+01 4.25E+02 4.91E+02 6.63E+02 *Not a parameter of the exponential model; however, it facilitates comparison with other models.

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

References

Dupont HL, Hornick RB, Dawkins AT, Heiner GG, Fabrikan.Ib, Wisseman CL and Woodward TE (1973) Rocky Mountain Spotted Fever - Comparative Study of  Active  Immunity Induced by Inactivated and Viable Pathogenic Rickettsia ricketsii. Journal of Infectious Diseases 128(3), 340-344.

Saslaw S and Carlisle HN (1966) Aerosol infection of monkeys with Rickettsia rickettsii. Bacteriological Reviews 30(3), 636-645.

Sammons LS, Kenyon RH and Pedersen CE (1976) Effect of vaccination schedule on immune response of Macaca mulatta to cell culture-grown Rocky Mountain spotted fever vaccine. Journal of Clinical Microbiology 4(3), 253-257.