Legionella pneumophila: Dose Response Models

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Legionella pneumophila

Author: Mark H. Weir


General overview

'Legionella pneumophila (L. pneumophila) causes both Pontiac Fever and an aggressive form of pneumonia. L. pneumophila is a facultative gram negative aerobic rod, commonly found in drinking water distribution systems, cooling tower basin waters, premise plumbing, surface waters, and other engineered water systems.

Legionellosis includes Legionnaires’ disease and a milder febrile illness called Pontiac Fever. Legionnaires’ disease, an atypical pneumonia caused by bacteria of the genus Legionella, is most commonly caused illness by the species L. pneumophila (Lp). Legionnaires' disease has an incubation period commonly cited as of 2 to 10 days from exposure to the appearance of clinical symptoms, but the upper end of the incubation period may be at least 19 days. Symptoms of Legionnaires include: a high fever, chills, headache, muscular pains, dry cough, difficulty breathing and diarrhea, but not all symptoms occur in all in cases [1]



Summary Data

Muller et al. (1983)[2] exposed outbred, specific pathogen-free, Hartley strain Guinea pigs to aerosols of Legionella Philadelphia 1 strain in a modified aerosol in- fection chamber (Tri-R Instruments, Rockville Centre, N.Y.).

Fitzgeorge et al. (1983)[3] challenged Female Dunkin-Hartley Guinea-pigs with aerosols of Legionella pneumophila Strain 74/81.

Breiman and Horwitz (1987)[4] exposed Hartley strain Guinea pigs to aerosols of Legionella Philadelphia 1 strain in an aerosol chamber constructed of lucite measuring 13 X 24 X 18 in.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
241* [2] guinea pig Philadelphia 1 inhalation 4 CFU infection exponential k = 5.99E-02 1.16E+01
242 [3] mice strain 74/81 inhalation 4 CFU death exponential k = 6.48E-05 1.07E+04
243 [4] guinea pig Philadelphia 1 inhalation 5 CFU death exponential k = 4.17E-05 1.66E+04
242, 243 [3][4] mice strain 74/81 Inhalation 9 CFU death exponential k = 4.99E-05 1.39E+04
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

*Recommended Model

It is recommended that experiment 241 should be used as the best dose response model. Infection as the endpoint is more protective and useful for disease transmission modeling over other endpoints such as illness and death.

Exponential and betapoisson model.jpg



Optimization Output for experiment 241

Guinea pigs/ Philadelphia 1 strain data [2]
Dose Infected Non-infected Total
1 0 4 4
5 4 10 14
50 17 1 18
100 8 0 8


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 0.582 0.000479 3 3.84
0.983
7.81
0.9
Beta Poisson 0.582 2 5.99
0.748
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 5.99E-02 3.26E-02 3.90E-02 4.18E-02 1.11E-01 1.31E-01 1.57E-01
ID50/LD50/ETC* 1.16E+01 4.42E+00 5.28E+00 6.25E+00 1.66E+01 1.78E+01 2.13E+01
*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

Optimization Output for experiment 242

mice/ Strain 74/81 data [3]
Dose Dead Survived Total
200 0 10 10
4000 1 9 10
5E+04 12 0 12
4E+05 16 0 16


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 2.34 -0.00145 3 3.84
1
7.81
0.506
Beta Poisson 2.34 2 5.99
0.311
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 6.48E-05 5.45E-05 5.45E-05 5.45E-05 9.71E-05 9.71E-05 1.24E-04
ID50/LD50/ETC* 1.07E+04 5.57E+03 7.14E+03 7.14E+03 1.27E+04 1.27E+04 1.27E+04
*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


Optimization Output for experiment 243

Guinea pigs/ Philadelphia 1 Strain model data [4]
Dose Dead Survived Total
1E+04 1 4 5
15000 0 3 3
2E+04 5 2 7
5E+04 3 0 3
1E+05 5 0 5


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 5.85 -0.000131 4 3.84
1
9.49
0.211
Beta Poisson 5.85 3 7.81
0.119
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 4.17E-05 2.29E-05 2.68E-05 3.00E-05 5.87E-05 6.78E-05 7.86E-05
ID50/LD50/ETC* 1.66E+04 8.82E+03 1.02E+04 1.18E+04 2.31E+04 2.59E+04 3.03E+04
*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


Optimization Output for experiment 242, 243

Dose response data [3][4]
Dose Dead Survived Total
200 0 10 10
4000 1 9 10
1E+04 1 4 5
15000 0 3 3
2E+04 5 2 7
5E+04 12 0 12
5E+04 3 0 3
1E+05 5 0 5
4E+05 16 0 16


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 8.92 -0.000282 8 3.84
1
15.5
0.349
Beta Poisson 8.92 7 14.1
0.258
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 4.99E-05 3.55E-05 3.87E-05 3.95E-05 6.48E-05 6.76E-05 7.46E-05
ID50/LD50/ETC* 1.39E+04 9.29E+03 1.03E+04 1.07E+04 1.75E+04 1.79E+04 1.95E+04
*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


Summary

By increasing the number of data points, the pooling narrows the range of the confidence region of the parameter estimates and enhances the statistical precision.




References

  1. Armstrong, T. W. (2005). A Quantitative Microbial Risk Assessment Model for Human Inhalation Exposure to Legionella. Department of Civil, Architectural and Environmental Engineering. Philadelphia, Drexel University. PhD thesis. "[1]" .
  2. 2.0 2.1 2.2 Muller, D., M. L. Edwards and D. W. Smith (1983). "Changes in iron and transferrin levels and body temperature in experimental airborne legionellosis." Journal of Infectious Diseases 147: 302-307.
  3. 3.0 3.1 3.2 3.3 3.4 Fitzgeorge, R. B., A. Baskerville, M. Broster, P. Hambleton and P. J. Dennis (1983). "Aerosol infection of animals with strains of Legionella pneumophila of different virulence: comparison with intraperitoneal and intranasal routes of infection." Epidemiology and Infection 90(1): 81-89.
  4. 4.0 4.1 4.2 4.3 4.4 Breiman, R. F. and M. A. Horwitz (1987). "Guinea pigs sublethally infected with aerosolized Legionella pneumophila develop humoral and cell-mediated immune responses and are protected against lethal aerosol challenge. A model for studying host defense against lung infections caused by intracellular pathogens." Journal of experimental medicine 165(3): 799-811.