Difference between revisions of "Naegleria fowleri: Dose Response Models"

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=== '''<sup>*</sup>Recommended Model''' ===
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It is recommended that the pooled experiments 1 and 2 should be used as the best dose-response model. Both strains are common in outbreaks. The pooling narrows the range of the confidence region of the parameter estimates and enhances the statistical precision.
  
 
==='''Optimized Models and Fitting Analyses'''===
 
==='''Optimized Models and Fitting Analyses'''===

Revision as of 15:44, 5 October 2011

Naegleria

Author: Yin Huang
If you want to download this chapter in pdf format, please click here
If you want to download the excel spreadsheet of tables, please click the captions of tables. If you want to download a specific figure, just click on the figure


General overview

Naegleria, an ameboflagellate, has three stages in its life cycle: trophozoite, cyst, and a temporary flagellate stage. Naegleria fowleri, a human pathogen, is thermophilic, tolerating temperatures of 40OC-45OC, while Naegleria gruberi is nonpathogenic, with an optimal growth temperature of 22OC-35OC. Other known nonpathogenic species include Naegleria lovaniensis, Naegleria jadini, and Naegleria australiensis, although Naegleria australiensis italica has been shown to be a highly pathogenic subspecies in experimental animals. Naegleria fowleri is highly pathogenic and death may follow within a few days after the symptom onset (Ma et al. 1990).

Sources for Naegleria have been reported as water, soil, sewage sludge, cooling towers, nasal and throat swabs, hospital hydrothermal pools, and swimming pools. Naegleria fowleri, the most pathogenic species, has been isolated frequently from thermally polluted waters and sewage wastes. Most human infections with Naegleria fowleri have been associated with swimming in warm waters, but also with the sources of tap water and hot baths (Ma et al. 1990).




Summary Data

Adams et al. (1976) challenged three groups of male DUB/ICR mice intravenously with graded doses of Naegleria fowleri LEE strain and the survival was monitored for two weeks.

Haggerty and John (1978) inoculated male DUB/ICR mice with Naegleria fowleri LEE strain via intravenous route and monitored the survival for three weeks.

Table 1.1. Summary of the Naegleria data and best fits
Experiment number Reference Host type/pathogen strain Route/number of doses Dose units Response Best fit model Best-fit parameters LD50
1 Adams et al. 1976 mice/Naegleria fowleri LEE strain intravenous /3 no. of organisms Death exponential k = 4.21E-07 1.64E+06
2 Haggerty and John 1978 mice/Naegleria fowleri LEE strain intravenous/4 no. of organisms Death exponential k = 3.07E-07 2.26E+06
1 and 2 * - - - - - exponential k = 3.42E-07 2.03E+06

The data from experiments 1 and 2 were able to be statistically pooled.



*Recommended Model

It is recommended that the pooled experiments 1 and 2 should be used as the best dose-response model. Both strains are common in outbreaks. The pooling narrows the range of the confidence region of the parameter estimates and enhances the statistical precision.

Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 1.2. mice/Naegleria fowleri LEE strain data
Dose Dead Survived Total
2500000 4 6 10
5000000 19 1 20
10000000 10 0 10
Adams et al. 1976


Table 1.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 4.11 5.00E-04 2 3.84
0.998
5.99
0.128
Beta Poisson 4.11 1 3.84
0.0426
Exponential is best fitting model
Table 1.4 Optimized parameters for the best fitting (Exponential), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 4.21E-07 2.77E-07 3.04E-07 3.25E-07 5.95E-07 6.22E-07 6.79E-07
LD50 1.64E+06 1.02E+06 1.11E+06 1.16E+06 2.13E+06 2.28E+06 2.50E+06


Figure 1.1 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 1.2 Exponential model plot, with confidence bounds around optimized model




Optimization Output for experiment 2

Table 1.5 Mice/Naegleria fowleri LEE strain data
Dose Dead Survived Total
1000000 4 16 20
2500000 12 8 20
5000000 14 6 20
10000000 20 0 20
Haggerty and John 1978


Table 1.6: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 3.47 9.00E-04 3 3.84
0.976
7.81
0.325
Beta Poisson 3.47 2 5.99
0.177
Exponential is best fitting model
Table 1.7 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 3.07E-07 2.14E-07 2.33E-07 2.43E-07 4.02E-07 4.26E-07 4.70E-07
LD50 (spores) 2.26E+06 1.47E+06 1.63E+06 1.73E+06 2.85E+06 2.97E+06 3.24E+06


Figure 1.3. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 1.4. Exponential model plot, confidence bounds around optimized model




Optimization Output for experiment 3

Table 1.8: mice/ Naegleria fowleri LEE strain model data
Dose Dead Survived Total
2500000 4 6 10
5000000 19 1 20
10000000 10 0 10
1000000 4 16 20
2500000 12 8 20
5000000 14 6 20
10000000 20 0 20
Adams et al. 1976 & Haggerty and John 1978


Table 1.9: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 8.85 5.00E-04 6 3.84
0.982
12.59
0.182
Beta Poisson 8.85 5 11.07
0.115
Exponential is best fitting model
Table 1.10 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 3.42E-07 2.59E-07 2.76E-07 2.86E-07 4.15E-07 4.31E-07 4.65E-07
LD50 (spores) 2.03E+06 1.49E+06 1.61E+06 1.67E+06 2.42E+06 2.51E+06 2.67E+06


Figure 1.5. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 1.6. Exponential model plot, 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

Adams, A.C., John, D.T. and Bradley, S.G. (1976) Modification of resistance of mice to naegleria fowleri infections. Infection and Immunity 13, 1387-1391.

Haggerty, R.M. and John, D.T. (1978) Innate resistance of mice to experimental infection with naegleria fowleri. Infection and Immunity 20, 73-77.

Ma, P., Visvesvara, G.S., Martinez, A.J., Theodore, F.H., Daggett, P.M. and Sawyer, T.K. (1990) Naegleria and acanthamoeba infections: Review. Reviews of Infectious Diseases 12, 490-513.