Difference between revisions of "SARS: Dose Response Models"

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(Summary Data)
(Summary Data)
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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 15:42, 5 October 2011

SARS

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

Coronaviruses cause acute and chronic respiratory, enteric, and central nervous system (CNS) diseases in humans and many species of animals. Coronaviruses are divided into three groups based on the genome sequences, including SARS-CoV (a member of group II) as well as murine hepatitis virus (MHV), bovine coronavirus, porcine hemagglutinating encephalomyelitis virus (HEV), equine coronavirus, and human coronavirues OC43 and NL63, which also cause respiratory infections. SARS-CoV, the causal pathogen of severe acute respiratory syndrome (SARS), caused a large outbreak of this severe pneumonia occurred in Hong Kong in 2003 and rapidly spread throughout the world. SARS-CoV can infect and replicate in mice, ferrets, hamsters, cats, and several species of nonhuman primates (cynomolgus and rhesus macaques, African green monkeys, and marmosets). MHV that infects both mice and rats often has been studied as a suitable model of human coronavirus diseases (Watanabe et al. 2010).




Summary Data

DeDiego et al. (2008) challenged four groups of the tg mice intranasally with graded doses of rSARS-CoV and the survival was monitored for 13 days.

De Albuquerque et al. (2006) inoculated A/J mice with MHV-1 intranasally via intranasal route and monitored the survival for 21 days.

Table 8.1. Summary of the SARS 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 DeDiego et al., 2008 mice/rSARS-CoV intranasal/4 pfu Death exponential k = 2.97E-03 233.25
2 De Albuquerque et al., 2006 Mice/MHV-1 intranasal/4 pfu Death exponential k = 2.14E-03 323.63
1 and 2 * - - - - - exponential k = 2.46E-03 281.97

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 8.2: human/type 14 strain model data
Dose Dead Survived Total
240 1 2 3
800 3 0 3
2400 2 0 2
12000 6 0 6
DeDiego et al., 2008


Table 8.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 0.97 9.00E-04 3 3.84
0.976
7.81
0.809
Beta Poisson 0.97 2 5.99
0.616
Exponential is best fitting model
Table 8.4 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 2.97E-03 0.0019 0.0019 0.0019 0.0051 0.092 0.092
LD50(spores) 233.25 7.54 7.54 135.59 364.19 364.19 364.19


Figure 8.1. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 8.2. Exponential model plot, confidence bounds around optimized model




Optimization Output for experiment 2

Table 8.5: human/type 14 and 39 strains model data
Dose Dead Survived Total
5 0 5 5
50 1 4 5
500 3 2 5
5000 5 0 5
De Albuquerque et al., 2006.


Table 8.6: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 0.61 0.069 3 3.84
0.793
7.81
0.895
Beta Poisson 0.54 2 5.99
0.765
Exponential is best fitting model
Table 8.7 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 2.14E-03 6.25E-04 6.55E-04 9.06E-04 6.58E-03 6.58E-03 9.86E-03
LD50(spores) 323.63 70.27 105.32 127.96 765.29 1058.68 1109.24


Figure 8.3. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 8.4. Exponential model plot, confidence bounds around optimized model



Optimization Output for experiment 1 and 2

Table 8.8: human/type 39 strain model data
Dose Dead Survived Total
240 1 2 3
800 3 0 3
2400 2 0 2
12000 6 0 6
5 0 5 5
50 1 4 5
500 3 2 5
5000 5 0 5
DeDiego et al., 2008 & De Albuquerque et al., 2006


Table 8.9: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 1.75 0.0018 7 3.84
0.966
14.07
0.972
Beta Poisson 1.75 6 12.59
0.941
Exponential is best fitting model
Table 8.10 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 2.46E-03 0.0011 0.0013 0.0014 0.0046 0.0053 0.0072
LD50(spores) 281.97 96.60 131.50 151.16 513.27 542.77 647.46


Figure 8.5. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 8.6. 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

De Albuquerque, N., Baig, E., Ma, X., Zhang, J., He, W., Rowe, A., Habal, M., Liu, M., Shalev, I., Downey, G.P., Gorczynski, R., Butany, J., Leibowitz, J., Weiss, S.R., McGilvray, I.D., Phillips, M.J., Fish, E.N. and Levy, G.A. (2006) Murine hepatitis virus strain 1 produces a clinically relevant model of severe acute respiratory syndrome in a/j mice Journal of Virology 80, 10382-10394.

DeDiego, M.L., Pewe, L., Alvarez, E., Rejas, M.T., Perlman, S. and Enjuanes, L. (2008) Pathogenicity of severe acute respiratory coronavirus deletion mutants in hace-2 transgenic mice. Virology 376, 379–389.

Watanabe, T., Bartrand, T.A., Weir, M.H., Omura, T. and Haas, C.N. (2010) Development of a dose-response model for sars coronavirus. Risk Analysis 30, 1129-1138.