Difference between revisions of "Enteroviruses: Dose Response Models"

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(→‎Summary Data)
(→‎Optimized Models and Uncertainty and Fitting Analyses)
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==='''Optimized Models and Uncertainty and Fitting Analyses'''===
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==='''Optimized Models and Fitting Analyses'''===
  
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'''Output for experiment 1.'''
+
'''Optimization Output for experiment 1'''
  
 
{|
 
{|
 
| STYLE="vertical-align: top; text-align: center"|
 
| STYLE="vertical-align: top; text-align: center"|
 
{| border = "1"
 
{| border = "1"
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|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_1.xls '''Table 20.2: Dose response data''']
+
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_1.xls '''Table 3.2.  Pigs/ Porcine enterovirus type 3 Strain  model data''']
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| Dose (pfu) || death || survival || Total
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| Dose || Infected || Non-infected || Total
 
|-
 
|-
 
| 1.00E+02 || 0 || 3 || 3
 
| 1.00E+02 || 0 || 3 || 3
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| STYLE="vertical-align: top; text-align: center"|
 
| STYLE="vertical-align: top; text-align: center"|
 
{| border = "1"
 
{| border = "1"
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|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_1.xls '''Table 20.3: Goodness of fit and model selection''']
+
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_1.xls '''Table 3.3: Goodness of fit and model selection''']
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| Model||Deviance||&Delta;||DF||&chi;<sup>2</sup><sub>0.95,df</sub>||&chi;<sup>2</sup><sub>0.95,1</sub>
+
| Model||Deviance||&Delta;||Degrees <br /> of Freedom||&chi;<sup>2</sup><sub>0.95,1</sub> <br /> ''p-value''||&chi;<sup>2</sup><sub>0.95,m-k</sub> <br /> ''p-value''
 
|-
 
|-
 
| Exponential
 
| Exponential
 
| 1.24
 
| 1.24
−
| rowspan = "2" | 0
+
| rowspan = "2" | 3.00E-04
 
| 2
 
| 2
−
| 5.99
+
| rowspan = "2" | 3.84 <br /> ''0.986''
−
| rowspan = "2" | 3.84
+
| 5.99 <br /> ''0.537''
 
|-
 
|-
−
| Beta Poisson<sup>*</sup>
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| Beta Poisson
 
| 1.24
 
| 1.24
 
| 1
 
| 1
−
| 3.84
+
| 3.84 <br /> ''0.265''
 
|-
 
|-
−
| colspan = "6" | '''*Conclusion:  Both models fit well, but the exponential model is better than beta-Poisson.'''
+
| colspan = "6" | '''Exponential is best fitting model'''
 
|}
 
|}
 
| STYLE="vertical-align: top; text-align: center"|
 
| STYLE="vertical-align: top; text-align: center"|
 
{| border = "1"
 
{| border = "1"
−
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_1.xls '''Table 20.4: Parameters for the best-fit model (exponential ), obtained from 1E4 bootstrap iterations''']
+
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_1.xls '''Table 3.4 Optimized parameters for the best fitting (Exponential), obtained from 10,000 bootstrap iterations''']
 
| rowspan = "2" | Parameter or value
 
| rowspan = "2" | Parameter or value
 
| rowspan = "2" | MLE Estimate
 
| rowspan = "2" | MLE Estimate
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|-
 
|-
 
| k
 
| k
−
| 0.000296
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| 2.96E-04
 
| 2.40E-17
 
| 2.40E-17
 
| 2.40E-17
 
| 2.40E-17
 
| 2.40E-17
 
| 2.40E-17
−
| 0.000719
+
| 7.19E-04
−
| 0.000719
+
| 7.19E-04
−
| 0.001025
+
| 1.03E-03
 
|-
 
|-
 
| LD<sub>50</sub> (spores)
 
| LD<sub>50</sub> (spores)
 
| 2340.15
 
| 2340.15
−
| 676.5683
+
| 676.57
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| 963.8791
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| 963.88
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| 963.8791
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| 963.88
 
| 2.89E+16
 
| 2.89E+16
 
| 2.89E+16
 
| 2.89E+16
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[[File:Cliver1981(1)_Enterovirus_ExpHist.png|thumb|left|500px|<center>'''(a)'''</center>]][[File:Cliver1981(1)_Enterovirus_ExpModel.png|thumb|none|500px|<center>'''(b)'''</center>]]
+
[[File:Cliver1981(1)_Enterovirus_ExpHist.png|thumb|left|500px|'''Figure 3.1  Parameter histogram for exponential model (uncertainty of the parameter)''']][[File:Cliver1981(1)_Enterovirus_ExpModel.png|thumb|none|500px|'''Figure 3.2  Exponential model plot, with confidence bounds around optimized model''']]
−
 
 
−
 
 
−
'''Fig 20.1. Models plot for experiment 1. (a) Uncertainty plot of exponential model; (b) Plot of exponential model with upper and lower 95% and 99% confidence.'''
 
  
  
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'''Output for experiment 2.'''
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'''Optimization Output for experiment 2'''
  
 
{|
 
{|
 
| STYLE="vertical-align: top; text-align: center"|
 
| STYLE="vertical-align: top; text-align: center"|
 
{| border = "1"
 
{| border = "1"
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|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_2.xls '''Table 20.5: Dose response data''']
+
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_2.xls '''Table 3.5 pigs/ Porcine enterovirus type 7''']
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| Dose (pfu) || death || survival || Total
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| Dose|| Infected || Non-infected || Total
 
|-
 
|-
 
| 2.50E+02 || 4 || 2 || 6
 
| 2.50E+02 || 4 || 2 || 6
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| STYLE="vertical-align: top; text-align: center"|
 
| STYLE="vertical-align: top; text-align: center"|
 
{| border = "1"
 
{| border = "1"
−
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_2.xls '''Table 20.6: Goodness of fit and model selection''']
+
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_2.xls '''Table 3.6: Goodness of fit and model selection''']
−
| Model||Deviance||&Delta;||DF||&chi;<sup>2</sup><sub>0.95,df</sub>||&chi;<sup>2</sup><sub>0.95,1</sub>
+
| Model||Deviance||&Delta;||Degrees <br /> of Freedom||&chi;<sup>2</sup><sub>0.95,1</sub> <br /> ''p-value''||&chi;<sup>2</sup><sub>0.95,m-k</sub> <br /> ''p-value''
 
|-
 
|-
 
| Exponential
 
| Exponential
 
| 0.61
 
| 0.61
−
| rowspan = "2" | 0
+
| rowspan = "2" | 1.00E-04
 
| 2
 
| 2
−
| 5.99
+
| rowspan = "2" | 3.84 <br /> ''0.994''
−
| rowspan = "2" | 3.84
+
| 5.99 <br /> ''0.736''
 
|-
 
|-
−
| Beta Poisson<sup>*</sup>
+
| Beta Poisson
 
| 0.61
 
| 0.61
 
| 1
 
| 1
−
| 3.84
+
| 3.84 <br /> ''0.433''
 
|-
 
|-
−
| colspan = "6" | '''*Conclusion:  Both models fit well, but the exponential model is better than beta-Poisson.'''
+
| colspan = "6" | '''Exponential is best fitting model'''
 
|}
 
|}
 
| STYLE="vertical-align: top; text-align: center"|
 
| STYLE="vertical-align: top; text-align: center"|
 
{| border = "1"
 
{| border = "1"
−
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_2.xls '''Table 20.7: Parameters for the best-fit model (exponential ), obtained from 1E4 bootstrap iterations''']
+
|+ [http://wiki.camra.msu.edu/index.php?title=File:Cliver1981_Enterovirus_datafitconf_2.xls '''Table 3.7 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations''']
 
| rowspan = "2" | Parameter or value
 
| rowspan = "2" | Parameter or value
 
| rowspan = "2" | MLE Estimate
 
| rowspan = "2" | MLE Estimate
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|-
 
|-
 
| k
 
| k
−
| 0.0037
+
| 3.75E-03
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| 0.001829
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| 1.83E-03
−
| 0.002191
+
| 2.19E-03
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| 0.002191
+
| 2.19E-03
−
| 0.005619
+
| 5.62E-03
−
| 0.005619
+
| 5.62E-03
−
| 0.005619
+
| 5.62E-03
 
|-
 
|-
 
| LD<sub>50</sub> (spores)
 
| LD<sub>50</sub> (spores)
 
| 185.10
 
| 185.10
−
| 123.3551
+
| 123.36
−
| 123.3551
+
| 123.36
−
| 123.3551
+
| 123.36
−
| 316.3171
+
| 316.32
−
| 316.3171
+
| 316.32
−
| 378.9585
+
| 378.96
 
|}
 
|}
 
|}
 
|}
  
  
−
[[File:Cliver1981(2)_Enterovirus_ExpHist.png|thumb|left|500px|<center>'''(a)'''</center>]][[File:Cliver1981(2)_Enterovirus_ExpModel.png|thumb|none|500px|<center>'''(b)'''</center>]]
+
[[File:Cliver1981(2)_Enterovirus_ExpHist.png|thumb|left|500px|'''Figure 3.3  Parameter histogram for exponential model (uncertainty of the parameter)''']][[File:Cliver1981(2)_Enterovirus_ExpModel.png|thumb|none|500px|'''Figure 3.4  Exponential model plot, with confidence bounds around optimized model''']]
−
 
 
−
 
 
−
 
 
−
 
 
−
'''Fig 20.2. Models plot for experiment 2. (a) Uncertainty plot of exponential model; (b) Plot of exponential model with upper and lower 95% and 99% confidence.'''
 
  
  

Revision as of 15:33, 7 July 2011

Enteroviruses

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

Enterovirus, a kind of small (30 nm), nonenveloped, single-stranded RNA viruses, belongs to the family Picornaviridae. While most of the enterovirus infections are relatively mild and result in complete recovery of the patient, they can also cause severe and fatal diseases such as meningitis, encephalitis, myocarditis, neonatal sepsis, and polio. Infection occurs mainly via fecal-oral transmission and less commonly by respiratory droplets. While no known non-human reservoirs have been identified, water-borne, foodborne, and blood-borne transmissions have been reported (Stalkup and Chilukuri 2002).



Summary Data

Cliver (1981) challenged pigs with Porcine enterovirus type 3 and 7 via oral exposure route.

Table 3.1. Summary of the enterovirus data and best fits
Experiment number Reference Host type/pathogen strain Route/number of doses Dose units Response Best-fit model Optimized parameters LD50
1 Cliver, 1981 pigs/ Porcine enterovirus type 3 oral/3 pfu infection Beta-Poisson k=2.96E-04 2340.15
2 Cliver, 1981 pigs/ Porcine enterovirus type 7 oral/3 pfu infection Beta-Poisson k=3.75E-03 185.10

The data from different experiments were not able to be statistically pooled.

Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 3.2. Pigs/ Porcine enterovirus type 3 Strain model data
Dose Infected Non-infected Total
1.00E+02 0 3 3
2.50E+02 0 6 6
1.00E+03 2 4 6
Cliver, 1981.


Table 3.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom		 χ20.95,1
p-value		 χ20.95,m-k
p-value
Exponential 1.24 3.00E-04 2 3.84
0.986 		5.99
0.537
Beta Poisson 1.24 1 3.84
0.265
Exponential is best fitting model
Table 3.4 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 2.96E-04 2.40E-17 2.40E-17 2.40E-17 7.19E-04 7.19E-04 1.03E-03
LD50 (spores) 2340.15 676.57 963.88 963.88 2.89E+16 2.89E+16 2.89E+16


Figure 3.1 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 3.2 Exponential model plot, with confidence bounds around optimized model



Optimization Output for experiment 2

Table 3.5 pigs/ Porcine enterovirus type 7
Dose Infected Non-infected Total
2.50E+02 4 2 6
2.50E+02 3 3 6
1.00E+03 5 0 5
Cliver, 1981.


Table 3.6: 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 1.00E-04 2 3.84
0.994 		5.99
0.736
Beta Poisson 0.61 1 3.84
0.433
Exponential is best fitting model
Table 3.7 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 3.75E-03 1.83E-03 2.19E-03 2.19E-03 5.62E-03 5.62E-03 5.62E-03
LD50 (spores) 185.10 123.36 123.36 123.36 316.32 316.32 378.96


Figure 3.3 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 3.4 Exponential model plot, with confidence bounds around optimized model


Summary

The different LD50 for these two experiments indicates various virulence between pathogen strains.



References

Cliver, D. O. (1981). "Experimental infection by waterborne enteroviruses." Journal of Food Protection 44: 861-865.

Stalkup, J. R. and S. Chilukuri (2002). "Enterovirus infections: a review of clinical presentation, diagnosis, and treatment." Dermatologic clinics 20(2): 217-223.

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