Difference between revisions of "Influenza: Dose Response Models"

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[[File:Pooling_influenza_BPScatter.png|thumb|left|500px|'''Figure 22.7. Scatter plot for beta-Poisson model(uncertainty of the parameter)''']][[File:Pooling_influenza_BPModel.png|thumb|none|500px|'''Figure 22.8. beta-Poisson model plot, confidence bounds around optimized model''']]<br>
 
[[File:Pooling_influenza_BPScatter.png|thumb|left|500px|'''Figure 22.7. Scatter plot for beta-Poisson model(uncertainty of the parameter)''']][[File:Pooling_influenza_BPModel.png|thumb|none|500px|'''Figure 22.8. beta-Poisson model plot, confidence bounds around optimized model''']]<br>
  
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==='''Advanced Dose Response Model'''===
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Incorporating the time postinoculation into the classical dose-response models for microbial infection generates a class of time-dose-response (TDR) models. The parameter k in the exponential dose-response model (equation 1) and the parameter N50 in the beta-Poisson model (equation 2) were set equal to functions of time that represent in vivo bacterial kinetics. Equations 1-2 with candidate G(t; θ,…) were fit to the time-dependent dose response data from experiment 3. The beta-Poisson TDR model (equation 2) incorporating an exponential-inverse-power distribution provided the best fit to the data. In Fig. 22.9, the best TDR models are plotted to compare with the observed mortalities (Kitajima et al. under review). As shown, the clear difference between the different times postinoculation gives a visible representation of the quantified results that the modification added to the classical models has a substantial effect on the dose response.
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[[File:TDR influenza2.png|thumb|left|800px|'''FIG. 22.9. The best-fit TDR model (curves) compared to observed mortalities against doses (symbols) from experiment 3.''']]
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[[File:Equation influenza.png|thumb|left|500px]]
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Revision as of 17:19, 24 March 2011

Influenza

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

Influenza A viruses are members of the family Orthomyxoviridae, which comprises enveloped viruses with segmented, negative-sense RNA genomes. Based on the antigenicity of the two surface glycoproteins, hemagglutinin (HA) and neuraminidase (NA), influenza A viruses are currently divided into 16 HA and 9 NA subtypes, designated as H1-H16 and N1-N9. Over the past century, viruses of the H1N1, H2N2, H3N2, and H1N2 subtypes have circulated in humans. Additionally, new subtypes such as H5N1 and H7N9 have been recently isolated from human as well as poultry. Influenza A virus is one of the most common causes of human respiratory infections and the most significant because they cause high morbidity and mortality. Transmission of influenza can be achieved via environmental reservoirs or human-to-human communication (Kitajima et al. under review; Watanabe et al. under review).




Summary Data

Murphy et al. (1984) intranasally challenged adult volunteers with influenza A (H1N1) California/10/78 cold-adpted viruses. Infection was defined as virus recovery and/or antibody response.

Murphy et al.(1985) challenged adult volunteers with influenza A (H3N2) Washington/897/80 avian-human reassortant viruses via intranasal route. Infection was defined as virus isolation and/or antibody response.

Fan et al. (2009) exposed six-week-old SPF BALB/c mice (five mice/dose) intranasally with a highly pathogenic avian influenza A (H5N1) virus (DKGX/35 strain).

Table 22.1. Summary of the echovirus 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 Murphy et al., 1984 humans/H1N1,A/California/10/78 attenuated strain intranasal/4 TCID50 infection beta-Poisson α = 0.90

N50 = 1250269

1083819
2 Murphy et al., 1985 humans/H3N2,A/Washington/897/80 attenuated strain intranasal/5 TCID50 infection beta-Poisson α = 0.43

N50 = 666301.4

670000
3 Fan et al., 2009 mice/ H5N1, DKGX/35 strain intranasal/6 EID50 death exponential k = 0.011 63.80
1 and 2 - - - - - beta-Poisson α = 0.58

N50 = 944572.2

940000

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




Optimized Models and Uncertainty and Fitting Analyses

Output for experiment 1.

Table 22.2: humans/H1N1 A/California/10/78 attenuated strain model data
Dose (TCID50) infected Non-infected Total
63095.734 0 15 15
630957.34 4 7 11
6309573.4 19 3 22
63095734 24 1 25
Murphy et al., 1984


Table 22.3: Goodness of fit and model selection
Model Deviance Δ DF χ20.95,df χ20.95,1
Exponential 23.56 21.54 3 7.81 3.84
Beta Poisson* 2.02 2 5.99
*Conclusion: Only the beta-Poisson model fits well.
Table 22.4: Parameters for the best-fit model (beta-Poisson), obtained from 1E4 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.90 4.23e-01 4.90e-01 5.40e-01 3.35e+04 5.79e+04 2.60e+05
N50 1250269 522079.6 626741.4 718534.2 2396930.9 2739793.0 3299127.2


Figure 22.1. Scatter plot for beta-Poisson model(uncertainty of the parameter)
Figure 22.2. beta-Poisson model plot, confidence bounds around optimized model




Output for experiment 2.

Table 22.5: humans/H3N2, A/Washington/897/80 attenuated strain model data
Dose (TCID50) infected Non-infected Total
100000 2 10 12
1000000 8 5 13
10000000 16 3 19
31622777 16 4 20
100000000 19 0 19
Murphy et al., 1985


Table 22.6: Goodness of fit and model selection
Model Deviance Δ DF χ20.95,df χ20.95,1
Exponential 39.05 34.79 4 9.49 3.84
Beta Poisson* 4.26 3 7.81
*Conclusion: Only the beta-Poisson model fits well.
Table 22.7: Parameters for the best-fit model (beta-Poisson), obtained from 1E4 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.43 0.22 0.26 0.28 0.75 0.85 1.15
N50 666301.4 140501.3 216731.3 263412.0 1553357.4 1800870.6 2333342.5


Figure 22.3. Scatter plot for beta-Poisson model(uncertainty of the parameter)
Figure 22.4. beta-Poisson model plot, confidence bounds around optimized model




Output for experiment 3.

Table 22.8: mice/ H5N1,DKGX/35 strain model data
Dose (TCID50) infected Non-infected Total
10 1 4 5
100 3 2 5
1000 5 0 5
10000 5 0 5
100000 5 0 5
1000000 5 0 5
Fan et al., 2009.


Table 22.9: Goodness of fit and model selection
Model Deviance Δ DF χ20.95,df χ20.95,1
Exponential 0.50 0.09 5 11.07 3.84
Beta Poisson* 0.41 4 9.49
*Conclusion: Both models fit well, but the exponential model is better than beta-Poisson.
Table 22.10: Parameters for the best-fit model (exponential), obtained from 1E4 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 0.011 0.0031 0.0033 0.0046 0.035 0.035 0.054
LD50 (spores) 63.80 12.78 19.94 19.94 151.94 210.65 220.81


Figure 22.5. Parameter histogram for exponential model (uncertainty of the parameter)
Figure 22.6. Exponential model plot, confidence bounds around optimized model




Output for experiment 1 and 2.

Table 22.11: humans/ H1N1 A/California/10/78 and H3N2, A/Washington/897/80 attenuated strain model data
Dose (TCID50) infected Non-infected Total
100000 2 10 12
1000000 8 5 13
10000000 16 3 19
31622777 16 4 20
100000000 19 0 19
63095.734 0 15 15
630957.34 4 7 11
6309573.4 19 3 22
63095734 24 1 25
Murphy et al., 1984 & Murphy et al., 1985


Table 22.12: Goodness of fit and model selection
Model Deviance Δ DF χ20.95,df χ20.95,1
Exponential 63.99 34.79 4 15.51 3.84
Beta Poisson* 8.56 3 14.07
*Conclusion: The pooling is successful. Only the beta-Poisson model fits well.
Table 22.13: Parameters for the best-fit model (beta-Poisson), obtained from 1E4 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.58 0.36 0.40 0.43 0.91 1.00 1.24
N50 944572.2 424537.2 512669.9 572105.1 1590942.1 1746830.3 2088468.3


Figure 22.7. Scatter plot for beta-Poisson model(uncertainty of the parameter)
Figure 22.8. beta-Poisson model plot, confidence bounds around optimized model



Advanced Dose Response Model

Incorporating the time postinoculation into the classical dose-response models for microbial infection generates a class of time-dose-response (TDR) models. The parameter k in the exponential dose-response model (equation 1) and the parameter N50 in the beta-Poisson model (equation 2) were set equal to functions of time that represent in vivo bacterial kinetics. Equations 1-2 with candidate G(t; θ,…) were fit to the time-dependent dose response data from experiment 3. The beta-Poisson TDR model (equation 2) incorporating an exponential-inverse-power distribution provided the best fit to the data. In Fig. 22.9, the best TDR models are plotted to compare with the observed mortalities (Kitajima et al. under review). As shown, the clear difference between the different times postinoculation gives a visible representation of the quantified results that the modification added to the classical models has a substantial effect on the dose response.


FIG. 22.9. The best-fit TDR model (curves) compared to observed mortalities against doses (symbols) from experiment 3.
Equation influenza.png




Summary

The pooling results indicate that the human responses to HIN1 and H3N2 viruses may have similar patterns.




References

Fan, S., Deng, G., Song, J., Tian, G., Suo, Y., Jiang, Y., Guan, Y., Bu, Z., Kawaoka, Y. and Chen, H. (2009) Two amino acid residues in the matrix protein m1 contribute to the virulence difference of h5n1 avian influenza viruses in mice. Virology 384, 28-32.

Kitajima, M., Huang, Y., Watanabe, T., Katayama, H. and Haas, C.N. (under review) Dose-response time modeling for highly pathogenic avian influenza a (h5n1) virus infection. Letters in Applied Microbiology.

Murphy, B.R., Clements, M.L., Madore, H.P., Steinberg, J., O'Donnell, S., Betts, R., Demico, D., Reichman, R.C., Dolin, R. and Maassab, H.F. (1984) Dose response of cold-adapted, reassortant influenza a/california/10/78 virus (h1n1) in adult volunteers. Journal of Infectious Diseases 149, 816.

Murphy, B.R., Clements, M.L., Tierney, E.L., Black, R.E., Stienberg, J. and Chanock, R.M. (1985) Dose response of influenza a/washington/897/80 (h3n2) avian-human reassortant virus in adult volunteers. Journal of Infectious Diseases 152, 225-229.

Watanabe, T., Bartrand, T.A., Omura, T. and Haas, C.N. (under review) Dose-response assessment for influenza a virus based on the datasets of infection with its live attenuated reassortants. Risk Analysis.