Difference between revisions of "Influenza: Dose Response Models"

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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''.
 
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''.
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[[Category:Dose Response Model]]

Revision as of 21:49, 11 November 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 4.1. Summary of the Influenza data and best fits
Experiment number Reference Host type/pathogen strain Route/number of doses Dose units Response Best-fit modela 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 = 1.25E+06

1.25E+06
2 Murphy et al., 1985 humans/H3N2,A/Washington/897/80 attenuated strain intranasal/5 TCID50 infection beta-Poisson α = 0.43

N50 = 6.66E+05

6.66E+05
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 = 9.45E+05

9.45E+05

*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 human outbreaks. The pooling narrows the range of the confidence region of the parameter estimates and enhances the statistical precision.

a:
Exponential and betapoisson model.jpg

Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 4.2: humans/H1N1 A/California/10/78 attenuated strain model data
Dose 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 4.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 23.56 21.54 3 3.84
0
7.81
0
Beta Poisson 2.02 2 5.99
0.365
Beta Poisson is best fitting model
Table 4.4 Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.90 -- -- -- -- -- --
N50 1.25E+06 -- -- -- -- -- --
LD50 1.25E+06 5.03E+05 6.27E+05 6.94E+05 2.39E+06 2.72E+06 3.36E+06


Figure 4.1 Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Figure 4.2 beta Poisson model plot, with confidence bounds around optimized model




Optimization Output for experiment 2

Table 4.5: humans/H3N2, A/Washington/897/80 attenuated strain model data
Dose 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 4.6: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 39.05 34.80 4 3.84
0
9.49
0
Beta Poisson 4.26 3 7.81
0.235
Beta Poisson is best fitting model
Table 4.7 Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.43 -- -- -- -- -- --
N50 6.66E+05 -- -- -- -- -- --
LD50 6.66E+05 1.41E+05 2.17E+05 2.63E+05 1.55E+06 1.80E+06 2.33E+06


Figure 4.3 Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Figure 4.4 beta Poisson model plot, with confidence bounds around optimized model




Optimization Output for experiment 3

Table 4.8: mice/ H5N1,DKGX/35 strain model data
Dose 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 4.9: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 0.50 0.092 5 3.84
0.762
11.07
0.992
Beta Poisson 0.41 4 9.49
0.982
Exponential is best fitting model
Table 4.10 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations
Parameter 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 4.5 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 4.6 Exponential model plot, with confidence bounds around optimized model




Optimization Output for experiment 4

Table 4.11: humans/ H1N1 A/California/10/78 and H3N2, A/Washington/897/80 attenuated strain model data
Dose 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 4.12: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 63.99 55.43 8 3.84
0
15.51
0
Beta Poisson 8.56 7 14.07
0.286
Beta Poisson is best fitting model
Table 4.13 Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.58 -- -- -- -- -- --
N50 9.45E+05 -- -- -- -- -- --
LD50 9.45E+05 4.25E+05 5.13E+05 5.72E+05 1.59E+06 1.75E+06 2.09E+06


Figure 4.7 Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Figure 4.8 beta Poisson model plot, with 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. 4.9, 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. 4.9. 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.