Echovirus: Dose Response Models

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Echovirus

Author: Yin Huang


General overview

Echoviruses, a member of the enterovirus genus, is a type of RNA virus that were shown to be a frequent cause of simple febrile illnesses and aseptic meningitis. Most infected persons experience no symptoms or have self-limited disease. Deaths and other adverse consequences are rare and limited to patients with severe echovirus encephalitis or to persons with B cell-deficiency syndromes who develop persistent infection (Modlin 1986).

Human echoviral infection occurs via fecal-oral transmission. Infants are particularly susceptible to echovirus infection. Both vertical transmission from an infected mother and nosocomial transmission via hospital personnel appear to be important sources of infection for the neonate. Severe disease and death may follow the infection that occurs with the first 10-14 days of life (Modlin 1986).




Summary Data

Schiff et al. (1984) challenged human volunteers lacking detectable serum antibody with echovirus-12 in chilled drinking water. The virus used in the study was originally recovered from a child with a clinical diagnosis of erythema infectiousum (fifth disease). The infection with echovirus-12 among volunteers was determined by intestinal shedding of virus and seroconversion.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
256 (excluding the outliers of exp 112)* [1] human strain 12 oral 4 PFU infection beta-Poisson α = 1.06E+00 , N50 = 9.22E+02 9.22E+02
112 [1] human strain 12 oral 6 PFU infection beta-Poisson α = 3.74E-01 , N50 = 1.01E+03 1.01E+03
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.


Exponential and betapoisson model.jpg



Optimization Output for experiment 256 (excluding the outliers of experiment 112)

humans/ echovirus-12 strain [1]
Dose infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
1E+04 12 0 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 7.39 4.18 3 3.84
0.041
7.81
0.0605
Beta Poisson 3.21 2 5.99
0.201
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.


Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.06E+00 3.07E-01 4.04E-01 4.69E-01 1.23E+01 6.22E+02 3.74E+04
N50 9.22E+02 4.68E+02 5.59E+02 6.15E+02 1.37E+03 1.49E+03 1.73E+03


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


Optimization Output for experiment 112

humans/ echovirus-12 strain [1]
Dose infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
1E+04 12 0 12
33000 2 2 4
330000 2 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 122 110 5 3.84
0
11.1
0
Beta Poisson 11.7 4 9.49
0.0196
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.


Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 3.74E-01 1.24E-01 1.81E-01 2.09E-01 7.79E-01 9.41E-01 2.01E+00
N50 1.01E+03 3.84E+02 5.32E+02 5.94E+02 1.75E+03 1.97E+03 2.54E+03


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



Summary

The limited numbers of subjects under dose 33000 and 330000 might have contributed to their deviations from other dose groups and the unsuccessful fitting. By excluding these two outliner groups, significantly better fit was achieved (The reduction of deviance is substantially greater than the chi-square value at the degree of freedom of 2).



References

  1. 1.0 1.1 1.2 1.3 Schiff, G. M., G. M. Stefanović, E. C. Young, D. S. Sander, J. K. Pennekamp and R. L. Ward (1984). "Studies of echovirus-12 in volunteers: determination of minimal infectious dose and the effect of previous infection on infectious dose." Journal of Infectious Diseases 150(6): 858-866.

Modlin, J. F. (1986). "Perinatal Echovirus Infection: Insights from a Literature Review of 61 Cases of SeriousInfection and 16 Outbreaks in Nurseries." Reviews of Infectious Diseases 8(6): 918-926.

Schiff, G. M., G. M. Stefanović, E. C. Young, D. S. Sander, J. K. Pennekamp and R. L. Ward (1984). "Studies of echovirus-12 in volunteers: determination of minimal infectious dose and the effect of previous infection on infectious dose." Journal of Infectious Diseases 150(6): 858-866.