Echovirus: Dose Response Models

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Echovirus

Author: Yin Huang
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General overview

Echoviruses, members 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 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.

Table 2.1. 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 Optimized Parameter(s) LD50
1 (excluding outliners) Schiff et al.,1984 humans/ echovirus-12 strain oral/4 pfu infection Beta-Poisson α = 1.06

N50 = 921.94

921.94



Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 2.2. humans/ echovirus-12 strain
Dose Infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
10000 12 0 12
33000 2 2 4
330000 2 1 3
Schiff et al.,1984.


Table 2.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 121.79 110.07 5 3.84
0
11.07
0
Beta Poisson 11.72 4 9.49
0.0196
Beta Poisson is best fitting model
Table 2.4: Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.37 -- -- -- -- -- --
N50 1006.31 -- -- -- -- -- --
LD50 1006.31 379.05 530.33 599.68 1697.50 1889.71 2405.62


Figure 2.1 Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters
Figure 2.2 beta Poisson model plot, with confidence bounds around optimized model




Optimization Output for experiment 1 (excluding the outliners).

Table 2.5: Dose response data
Dose Infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
10000 12 0 12
Schiff et al.,1984.


Table 2.6: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 7.39 4.18 3 3.84
0.041
7.81
0.0605
Beta Poisson 3.21 2 5.99
0.201
Beta Poisson is best fitting model
Table 2.7: Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter or value MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 1.06 -- -- -- -- -- --
N50 921.94 -- -- -- -- -- --
LD50 921.94 477.12 569.23 616.28 1378.01 1489.05 1693.95


Figure 2.3 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 2.4 Exponential 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, it can be seen that 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

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.