Rhinovirus: Dose Response Models

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Rhinovirus

Author: Yin Huang


General overview

Rhinovirus, a small icosahedral viruses made of a protein capsid that encases a single-stranded, positive-sense RNA molecule, belongs to the Picornaviridae family. About 100 different serotypes have been identified and characterized by their own specific antigens.

Rhinoviruses are responsible for 30 to 50% of adult colds and 10 to 25% of colds in children. Other cold-causing viruses are adenoviruses, coronaviruses, coxsackieviruses, echoviruses, orthomyxoviruses, paramyxoviruses, respiratory syncytial virus, and enteroviruses, each of which produces infections with slightly different patterns of symptoms and severity. Several of the above-mentioned viruses also account for other more severe illnesses (Bella and Rossmann 1999).




Summary Data

Hendley et al. (1972) inoculated young adult human volunteers over the age of 21 with Rhinovirus type 39 (RV 39), strain SF 299, and rhinovirus type 14 (RV 14), strain SF 765, via intranasal exposure route. Shedding of the challenge virus and/or a fourfold or greater increase in titer of serum antibody to a homotypic rhinovirus were accepted as evidence of infection.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
65* [1] human type 39 intranasal 6 TCID50 doses infection beta-Poisson α = 2.21E-01 , N50 = 1.81E+00 1.81E+00
64 [1] human type 14 intranasal 6 TCID50 doses infection beta-Poisson α = 2.01E-01 , N50 = 9.22E+00 9.22E+00
310 [1] human type 14 intranasal 6 TCID50 doses infection beta-Poisson α = 2.52E-01 , N50 = 3.83E+00 3.83E+00
311 [1] human type 39 intranasal 6 TCID50 doses infection beta-Poisson α = 7.01E-01 , N50 = 1.9E-01 1.9E-01
312 [1] human type 14 intranasal 6 TCID50 doses infection beta-Poisson α = 1.81E-01 , N50 = 2.22E+01 2.22E+01
313 [1] human type 39 intranasal 6 TCID50 doses infection beta-Poisson α = 2E-01 , N50 = 1.05E+01 1.05E+01
312, 313 [1] human type 14 intranasal 12 TCID50 doses infection beta-Poisson α = 1.82E-01 , N50 = 1.38E+01 1.38E+01
*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 65

human/type 39 strain SF 299 model data [1]
Dose Infected Non-infected Total
0.05 0 11 11
0.15 2 7 9
0.5 8 16 24
5 5 11 16
50 47 15 62


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 50.3 44.3 4 3.84
2.76e-11
9.49
3.06e-10
Beta Poisson 6.01 3 7.81
0.111
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 2.24E-01 9.88E-04 1.40E-01 1.53E-01 3.71E-01 4.27E-01 7.63E-01
N50 3.29E+00 1.90E-02 1.34E+00 1.59E+00 7.67E+00 9.27E+00 1.59E+01


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 64

human/type 14 strain SF 765model data [1]
Dose Infected Non-infected Total
0.5 1 8 9
1.5 4 6 10
5 4 6 10
15 6 4 10
150 27 13 40
300 10 2 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 51.8 50.2 5 3.84
1.42e-12
11.1
5.8e-10
Beta Poisson 1.68 4 9.49
0.794
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 2.01E-01 7.76E-02 1.07E-01 1.22E-01 3.36E-01 3.69E-01 4.61E-01
N50 9.22E+00 1.41E+00 2.57E+00 3.40E+00 2.47E+01 3.14E+01 5.26E+01


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 310

TITLE [1]
Dose INFECTION NOT

INFECTION || Total

0.5 1 4 5
1.5 2 3 5
5 3 2 5
15 2 1 3
150 14 5 19
300 5 0 5
Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 29.7 27.3 5 3.84
{{{pbPbetter}}}
11.1
1.71e-05
Beta Poisson 2.42 4 9.49
0

selection

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 2.52E-01 9.79E-04 9.14E-02 1.16E-01 5.50E-01 6.41E-01 1.06E+00
N50 3.83E+00 9.08E-03 3.23E-01 6.41E-01 1.48E+01 2.04E+01 8.86E+01
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 311

TITLE [1]
Dose INFECTION NOT

INFECTION || Total

0.05 0 2 2
0.15 1 3 4
0.5 5 2 7
1.5 18 1 19
5 1 0 1
50 19 1 20
Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 61.7 56.8 5 3.84
{{{pbPbetter}}}
11.1
5.32e-12
Beta Poisson 4.95 4 9.49
0

selection

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 7.01E-01 2.29E-01 3.14E-01 3.63E-01 1.81E+06 3.82E+06 1.41E+07
N50 1.9E-01 2.27E-02 5.85E-02 7.93E-02 4.20E-01 4.52E-01 5.56E-01
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 312

TITLE [1]
Dose INFECTION NOT

INFECTION || Total

0.5 0 4 4
1.5 2 3 5
5 1 4 5
15 4 3 7
150 13 8 21
300 5 2 7
Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 24.3 21.5 5 3.84
{{{pbPbetter}}}
11.1
0.000194
Beta Poisson 2.77 4 9.49
0

selection

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 1.81E-01 3.92E-02 7.30E-02 9.02E-02 4.00E-01 4.79E-01 7.28E-01
N50 2.22E+01 3.12E+00 5.01E+00 6.38E+00 1.22E+02 2.06E+02 1.26E+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 313

TITLE [1]
Dose INFECTION NOT

INFECTION || Total

0.05 0 4 4
0.15 1 4 5
0.5 3 14 17
1.5 4 10 14
5 4 11 15
50 28 14 42
Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 29.2 26.2 5 3.84
{{{pbPbetter}}}
11.1
2.16e-05
Beta Poisson 2.93 4 9.49
0

selection

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 2E-01 7.86E-02 9.79E-02 1.11E-01 4.65E-01 5.58E-01 8.66E-01
N50 1.05E+01 3.00E+00 3.98E+00 4.65E+00 3.67E+01 5.32E+01 1.22E+02
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 pooled experiments of 312&313

TITLE [1]
Dose INFECTION NOT

INFECTION || Total

0.05 0 4 4
0.15 1 4 5
0.5 0 4 4
0.5 3 14 17
1.5 2 3 5
1.5 4 10 14
5 1 4 5
5 4 11 15
15 4 3 7
50 28 14 42
150 13 8 21
300 5 2 7
"
Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 78.6 72.3 11 3.84
{{{pbPbetter}}}
19.7
2.8e-12
Beta Poisson 6.22 10 18.3
0.796
{{{interpretation}}}
"
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 1.82E-01 1.04E-03 1.03E-01 1.14E-01 3.04E-01 3.38E-01 4.09E-01
N50 1.38E+01 2.98E+00 5.64E+00 6.67E+00 3.77E+01 4.98E+01 1.32E+02
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 responses caused by doses less than one observed in these two experiments are probably due to the uncertainties of dose counting in the original study.



References

  1. 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 Hendley, J.O., Edmondson Jr., W.P. and Gwaltney Jr., J.M. (1972) Relation between naturally acquired immunity and infectivity of two rhinoviruses involunteers. Journal of Infectious Diseases 125, 243-248. Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hendley_et_al..2C_1972" defined multiple times with different content

Bella, J. and Rossmann, M.G. (1999) Review: Rhinoviruses and their icam receptors. Journal of Structural Biology 128, 69–74.