Rotavirus: Dose Response Models

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Rotavirus

Kyle S. Enger, MPH


Overview

Rotaviruses are highly remarkably infectious causing diarrhea. Rotaviruses are non-enveloped viruses 70 nm in diameter that resist inactivation in the environment. They are classified into groups A through F; with group A being the most common group in humans, and is divided into four major serotypes (Heymann 2004).

Although improved sanitation and hygiene greatly inhibit transmission of many other diarrheal pathogens, rotaviruses generally infected all children before 4 years of age in both developing and developed countries before rotavirus vaccine was available (Cook 1990). Rotaviruses cause gastroenteritis with watery diarrhea, vomiting, and fever (Heymann 2004). The disease is self-limiting, lasting 3-7 days, but infection is often asymptomatic (CDC 2011). However, rotavirus disease can be severe and lethal, particularly in underdeveloped settings; approximately 400,000 deaths per year worldwide are attributable to rotaviruses (Parashar 2003).

Two live-virus vaccines have been developed, RotaTeq and Rotarix. They are highly effective: 74% against diarrhea and 100% against severe diarrhea for RotaTeq, and 95% against severe diarrhea for Rotarix (Greenberg 2009).It is unclear whether these vaccines will be as effective in severely underdeveloped environments, although trials are underway (Greenberg 2009).


Summary of data

Ward et al. (1986) fed the CJN rotavirus strain to healthy 18-45 year old men with 0.2g of NaHCO3, and measured the outcomes of infection (i.e., increased antibody titer to the CJN strain), symptoms, and detectable shedding of rotavirus. Both the virus strain and the people challenged were chosen to minimize preexisting immunity to the virus. The ID50 was approximately 6 focus-forming units (FFU); however, there were 1.56 x 104 particles per FFU. A beta-Poisson dose response model has been previously fit to the response of infection (Haas, Rose, and Gerba 1999), yielding similar results to those presented here. Other responses (illness or shedding) indicated lower potency.

Vaccine trials have been published in which live rotavirus vaccine strains were fed to healthy human infants (Pichichero et al. 1990, Vesikari et al. 1985). However, their ID50 estimates were several orders of magnitude higher than that observed by Ward et al. (1986), probably because the virus strains were attenuated. In addition, seroconversion occurred in 7/24 of the placebo recipients in one of the studies (Pichichero et al. 1990). Therefore, these results do not appear applicable to natural rotavirus infection, and dose response models are not included here.

Piglets aged 4-5 days that had not consumed colostrum were administered porcine rotavirus (OSU strain) intragastrically (Payment & Morin 1990). This study also showed high potency of rotavirus, with an ID50 of 40 viral particles. Tissue culture methods for quantifying this porcine rotavirus were several orders of magnitude less sensitive at detecting viable virus than visualization using electron microscopy (Payment & Morin 1990).

When conducting risk assessments of rotavirus, the units of the dose should be carefully considered, since culture methods may inefficiently detect infectious particles (Payment & Morin 1990) or large numbers of viral particles visible with electron microscopy may be noninfectious (Ward et al. 1984, Ward et al. 1986).


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
70* [1] human CJN strain (unpassaged) oral 8 FFU infection beta-Poisson α = 2.53E-01 , N50 = 6.17E+00 6.17E+00
71 [1] human CJN strain (unpassaged) oral 8 FFU symptoms and infection beta-Poisson α = 7.28E-02 , N50 = 1.47E+03 1.47E+03
125 [1] human CJN strain (unpassaged) oral 8 FFU detectable shedding beta-Poisson α = 9.6E-02 , N50 = 9.61E+01 9.61E+01
68 [2] pig OSU (ATCC VR892) intragastric 10 particles infection exponential k = 1.73E-02 4E+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 70

Model data for rotavirus (CJN strain) in the human [1]
Dose Infected Non-infected Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 8 3 11
90 6 1 7
900 7 1 8
9000 5 2 7
9E+04 3 0 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 125 119 7 3.84
0
14.1
0
Beta Poisson 6.2 6 12.6
0.401
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 2.53E-01 1.28E-01 1.51E-01 1.64E-01 5.18E-01 6.58E-01 6.76E+02
N50 6.17E+00 1.46E+00 2.17E+00 2.49E+00 1.89E+01 2.49E+01 4.37E+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 71

Model data for rotavirus (CJN strain) in the human [1]
Dose Symptoms and infection No symptoms and infection Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 5 6 11
90 2 5 7
900 4 4 8
9000 3 4 7
9E+04 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 103 99.5 7 3.84
0
14.1
0
Beta Poisson 3.14 6 12.6
0.791
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 7.28E-02 9.93E-04 9.95E-04 9.96E-04 1.32E-01 1.46E-01 1.83E-01
N50 1.47E+03 6.55E-03 1.85E-02 4.58E-02 5.47E+06 1.82E+31 6.68E+122


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 125

Model data for rotavirus (CJN strain) in the human [1]
Dose Detectable shedding No detectable shedding Total
9E-03 0 7 7
0.09 0 7 7
0.9 1 6 7
9 8 3 11
90 4 3 7
900 3 5 8
9000 4 3 7
9E+04 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 157 148 7 3.84
0
14.1
0
Beta Poisson 9.42 6 12.6
0.151
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 9.6E-02 9.94E-04 9.96E-04 9.98E-04 1.59E-01 1.74E-01 2.05E-01
N50 9.61E+01 2.95E-03 1.59E-02 4.56E-02 2.83E+03 1.46E+04 1.58E+80


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 68

Model data for rotavirus (OSU (ATCC VR892)) in the pig [2]
Dose Infected Non-infected Total
0.9 0 3 3
9 0 3 3
90 5 1 6
900 3 0 3
2800 2 0 2
9000 3 0 3
56000 2 0 2
1.1E+07 2 0 2
2.2E+08 2 0 2
4.5E+09 2 0 2


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 1.1 -0.0019 9 3.84
1
16.9
0.999
Beta Poisson 1.1 8 15.5
0.998
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.


Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.73E-02 4.64E-03 7.21E-03 7.21E-03 3.28E-02 3.28E-02 3.28E-02
ID50/LD50/ETC* 4E+01 2.11E+01 2.11E+01 2.11E+01 9.61E+01 9.61E+01 1.49E+02
*Not a parameter of the exponential model; however, it facilitates comparison with other models.


Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model



References

  1. 1.0 1.1 1.2 1.3 1.4 1.5 Ward RL, Bernstein DI, Young EC, Sherwood JR, Knowlton DR, Schiff GM. Human rotavirus studies in volunteers: determination of infectious dose and serological response to infection. J. Infect. Dis. 1986 Nov;154(5):871-880. Full text
  2. 2.0 2.1 Payment P, Morin E. Minimal infective dose of the OSU strain of porcine rotavirus. Arch. Virol. 1990;112(3-4):277-282. Full text


Centers for Disease Control and Prevention. Epidemiology and Prevention of Vaccine-Preventable Diseases, 12th edition [Internet]. Washington, DC: Public Health Foundation; 2011. Available from: [1]

Cook SM, Glass RI, LeBaron CW, Ho MS. Global seasonality of rotavirus infections. Bull. World Health Organ. 1990;68(2):171-177. Full text

Greenberg HB, Estes MK. Rotaviruses: from pathogenesis to vaccination. Gastroenterology. 2009 May;136(6):1939-1951. Full text

Haas CN, Rose JB, Gerba CP. Quantitative Microbial Risk Assessment. New York, NY: John Wiley & Sons, Inc. 1999.

Heymann DL. Control of Communicable Diseases Manual. 18th ed. American Public Health Association; 2004.

Parashar UD, Hummelman EG, Bresee JS, Miller MA, Glass RI. Global illness and deaths caused by rotavirus disease in children. Emerging Infect. Dis. 2003 May;9(5):565-572. Full text

Payment P, Morin E. Minimal infective dose of the OSU strain of porcine rotavirus. Arch. Virol. 1990;112(3-4):277-282. Full text

Pichichero ME, Losonsky GA, Rennels MB, Disney FA, Green JL, Francis AB, et al. Effect of dose and a comparison of measures of vaccine take for oral rhesus rotavirus vaccine. The Maryland Clinical Studies Group. Pediatr. Infect. Dis. J. 1990 May;9(5):339-344. Abstract

Vesikari T, Ruuska T, Bogaerts H, Delem A, André F. Dose-response study of RIT 4237 oral rotavirus vaccine in breast-fed and formula-fed infants. Pediatr Infect Dis. 1985 Dec;4(6):622-625.

Ward RL, Bernstein DI, Young EC, Sherwood JR, Knowlton DR, Schiff GM. Human rotavirus studies in volunteers: determination of infectious dose and serological response to infection. J. Infect. Dis. 1986 Nov;154(5):871-880. Full text

Ward RL, Knowlton DR, Pierce MJ. Efficiency of human rotavirus propagation in cell culture. J. Clin. Microbiol. 1984 Jun;19(6):748-753. Full text