Rotavirus: Dose Response Models

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Rotavirus

Kyle S. Enger, MPH
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Overview

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

Although improved santitation 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). They can cause a 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).


Table 1. Summary of dose response data and models

Experiment number
Reference
Host type
Pathogen type
Route
Dose units
Response
Best fit model
Optimized parameters
ID50
70
Ward et al. 1986
human
CJN strain
oral
FFU
infection
Beta-Poisson
α = 2.53E-01
N50 = 6.17E+00
6.17
71
Ward et al. 1986
human
CJN strain
oral
FFU
infection
Beta-Poisson
α = 7.28E-02
N50 = 1.47E+03
1.47E+03
125
Ward et al. 1986
human
CJN strain
oral
FFU
infection
Beta-Poisson
α = 9.60E-02
N50 = 9.61E+01
9.61E+01
68
Payment & Morin 1990
pig
OSU strain
intragastric
particles
infection
Exponential
k = 1.73E-02
4.00E+01



Optimized models and fitting analysis

Optimization Output for experiment 1


Table 2. Model data for rotavirus (CJN strain) in the human
Dose
Positive
Negative
Total
9 (10-3)
0
7
7
9 (10-2)
0
7
7
9 (10-1)
1
6
7
9 (100)
8
3
11
9 (101)
6
1
7
9 (102)
7
1
8
9 (103)
5
2
7
9 (104)
3
0
3
Altboum et al. (2002)
Table 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
125.5
119.3
7
3.8
0.000
14.1
0.000
Beta-Poisson
6.2
6
12.6
0.401
Beta-Poisson is best fitting model


Table 4. Optimized parameters and LD50 for best fitting model (beta-Poisson); percentiles from 104 bootstrap iterations
Parameter
MLE estimate
Percentiles
0.5%
2.5%
5%
95%
97.5%
99.5%
a
2.53E-01
1.31E-01
1.53E-01
1.67E-01
5.18E-01
6.35E-01
2.09E+01
N50
6.17E+00
1.52E+00
2.07E+00
2.49E+00
1.89E+01
2.45E+01
4.17E+001
Figure 1. Parameter scatter plot for beta-Poisson model. Ellipses signify the 0.90, 0.95 and 0.99 confidence intervals.
Figure 2. Beta-Poisson model plot, with confidence bounds around the optimized model.


Optimization output for experiment 2

Table 5. Model data for rotavirus (CJN strain) in the human
Dose
Positive
Negative
Total
9 (10-3)
0
7
7
9 (10-2)
0
7
7
9 (10-1)
1
6
7
9 (100)
5
6
11
9 (101)
2
5
7
9 (102)
4
4
8
9 (103)
3
4
7
9 (104)
2
1
3
Ward et al. (1986)
Table 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
102.6
99.5
7
3.8
0.000
14.1
0.000
Beta-Poisson
3.1
6
12.6
0.791
Beta-Poisson is best fitting model


Table 7. Optimized parameters and LD50 for best fitting model (beta-Poisson); percentiles from 104 bootstrap iterations
Parameter
MLE estimate
Percentiles
0.5%
2.5%
5%
95%
97.5%
99.5%
a
7.28E-02
9.93E-04
9.95E-04
9.96E-04
1.32E-01
1.48E-01
1.89E-01
N50
1.47E+03
6.79E-03
1.87E-02
4.86E-02
5.76E+06
5.90E+34
7.21E+122
Figure 3. Parameter scatter plot for beta-Poisson model. Ellipses signify the 0.90, 0.95 and 0.99 confidence intervals.
Figure 4. Beta-Poisson model plot, with confidence bounds around the optimized model.




Optimization output for experiment 3

Table 8. Model data for rotavirus (CJN strain) in the human
Dose
Positive
Negative
Total
9 (10-3)
0
7
7
9 (10-2)
0
7
7
9 (10-1)
1
6
7
9 (100)
8
3
11
9 (101)
4
3
7
9 (102)
3
5
8
9 (103)
4
3
7
9 (104)
2
1
3
Ward et al. (1986)
Table 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
157.2
147.8
7
3.8
0.000
14.1
0.000
Beta-Poisson
9.4
6
12.6
0.151
Beta-Poisson is best fitting model


Table 10. Optimized parameters and LD50 for best fitting model (beta-Poisson); percentiles from 104 bootstrap iterations
Parameter
MLE estimate
Percentiles
0.5%
2.5%
5%
95%
97.5%
99.5%
a
9.60E-02
9.94E-04
9.96E-04
9.98E-04
1.59E-01
1.77E-01
2.15E-01
N50
9.61E+01
2.85E-03
1.59E-02
4.63E-02
3.07E+03
1.75E+04
6.98E+078
Figure 5. Parameter scatter plot for beta-Poisson model. Ellipses signify the 0.90, 0.95 and 0.99 confidence intervals.
Figure 6. Beta-Poisson model plot, with confidence bounds around the optimized model.

Optimization output for experiment 4

Table 11. Model data for rotavirus (OSU (ATCC VR892)) in the pig
Dose
Positive
Negative
Total
9 (10-1)
0
3
3
9 (100)
0
3
3
9 (101)
5
1
6
2.8 (103)
2
0
2
9 (103)
3
0
3
5.6 (104)
2
0
2
1.1 (107)
2
0
2
2.2 (108)
2
0
2
4.5 (109)
2
0
2
Payment & Morin (1990)
Table 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
1.1
0.00
9
3.8
1.000
16.9
0.999
Beta-Poisson
1.1
8
15.51
0.998
Exponential is best fitting model


Table 13. Optimized parameter(k) and ID50 for best fitting model (exponential); percentiles from 104 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
4.00E+01
2.11E+01
2.11E+01
2.11E+01
9.61E+01
9.61E+01
1.49E+02
Figure 7. Histogram of k parameter for exponential model.
Figure 8. Exponential model plot, with confidence bounds around the optimized model.

References

Centers for Disease Control and Prevention. Epidemiology and Prevention of Vaccine-Preventable Diseases, 12th edition [Internet]. Washington, DC: Public Health Foundation; 2011. Available from: [http://www.cdc.gov/vaccines/pubs/pinkbook/pink-chapters.htm]

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