Vibrio cholerae: Dose Response Models

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Vibrio cholerae

(Cholera)
Author: Mark Weir


Vibrio cholerae and Cholera

The famous case of John Snow in London is well known, as an investigation of a cholera outbreak and provided the first in proof of a linkage between the presence of a pathogen in water and a water borne current outbreak. Cholera has remained a major health risk to populations around the world. Vibrio cholerae (V. cholerae) is a gram negative bacterium, the causative agent of cholera, which causes very watery stool, typically referred to rice-watery stool.


Person to person transmission has been typically assumed to be minimal probably due the dose response parameters. However, the main risk posed from this pathogen has always been considered from primary exposure, contaminated water.


http://www.cdc.gov/cholera/index.html




Summary Data

Hornick et al. (1971) has a broad repository of both human and animal data. The most interesting data sets in this study are human exposure where the onset of symptoms as well as indication of asymptomatic infection were monitored. Additionally, both diarrhea and cholera diarrhea (very different in appearance) were also monitored as symptoms.

Cash et al. (1974) has only one dataset which showed a significant trend between dose and observed probability of response. Interestingly, this study determined that in human volunteer feeding trials, the reduction of pH in subject stomachs decreased the overall dose required for a similar response. This was accomplished using sodium bicarbonate, essentially ant-acid treatment, thus demonstrating the effectiveness of higher pH in some protection from V. cholerea.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
249* [1] human Inaba 569B oral (with NaHCO3) 6 CFU infection beta-Poisson α= 2.50E-01 , N50 = 2.43E+02 2.43E+02
35 [1] human Inaba 569B oral (no NaHCO3) 7 CFU diarrhea or culture positive beta-Poisson α = 1.98E-01 , N50 = 6.36E+08 6.36E+08
126 [1] human Inaba 569B oral (with NaHCO3) 6 CFU any diarrhea beta-Poisson α = 3.18E-01 , N50 = 6.82E+03 6.82E+03
128 [1] human Inaba 569B oral (with NaHCO3) 6 CFU cholera diarrhea beta-Poisson α = 1.10E-01 , N50 = 3.88E+07 3.88E+07
167 [2] human Inaba 569B (classical) oral (no NaHCO3) 7 CFU diarrhea and culture positive beta-Poisson α = 1.31E-01 , N50 = 2.91E+09 2.91E+09
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.


*Recommended Model

Experiment number 249 is recommended model as it has lowest ID50 among the models.


Exponential and betapoisson model.jpg



Optimization Output for experiment 249 (Vibrio cholerae)

Human Inaba Strain 569B [1]
Dose Infected Non-infected Total
10 0 2 2
1000 3 1 4
1E+04 11 2 13
1E+05 7 1 8
1E+06 21 2 23
1E+08 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 92.4 91.2 5 3.84
0
11.1
0
Beta Poisson 1.16 4 9.49
0.885
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 2.5E-01 1.14E-01 1.48E-01 1.66E-01 5.44E-01 6.55E-01 2.91E+00
N50 2.43E+02 1.88E+01 4.82E+01 6.35E+01 1.52E+03 2.08E+03 3.60E+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 35 (Vibrio cholerae)

Please Note

The results from this experiment are not recommended for use, rather they are present for reference purposes. The confidence intervals are not complete for this experiment since the data is not allowing for a stable bootstrap outcome. It is recommended to use the recommended model as this data is likely just capable of passing the test of trend, but still likely suboptimal for dose response modeling purposes.


Human Inaba Strain 569B [1]
Dose Diarrhea or culture positive No diarrhea or culture positive Total
1E+04 0 2 2
1E+06 0 4 4
1E+07 0 4 4
1E+08 2 2 4
1E+09 1 1 2
1E+10 0 1 1
1E+11 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 15.1 10.4 6 3.84
0.00126
12.6
0.0193
Beta Poisson 4.72 5 11.1
0.451
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 1.98E-01 9.92E-04 9.92E-04 1.04E-03 3.20E-01 3.65E-01 4.07E-01
N50 6.36E+08 8.26E+05 8.26E+05 1.18E+08 5.33E+207 5.33E+207 8.87E+254


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 126 (Vibrio cholerae)

Human Inaba Strain 569 B [1]
Dose Diarrhea No diarrhea Total
10 0 2 2
1000 0 4 4
1E+04 9 4 13
1E+05 6 2 8
1E+06 20 3 23
1E+08 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 55.2 51.9 5 3.84
5.88e-13
11.1
1.19e-10
Beta Poisson 3.3 4 9.49
0.508
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 3.18E-01 1.51E-01 1.84E-01 2.00E-01 6.52E-01 7.34E-01 1.66E+00
N50 6.82E+03 1.68E+03 2.35E+03 2.75E+03 1.83E+04 2.25E+04 3.38E+04


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 128 (Vibrio cholerae)

Human Inaba Strain 569 B [1]
Dose Cholera diarrhea No cholera diarrhea Total
10 0 2 2
1000 0 4 4
1E+04 0 13 13
1E+05 1 7 8
1E+06 6 17 23
1E+08 1 1 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 23.3 22.8 5 3.84
1.81e-06
11.1
0.000297
Beta Poisson 0.504 4 9.49
0.973
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 1.1E-01 1.94E-02 3.52E-02 3.83E-02 6.23E+01 4.54E+02 1.10E+03
N50 3.88E+07 1.13E+06 1.47E+06 1.71E+06 7.30E+11 4.70E+12 6.70E+18


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 167 (Vibrio cholerae)

Human Inaba 569B [2]
Dose Diarrhea and culture positive No diarrhea and culture positive Total
1E+04 0 2 2
1E+06 0 4 4
1E+07 0 4 4
1E+08 2 2 4
1E+09 0 2 2
1E+10 0 1 1
1E+11 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 14.9 7.58 6 3.84
0.00589
12.6
0.0207
Beta Poisson 7.36 5 11.1
0.195
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 1.31E-01 1.04E-03 1.04E-03 1.04E-03 1.67E-01 1.67E-01 1.67E-01
N50 2.91E+09 3.23E+08 3.23E+08 3.23E+08 8.87E+254 8.87E+254 8.87E+254


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



References

  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Hornick, R.B., Music, S.I., Wenzel, R., Cash, R.A., Libonati, J.P., Snyder, M.J., Woodward, T.E. (1971) The Broad Street Pump Revisited: Response of Volunteers to Ingested Cholera Vibrios Bulletin New York Academy of Medicine 47(10): 1181-1191 Free Full Text via NIH
  2. 2.0 2.1 Cash, R.A., Music, S.I., Libonati, J.P., Snyder, M.J., Wenzel, R.P., Hornick, R.B. (1974) Response of Man to Infection with Vibrio cholerae. I Clinical Serologic and Bacteriologic Responses to a Known Inoculum Journal of Infectious Diseases 129(1): Full Text from JSTOR

Cash RA, Music SI, Libonati JP, Snyder MJ, Wenzel RP and Hornick RB (1974) Response of Man to Infection with Vibrio cholerae. I. Clinical, Serologic, and Bacteriologic Responses to a Known Inoculum. The Journal of Infectious Diseases 129(1), 45-52.

Hornick RB, Music SI, Wenzel R, Cash R, Libonati JP, Snyder MJ and Woodward TE (1971) The Broad Street pump revisited: response of volunteers to ingested cholera vibrios. Bulletin New York Academy of Medicine 47(10), 1181-1191