Vibrio cholerae: Dose Response Models

General Overview

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.

Recommended Model

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

Exponential and betapoisson model.jpg

ID	Exposure Route	# of Doses	Agent Strain	Dose Units	Host type	Μodel	LD50/ID50	Optimized parameters	Response type	Reference
126	oral (with NaHCO3)	6.00	Inaba 569B	CFU	human	beta-Poisson	6.82E+03	a = 3.18E-01 N₅₀ = 6.82E+03	any diarrhea	Kotak, B. G., Kenefick, S. L., Fritz, D. L., Rousseaux, C. G., Prepas, E. E., & Hrudey, S. E. (1993). Occurrence and toxicological evaluation of cyanobacterial toxins in Alberta lakes and farm dugouts. Water Research, 27, 3.
128	oral (with NaHCO3)	6.00	Inaba 569B	CFU	human	beta-Poisson	3.88E+07	a = 1.10E-01 N₅₀ = 3.88E+07	cholera diarrhea	McCullough, N. ., & Elsele, C. . (1951). Experimental Human Salmonellosis: I. Pathogenicity of Strains of Salmonella Meleagridis and Salmonella Anatum Obtained from Spray-Dried Whole Egg. Oxford Journal of Infectious Diseases, 88(3). https://doi.org/https://doi.org/10.1093/infdis/88.3.278
167	oral (no NaHCO3)	7.00	Inaba 569B (classical)	CFU	human	beta-Poisson	2.91E+09	a = 1.31E-01 N₅₀ = 2.91E+09	diarrhea and culture positive	Levine, M. ., Black, R. ., , Clements, M. ., Fusco, P. ., Hughes, T. ., … Young, C. . (1982). Reactogenicity, immunogenicity and efficacy studies of Escherichia coli type 1 somatic pili parenteral vaccine in man. Scandinavian Journal of Infectious Diseases. Supplementum, 33, 83–95.
249	oral (with NaHCO3)	6.00	Inaba 569B	CFU	human	beta-Poisson	2.43E+02	a = 2.50E-01 N₅₀ = 2.43E+02	infection	Diringer, H. ., Roehmel, J. ., & Beekes, M. . (1998). Effect of repeated oral infection of hamsters with scrapie. Journal of General Virology, 79. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.541.3587&rep=rep1&type=pdf
35	oral (no NaHCO3)	7.00	Inaba 569B	CFU	human	beta-Poisson	6.36E+08	a = 1.98E-01 N₅₀ = 6.36E+08	diarrhea or culture positive	Hornick, R. B., Music, S. I., Wenzel, R. ., Cash, R. ., Libonati, J. P., Snyder, M. J., & Woodward, T. E. (1971). The Broad Street pump revisited: response of volunteers to ingested cholera vibrios. Bulletin of the New York Academy of Medicine, 47, 10. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1749960/

Exposure Route:

oral (with NaHCO3)

# of Doses:

6.00

Agent Strain:

Inaba 569B

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

6.82E+03

Optimized parameters: a = 3.18E-01 N₅₀ = 6.82E+03

Response type:

any diarrhea

Reference:

Occurrence and toxicological evaluation of cyanobacterial toxins in Alberta lakes and farm dugouts

**Human Inaba Strain 569 B**
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	55.2	51.9	5	3.84 5.88e-13	11.1 1.19e-10
Beta Poisson	3.3	51.9	4	3.84 5.88e-13	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
Parameter	MLE estimate	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

Exposure Route:

oral (with NaHCO3)

# of Doses:

6.00

Agent Strain:

Inaba 569B

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

3.88E+07

Optimized parameters: a = 1.10E-01 N₅₀ = 3.88E+07

Response type:

cholera diarrhea

Reference:

Experimental Human Salmonellosis: I. Pathogenicity of Strains of Salmonella Meleagridis and Salmonella Anatum Obtained from Spray-Dried Whole Egg

**Human Inaba Strain 569 B**
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	23.3	22.8	5	3.84 1.81e-06	11.1 0.000297
Beta Poisson	0.504	22.8	4	3.84 1.81e-06	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
Parameter	MLE estimate	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

Exposure Route:

oral (no NaHCO3)

# of Doses:

7.00

Agent Strain:

Inaba 569B (classical)

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

2.91E+09

Optimized parameters: a = 1.31E-01 N₅₀ = 2.91E+09

Response type:

diarrhea and culture positive

Reference:

Reactogenicity, immunogenicity and efficacy studies of Escherichia coli type 1 somatic pili parenteral vaccine in man.

**Human Inaba 569B**
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	14.9	7.58	6	3.84 0.00589	12.6 0.0207
Beta Poisson	7.36	7.58	5	3.84 0.00589	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
Parameter	MLE estimate	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

Highest quality

Exposure Route:

oral (with NaHCO3)

# of Doses:

6.00

Agent Strain:

Inaba 569B

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

2.43E+02

Optimized parameters: a = 2.50E-01 N₅₀ = 2.43E+02

Response type:

infection

Reference:

Effect of repeated oral infection of hamsters with scrapie

**Human Inaba Strain 569B**
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	92.4	91.2	5	3.84 0	11.1 0
Beta Poisson	1.16	91.2	4	3.84 0	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
Parameter	MLE estimate	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

Exposure Route:

oral (no NaHCO3)

# of Doses:

7.00

Agent Strain:

Inaba 569B

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

6.36E+08

Optimized parameters: a = 1.98E-01 N₅₀ = 6.36E+08

Response type:

diarrhea or culture positive

Reference:

The Broad Street pump revisited: response of volunteers to ingested cholera vibrios

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**
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	15.1	10.4	6	3.84 0.00126	12.6 0.0193
Beta Poisson	4.72	10.4	5	3.84 0.00126	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
Parameter	MLE estimate	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

Vibrio cholerae: Dose Response Models Dose response experiments

General Overview

Summary Data

Recommended Model

Please Note

References