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 ricewatery 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 antacid 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) 
LD_{50}/ID_{50}

249* 
^{[1]} 
human 
Inaba 569B 
oral (with NaHCO3) 
6 
CFU 
infection 
betaPoisson 
α= 2.50E01 , N_{50} = 2.43E+02 
2.43E+02

35 
^{[1]} 
human 
Inaba 569B 
oral (no NaHCO3) 
7 
CFU 
diarrhea or culture positive 
betaPoisson 
α = 1.98E01 , N_{50} = 6.36E+08 
6.36E+08

126 
^{[1]} 
human 
Inaba 569B 
oral (with NaHCO3) 
6 
CFU 
any diarrhea 
betaPoisson 
α = 3.18E01 , N_{50} = 6.82E+03 
6.82E+03

128 
^{[1]} 
human 
Inaba 569B 
oral (with NaHCO3) 
6 
CFU 
cholera diarrhea 
betaPoisson 
α = 1.10E01 , N_{50} = 3.88E+07 
3.88E+07

167 
^{[2]} 
human 
Inaba 569B (classical) 
oral (no NaHCO3) 
7 
CFU 
diarrhea and culture positive 
betaPoisson 
α = 1.31E01 , N_{50} = 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 ID_{50} among the models.
Optimization Output for experiment 249 (Vibrio cholerae)
Human Inaba Strain 569B ^{[1]}
Dose 
Infected 
Noninfected 
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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

92.4

91.2

5

3.84 0

11.1 0

Beta Poisson

1.16

4

9.49 0.885

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

2.5E01

1.14E01 
1.48E01 
1.66E01 
5.44E01 
6.55E01 
2.91E+00

N_{50}

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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

15.1

10.4

6

3.84 0.00126

12.6 0.0193

Beta Poisson

4.72

5

11.1 0.451

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

1.98E01

9.92E04 
9.92E04 
1.04E03 
3.20E01 
3.65E01 
4.07E01

N_{50}

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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

55.2

51.9

5

3.84 5.88e13

11.1 1.19e10

Beta Poisson

3.3

4

9.49 0.508

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

3.18E01

1.51E01 
1.84E01 
2.00E01 
6.52E01 
7.34E01 
1.66E+00

N_{50}

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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

23.3

22.8

5

3.84 1.81e06

11.1 0.000297

Beta Poisson

0.504

4

9.49 0.973

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

1.1E01

1.94E02 
3.52E02 
3.83E02 
6.23E+01 
4.54E+02 
1.10E+03

N_{50}

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 
χ^{2}_{0.95,1} pvalue 
χ^{2}_{0.95,mk} pvalue

Exponential

14.9

7.58

6

3.84 0.00589

12.6 0.0207

Beta Poisson

7.36

5

11.1 0.195

BetaPoisson fits better than exponential; cannot reject good fit for betaPoisson.


Optimized parameters for the betaPoisson model, from 10000 bootstrap iterations
Parameter

MLE estimate

Percentiles

0.5% 
2.5% 
5% 
95% 
97.5% 
99.5%

α

1.31E01

1.04E03 
1.04E03 
1.04E03 
1.67E01 
1.67E01 
1.67E01

N_{50}

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
 ↑ ^{1.0} ^{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): 11811191 Free Full Text via NIH
 ↑ ^{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), 4552.
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), 11811191