General overview

Various species of Cryptosporidium infect most vertebrates. C. parvum infects cattle but can also infect humans; C. hominis appears to be restricted to humans, and began to be recognized in the early 2000s (Hunter 2005) [1]. The oocysts are the infective stage and are about 5 microns in size; they are excreted in feces and are transmitted to new hosts by the fecal-oral route. They are highly resistant to chlorine, but are vulnerable to ultraviolet light disinfection (AWWA 1999) [2]. The durability and infectiousness of the oocysts, as well as their documented ability to cause large outbreaks (Mac Kenzie et al., 1994) [3], means that control of Cryptosporidium is very important for drinking water treatment. Water treatment utilities should consider all surface water to be contaminated with oocysts (AWWA 1999) [2]. Effective control of Cryptosporidium is generally achieved in drinking water treatment through filtration yielding nonturbid water (<= 0.1 nephelometric turbidity unit) (AWWA 1999).

Cryptosporidiosis is a disease described by a self-limited watery diarrhea with an incubation period of 3 to 7 days (Miliotis & Bier 2003) [4]. Asymptomatic infections are also common in apparently healthy children and adults (Blaser 2002) [5]. However, the disease is particularly dangerous to people with HIV/AIDS because there is no effective treatment (Miliotis & Bier 2003) [4]. This can lead to lethal infections, or chronic disease lasting months or years that severely damages the gut.

Summary of Data

An experiment (DuPont et al., 1995) [6] from feeding an isolate from a calf (Iowa isolate) to human volunteers yields an exponential model with an ID50 of 165 oocysts (Teunis 1999) [7] also fitted a model to these data which is similar to the model presented here.

Messner et al. (2001) [8] described dose response model fits using the complete unpublished data set from DuPont et al., 1995 [6]:

  • Reanalysis of stool samples from the above experiment (DuPont et al., 1995) [6] using flow cytometry revealed that 2 individuals thought to be uninfected were actually infected (Messner 2001) [8].
  • Two other feeding studies (Okhuysen et al., 1999) [9] in human volunteers using different isolates yielded models with ID50s of 179 oocysts (UCP isolate, also from a calf) and 9 oocysts (TAMU isolate, from an infected veterinary student).

Messner et al. (2001) [8] fit the exponential model to these three datasets. This was appropriate for the Iowa and TAMU isolates, but the Beta-Poisson model provided a better fit than the exponential model for the UCP isolate. The UCP and TAMU datasets are smaller than the Iowa datasets.

Okhuysen et al. (2002) [10] also conducted a feeding study in adult humans using C. parvum originating from red deer (Moredun isolate).

Chappell et al. (1999) [10] also conducted a feeding study in humans using the Iowa isolate of C. parvum. Although the data were not published, they estimated an ID50 of 83 oocysts for volunteers lacking anti-C. parvum IgG, and an ID50 of 1,880 oocysts for volunteers who had anti-C. parvum IgG.


References

  1. Hunter, P. R., & Thompson RC. Andrew (2005).  The zoonotic transmission of Giardia and Cryptosporidium. International journal for parasitology. 35, 1181–1190.
  2. American Water Works Association (1999).  Waterborne pathogens: manual of water supply practices.
  3. Kenzie, W. R. Mac, Hoxie N. J., Proctor M. E., Gradus M. S., Blair K. A., Peterson D. E., et al. (1994).  A Massive Outbreak in Milwaukee of Cryptosporidium Infection Transmitted through the Public Water Supply. The New England Journal Medicine. 126(4), 
  4. Miliotis, M. D., & Bier J. W. (2003).  International handbook of foodborne pathogens. 125,
  5. Blaser, MJ., Smith PD., & Ravdin JI. (2003).  Infections of the Gastrointestinal Tract. PRACTICAL GASTROENTEROLOGY. 63.
  6. DuPont, H. L., Chappell C. L., Sterling C. R., Okhuysen P. C., Rose J. B., & Jakubowski W. (1995).  The infectivity of Cryptosporidium parvum in healthy volunteers. The New England journal of medicine. 332, 13.
  7. Teunis, P. F. M., Nagelkerke N. J. D., & Haas C. N. (1999).  Dose response models for infectious gastroenteritis. Risk Analysis. 19(6), 
  8. Messner, M. J., Chappell C. L., & Okhuysen P. C. (2001).  Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data. Water Research. 35, 16.
  9. Okhuysen, P. C., Chappell C. L., Crabb J. H., Sterling C. R., & Dupont H. L. (1999).  Virulence of three distinct Cryptospovidium parvum isolates for healthy adults. The Journal of infectious diseases. 180, 1275–1281.
  10. Chappell, C. L., Okhuysen P. C., Sterling C. R., Wang C., Jakubowski W., & Dupont H. L. (1999).  Infectivity of Cryptosporidium parvum in healthy adults with pre-existing anti-C. parvum serum immunoglobulin G.. The American journal of tropical medicine and hygiene. 60, 157–164.
ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
108 8 Iowa strain oocysts human exponential
k = 4.19E-03
LD50/ID50 = 1.65E+02

infection DuPont, H L., et al. "The infectivity of Cryptosporidium parvum in healthy volunteers." The New England journal of medicine. 332 (1995): 13.
139 8 Iowa isolate oocysts human exponential
k = 5.26E-03
LD50/ID50 = 1.32E+02

infection Messner, M J., C L. Chappell, and P C. Okhuysen. "Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data." Water Research. 35 (2001): 16.
140 4 TAMU isolate oocysts human exponential
k = 5.72E-02
LD50/ID50 = 1.21E+01

infection Messner, M J., C L. Chappell, and P C. Okhuysen. "Risk Assessment for Cryptosporidium: A Hierarchical Bayesian Analysis of Human Dose Response Data." Water Research. 35 (2001): 16.
141 4 UCP isolate oocysts human beta-Poisson a = 1.45E-01

LD50/ID50 = 1.79E+02
N50 = 1.79E+02
infection Coster, T S., et al. "Immune response, ciprofloxacin activity, and gender differences after human experimental challenge by two strains of enterotoxigenic Escherichia coli." Infection and immunity. 75 (2007): 1.
181 4 *C. hominis*, TU502 oocysts human beta-Poisson a = 2.7E-01

LD50/ID50 = 1.68E+01
N50 = 1.68E+01
diarrhea Okhuysen, P C., et al. "Infectivity of a Cryptosporidium parvum Isolate of Cervine Origin for Healthy Adults and Interferon-γ Knockout Mice." Journal of Infectious Diseases. 185 (2002): 9.
183 4 Moredun isolate oocysts human beta-Poisson a = 1.14E-01

LD50/ID50 = 4.55E+02
N50 = 4.55E+02
infection Blaser, M J., et al. "Experimental Campylobacter jejuni Infection of Adult Mice." Infection and Immunity. 39 (1983): 2.
Experiment ID:
108
# of Doses:
8
Agent Strain:
Iowa strain
Dose Units:
oocysts
Host type:
human
Μodel:
exponential
Optimized parameters:
k = 4.19E-03
LD50/ID50 = 1.65E+02

Reference:
Iowa strain data [1]
Dose Infected Non-infected Total
30 1 4 5
100 3 5 8
300 2 1 3
500 5 1 6
1000 2 0 2
1E+04 3 0 3
1E+05 1 0 1
1E+06 1 0 1

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 0.503 0.131 7 3.84 
0.717
14.1 
0.999
Beta Poisson 0.372 6 12.6 
0.999
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 4.19E-03 1.80E-03 2.22E-03 2.46E-03 7.52E-03 8.52E-03 1.12E-02
ID50/LD50/ETC* 1.65E+02 6.17E+01 8.14E+01 9.22E+01 2.82E+02 3.12E+02 3.84E+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

Experiment ID:
139
# of Doses:
8
Agent Strain:
Iowa isolate
Dose Units:
oocysts
Host type:
human
Μodel:
exponential
Optimized parameters:
k = 5.26E-03
LD50/ID50 = 1.32E+02

Reference:
Iowa isolate data [1]
Dose Infected Not infected Total
30 2 3 5
100 4 4 8
300 2 1 3
500 5 1 6
1000 2 0 2
1E+04 3 0 3
1E+05 1 0 1
1E+06 1 0 1

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 3.07 2 7 3.84 
0.157
14.1 
0.879
Beta Poisson 1.07 6 12.6 
0.983
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 5.26E-03 2.25E-03 2.75E-03 3.08E-03 1.03E-02 1.19E-02 1.60E-02
ID50/LD50/ETC* 1.32E+02 4.33E+01 5.80E+01 6.72E+01 2.25E+02 2.52E+02 3.08E+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

Best Fit
Experiment ID:
140
# of Doses:
4
Agent Strain:
TAMU isolate
Dose Units:
oocysts
Host type:
human
Μodel:
exponential
Optimized parameters:
k = 5.72E-02
LD50/ID50 = 1.21E+01

Reference:
TAMU data [1]
Dose Infected Non-infected Total
10 2 1 3
30 2 1 3
100 3 0 3
500 5 0 5

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 1.07 0.21 3 3.84 
0.647
7.81 
0.783
Beta Poisson 0.864 2 5.99 
0.649
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 5.72E-02 1.80E-02 1.92E-02 2.46E-02 2.65E+00 2.65E+00 2.65E+00
ID50/LD50/ETC* 1.21E+01 2.61E-01 2.61E-01 2.61E-01 2.82E+01 3.61E+01 3.84E+01
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

Exponential model plot, with confidence bounds around optimized model

Parameter histogram for exponential model (uncertainty of the parameter)

 

 


References

Experiment ID:
141
# of Doses:
4
Agent Strain:
UCP isolate
Dose Units:
oocysts
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.45E-01

LD50/ID50 = 1.79E+02
N50 = 1.79E+02
Reference:
UCP isolate [1]
Dose Infected Non-infected Total
500 3 2 5
1000 2 1 3
5000 2 3 5
1E+04 4 0 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 11.5 6.99 3 3.84 
0.0082
7.81 
0.00945
Beta Poisson 4.48 2 5.99 
0.107
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 1.45E-01 9.81E-04 4.63E-03 9.53E-03 1.27E+00 1.46E+02 9.10E+02
N50 1.79E+02 2.74E-13 7.60E-10 4.54E-09 2.62E+03 3.22E+03 6.10E+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


References

Experiment ID:
181
# of Doses:
4
Agent Strain:
*C. hominis*, TU502
Dose Units:
oocysts
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 2.7E-01

LD50/ID50 = 1.68E+01
N50 = 1.68E+01
Reference:
TU502 data [1]
Dose Diarrhea Not diarrhea Total
10 2 3 5
30 3 2 5
100 5 2 7
500 3 1 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 11.6 11.5 3 3.84 
0.000708
7.81 
0.00894
Beta Poisson 0.119 2 5.99 
0.942
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 2.7E-01 9.83E-04 9.85E-04 2.03E-03 6.60E+00 6.70E+02 3.19E+03
N50 1.68E+01 3.41E-16 9.86E-09 1.68E-06 7.15E+01 9.76E+01 6.59E+02

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

Experiment ID:
183
# of Doses:
4
Agent Strain:
Moredun isolate
Dose Units:
oocysts
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 1.14E-01

LD50/ID50 = 4.55E+02
N50 = 4.55E+02
Reference:
Moredunn isolate data [1]
Dose Infected Non-infected Total
100 2 2 4
300 2 3 5
1000 1 2 3
3000 3 1 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 7.37 6.16 3 3.84 
0.0131
7.81 
0.0611
Beta Poisson 1.21 2 5.99 
0.546
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 1.14E-01 9.79E-04 9.81E-04 9.82E-04 1.17E+03 2.25E+03 5.52E+03
N50 4.55E+02 2.13E-09 2.19E-06 1.55E-05 5.62E+05 3.59E+09 1.43E+16

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