Cryptosporidium parvum and Cryptosporidium hominis: Dose Response Models

Cryptosporidium parvum and Cryptosporidium hominis

Author: Kyle S. Enger

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). 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). The durability and infectiousness of the oocysts, as well as their documented ability to cause large outbreaks (Mac Kenzie et al., 1994), 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). 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). Asymptomatic infections are also common in apparently healthy children and adults (Blaser 2002). However, the disease is particularly dangerous to people with HIV/AIDS because there is no effective treatment (Miliotis & Bier 2003). This can lead to lethal infections, or chronic disease lasting months or years that severely damages the gut.

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Summary of Data

Cryptosporidium hominis

Chappell et al. (2006) describe a feeding study of C. hominis in adult humans. Although infection and diarrhea were both measured, only diarrhea demonstrated an approximately increasing response with dose. This is in contrast to the subsequent model fits for C. parvum, all of which use infection as the response.

Cryptosporidium parvum

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

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 (2001) described dose response model fits using the complete unpublished data set from DuPont et al., 1995:

• Reanalysis of stool samples from the above experiment (DuPont et al., 1995) using flow cytometry revealed that 2 individuals thought to be uninfected were actually infected (Messner 2001).
• Two other feeding studies (Okhuysen et al., 1999) 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) 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) also conducted a feeding study in adult humans using C. parvum originating from red deer (Moredun isolate).

Chappell et al. (1999) 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.

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50 140* human TAMU isolate oral 4 oocysts infection exponential k = 5.72E-02 1.21E+01 181 human C. hominis, TU502 oral 4 oocysts diarrhea beta-Poisson α= 2.7E-01 , N50 = 1.68E+01 1.68E+01 108 human Iowa strain oral 8 oocysts infection exponential k = 4.19E-03 1.65E+02 139 human Iowa isolate oral 8 oocysts infection exponential k = 5.26E-03 1.32E+02 183 human Moredun isolate oral 4 oocysts infection beta-Poisson α = 1.14E-01 , N50 = 4.55E+02 4.55E+02 141 human UCP isolate oral 4 oocysts infection beta-Poisson α = 1.45E-01 , N50 = 1.79E+02 1.79E+02 *This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

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Optimization Output for experiment 140

TAMU data 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.

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

Optimization Output for experiment 181

TU502 data 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

Optimization Output for experiment 108

Iowa strain data 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

Optimization Output for experiment 139

Iowa isolate data 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

Optimization Output for experiment 183

Moredunn isolate data 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

Optimization Output for experiment 141

UCP isolate 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

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References

American Water Works Association (1999) Waterborne Pathogens: Manual of Water Supply Practices. Denver, CO: American Water Works Association

Blaser, M.J. et al., eds. 2002. Infections of the Gastrointestinal Tract 2nd ed., Philadelphia: Lippincott Williams & Wilkins.  

Chappell, C.L. et al., 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(1), pp.157-164.  

Chappell, C.L. et al., 2006. Cryptosporidium hominis: experimental challenge of healthy adults. The American Journal of Tropical Medicine and Hygiene, 75(5), pp.851-857.

DuPont, H.L. et al., 1995. The infectivity of Cryptosporidium parvum in healthy volunteers. The New England Journal of Medicine, 332(13), pp.855-859.  

Hunter, P.R. & Thompson, R.C.A., 2005. The zoonotic transmission of Giardia and Cryptosporidium. International Journal for Parasitology, 35(11-12), pp.1181-1190.  

Mac Kenzie, W.R. et al., 1994. A massive outbreak in Milwaukee of cryptosporidium infection transmitted through the public water supply. The New England Journal of Medicine, 331(3), pp.161-167.  

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), pp.3934-3940.  

Miliotis, M., & Bier, J., eds. 2003. International Handbook of Foodborne Pathogens, New York: M. Dekker.  

Okhuysen, P.C. et al., 1999. Virulence of three distinct Cryptosporidium parvum isolates for healthy adults. The Journal of Infectious Diseases, 180(4), pp.1275-1281.

Okhuysen, P.C. et al., 2002. Infectivity of a Cryptosporidium parvum isolate of cervine origin for healthy adults and interferon-gamma knockout mice. The Journal of Infectious Diseases, 185(9), pp.1320-1325.

Teunis, P.F., Nagelkerke, N.J. & Haas, C.N., 1999. Dose response models for infectious gastroenteritis. Risk Analysis: An Official Publication of the Society for Risk Analysis, 19(6), pp.1251-1260.