Escherichia coli enterohemorrhagic (EHEC): Dose Response Models

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Escherichia coli enterohemorrhagic (EHEC)

Author: Mark H. Weir

Overview: EHEC and HUS (Hemolytic uremic syndrome)

Escherichia coli resides as a commensal gram negative bacterium in the mammalian and bird intestinal tract and is excreted in feces. Enterohemorrhagic E. coli (EHEC; particularly serotype O157:H7) is a highly pathogenic variant which can cause life-threatening disease and has been the cause of many major outbreaks from fecally contaminated food (e.g., ground beef)[1] and drinking water as evidenced by the outbreak in Walkerton, Ontario following heavy rains[2]

EHEC is technically part of the larger group of Shiga toxin producing E. coli (STEC), many of which cause little or no disease. EHEC attaches to the large intestinal wall and produces ‘attaching and effacing lesions’, which can cause bloody or non-bloody diarrhea, as well hemorrhagic colitis and hemolytic uremic syndrome (HUS). Its principal reservoir is the bovine intestinal tract. It has a lower ID50 than other pathogenic E. coli types [3][4]

It is unethical to conduct feeding experiments on humans with EHEC due to its virulence. However, feeding experiments on animals have been conducted. Information from EHEC outbreaks in humans has also been used to inform dose response models [5].

Pai et al. (1986)[6] inoculated 3 day old rabbits intragastrically with EHEC O157:H7, measuring diarrhea and death as responses. Using the response of diarrhea, these data were fit to the beta-Poisson model by Haas et al. (2000).[7]

Cornick and Helgerson (2004)[8] dosed 3-month-old pigs with EHEC O157:H7 strain 86-24. The response was shedding of that strain in the feces.

Teunis et al. (2004)[5] examined dose response models consistent with EHEC O157:H7 outbreak data from a Japanese school. This outbreak was unusual in that the quantities of contaminated foods (a salad and a sauce) consumed by exposed persons were well defined, the foods were well mixed, and EHEC O157:H7 was actually quantified in the foods. Although this only allowed determination of a single dose for each population (31 CFU for pupils and 35 CFU for teachers), the response to this dose was known precisely since many persons were exposed (208 of 828 pupils infected; 7 of 43 teachers infected). This information was consistent with the dose response model of S. dysenteriae[9], but not with the dose response models of EHEC O157:H7 in rabbits[7] or EPEC in humans[9]. Under actual outbreak conditions, EHEC O157:H7 appeared more infectious than previously published dose response models for EHEC O157:H7 suggested. This analysis produced a beta-Poisson model with an alpha parameter for this model was 8.4E-2 and an ID50 of 5.52E3.

Strachan et al. (2005)[1] expanded upon the strategy of Teunis et al. (2004)[5] for assessing EHEC O157:H7 dose response models. They compiled information from several other outbreaks (in addition to the Japanese school outbreak, above) to fit a dose response model for EHEC O157:H7. This model fit poorly, probably due to variation in the populations affected and difficulty in estimating the ingested dose. However, comparing dose response models with the outbreak data, Strachan et al. (2005)[1] concluded that a pooled dose response model for Shigella (Crockett et al. 1996) was more consistent with outbreak data for E. coli O157 than other published dose response models for E. coli. This model and similar models are described in the Shigella chapter of this monograph.

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
213* [8] pig EHEC O157:H7, strain 86-24 oral (in food) 3 CFU shedding in feces exponential k=2.18E-04 3.18E+03
177 [6] rabbit EHEC UC741 (O157:H7) intragastric (w. NaHCO3) 7 CFU diarrhea beta-Poisson α = 4.87E-01 , N50 = 5.97E+05 5.97E+05
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.
Exponential and betapoisson model.jpg
Model data for Escherichia coli (EHEC O157:H7, strain 86-24) in the pig [8]
Dose Shedding in feces No shedding in feces Total
170 0 8 8
6000 6 2 8
4E+04 8 0 8

Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
Exponential 0.613 -0.000647 2 3.84
Beta Poisson 0.613 1 3.84
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 2.18E-04 9.40E-05 9.40E-05 1.20E-04 5.99E-04 5.99E-04 5.99E-04
ID50/LD50/ETC* 3.18E+03 1.16E+03 1.16E+03 1.16E+03 5.77E+03 7.37E+03 7.37E+03
*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

Model data for Escherichia coli (EHEC O157:H7) in the rabbit [6]
Dose Diarrhea No diarrhea Total
1E+05 1 2 3
1E+06 2 3 5
1E+07 5 0 5
1E+08 12 1 13
1E+09 5 0 5
3E+09 2 0 2
1E+10 6 0 6

Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
Exponential 64.1 61 6 3.84
Beta Poisson 3.12 5 11.1
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 4.87E-01 1.60E-01 2.20E-01 2.47E-01 9.55E+02 1.42E+03 1.94E+03
N50 5.97E+05 3.20E+03 2.88E+04 6.19E+04 2.54E+06 2.96E+06 5.10E+06

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


  1. 1.0 1.1 1.2 Strachan NJC et al. (2005) Dose response modelling of Escherichia coli O157 incorporating data from foodborne and environmental outbreaks. International Journal of Food Microbiology. 103(1), pp.35-47. Full Text Cite error: Invalid <ref> tag; name "Strachan_et_al_2005" defined multiple times with different content
  2. Auld H, MacIver D & Klaassen J (2004) Heavy rainfall and waterborne disease outbreaks: the Walkerton example. Journal of Toxicology and Environmental Health. Part A. 67(20-22), pp.1879-1887. Full Text
  3. Kaper JB, Nataro JP & Mobley HL (2004) Pathogenic Escherichia coli. Nature Reviews. Microbiology. 2(2), pp.123-140. Full Text
  4. Nataro JP & Kaper JB (1998) Diarrheagenic Escherichia coli. Clinical Microbiology Reviews. 11(1), pp.142-201. Full Text
  5. 5.0 5.1 5.2 Teunis P, Takumi K & Shinagawa K (2004) Dose response for infection by Escherichia coli O157:H7 from outbreak data. Risk Analysis: An Official Publication of the Society for Risk Analysis. 24(2), pp.401-407. Full Text
  6. 6.0 6.1 6.2 Pai CH, Kelly JK & Meyers GL (1986) Experimental infection of infant rabbits with verotoxin-producing Escherichia coli. Infection and Immunity. 51(1), pp.16-23. Full Text
  7. 7.0 7.1 Haas CN et al. (2000) Development of a dose-response relationship for Escherichia coli O157:H7. International Journal of Food Microbiology. 56(2-3), pp.153-159. Full Text
  8. 8.0 8.1 8.2 Cornick NA & Helgerson AF (2004) Transmission and infectious dose of Escherichia coli O157:H7 in swine. Applied and Environmental Microbiology. 70(9), pp.5331-5335. Full Text
  9. 9.0 9.1 Powell MR (2000) Dose-response envelope for Escherichia coli O157:H7. Quantitative Microbiology. 2, pp.141-163. Full Text