View source for Escherichia coli: Dose Response Models

==<center>'''Pathogenic ''Escherichia coli'''''</center>==

<center><big>'''Author: Kyle S. Enger'''</big></center>

==='''Overview'''===

''Escherichia coli'' typically resides as a symbiotic bacterium in the mammalian large intestine, benefiting itself as well as the host. However, there are several well-established pathotypes of disease-causing ''E. coli''<ref name="Kaper 2004">Kaper JB, Nataro JP & Mobley HL (2004) Pathogenic Escherichia coli. Nature Reviews. Microbiology. 2(2), pp.123-140. [http://www.nature.com/nrmicro/journal/v2/n2/pdf/nrmicro818.pdf Full text]</ref><ref name="Nataro 1998">Nataro JP & Kaper JB (1998) Diarrheagenic Escherichia coli. Clinical Microbiology Reviews. 11(1), pp.142-201. [http://cmr.asm.org/cgi/reprint/11/1/142 Full text] </ref>:

*Enteropathogenic (EPEC)
** Attaches to small intestinal wall and produces ‘attaching and effacing lesions’, in which microvilli are destroyed and the bacteria become perched on pedestals on the surface of the epithelial cell. This ability is encoded on the locus of enterocyte effacement (LEE) pathogenicity island.
** Causes an inflammatory response and diarrhea, but seldom in persons older than 2y; it can also be isolated from healthy older persons.
** Primarily found in developing countries.
* Enterohemorrhagic (EHEC)
** This is discussed in more detail in its own chapter.
* Enterotoxigenic (ETEC)
** Attaches to small intestinal wall.
** Produces a heat-labile (LT) and/or heat-stable (ST) toxins, both of which cause secretion from the small intestinal wall, leading to mild to severe watery diarrhea. LT is an immunogenic multisubunit protein similar to cholera enterotoxin. ST is a nonimmunogenic polypeptide containing 18-19 amino acids.
** Primarily found in developing countries and is a major cause of diarrhea in weaned infants, as well as traveler’s diarrhea.
** Can be shed even by immune asymptomatic individuals.
* Enteroaggregative (EAEC)
** Loosely classified group, some of which may be nonpathogenic.
** Produces a thick biofilm (‘stacked brick’ configuration) in the small or large intestines.
** Thought to cause persistent diarrhea (lasting >14 days).
** Can produce many different secretory toxins and cytotoxins, but not ST or LT.
* Enteroinvasive (EIEC)
** Actually invades the epithelial cells of the large intestine, where it multiplies.
** Usually produces watery diarrhea similar to that of EPEC and ETEC, sometimes inflammatory colitis or dysentery.
** Particularly closely related to ''Shigella'' sp. (which are now thought to be subgroups of ''E. coli''); much pathogenesis from EIEC and Shigella sp. is mediated by the pWR100 virulence plasmid.
* Diffusely adherent (DAEC)
** Attaches to the small intestinal wall and induces formation of projections which wrap around the bacterium.

Enterotoxigenic ''Escherichia coli'' (ETEC) is the most common type of diarrheagenic E. coli.<ref name="Qadri 2005">Qadri F, et al. (2005) Enterotoxigenic Escherichia coli in developing countries: epidemiology, microbiology, clinical features, treatment, and prevention. Clinical Microbiology Reviews. 18(3), pp.465-483. [http://cmr.asm.org/cgi/reprint/18/3/465 Full text] </ref> It may also be the most common cause of childhood diarrhea in the developing world, responsible for approximately 1/7 of diarrheal episodes in children aged less than 1 year and almost 1/4 of diarrheal episodes in 1-4 year olds.<ref name="Wenneras 2004">Wennerås C & Erling V (2004) Prevalence of enterotoxigenic Escherichia coli-associated diarrhoea and carrier state in the developing world. Journal of Health, Population, and Nutrition. 22(4), pp.370-382. [http://imsear.hellis.org/handle/123456789/542 Abstract]</ref> It can also cause severe dehydrating cholera-like disease in adults.<ref name="Qadri 2005"></ref> Diagnosis is complicated since many other Gram-negative bacteria produce similar toxins, so toxins as well as the ''E. coli'' bacterium must be tested for in order to yield accurate results.<ref name="Wenneras 2004"></ref>

ETEC can often be detected in apparently healthy people. In developing countries among healthy 0-11 month olds, and 1-4 year olds, 11.7% and 7.1%, respectively, are estimated to be colonized with ETEC.<ref name="Wenneras 2004"></ref>

Feeding studies of ETEC or EPEC in healthy volunteers first gave 2-3g of NaHCO<sub>3</sub>, which neutralizes stomach acid and reduces the infectious dose.<ref name="Levine et al. 1977"></ref> However, it has been suggested that food as a vehicle has a similar acid-neutralizing effect, so feeding studies given with NaHCO<sub>3</sub> may better represent natural foodborne infection.<ref name="Levine et al. 1977"></ref> ETEC and EPEC generally have high ID<sub>50</sub>, and partly as a consequence of this, they do not appear to be transmitted person-to-person; a study of ETEC-infected volunteers co-housed with uninfected volunteers did not result in any transmission of infection.<ref name="Levine 1980">Levine MM, et al. (1980) Lack of person-to-person transmission of enterotoxigenic Escherichia coli despite close contact. American Journal of Epidemiology. 111(3), pp.347-355. [http://aje.oxfordjournals.org/content/111/3/347.full.pdf+html Full text]</ref> Food was all served individually to the volunteers over the course of the experiment, so there was no opportunity for ETEC to spread via that route.<ref name="Levine 1980"></ref> 

http://www.cdc.gov/ecoli/index.html


==='''Summary of data and models'''===

There are many human feeding studies of various ''E. coli'' types and strains, which can be pooled in various ways to yield different dose response models. Many of these have small sample sizes and cannot be used on their own to reliably fit a dose response model. Most datasets for ''E. coli'' infections describe high levels of infection resulting from high doses. Lower doses remain to be investigated, and dose response models for infection are therefore uncertain. Another important factor is whether the dose was given with bicarbonate, which would neutralize some stomach acid and possibly increase infectivity. 

Haas, Rose, and Gerba (1999)<ref name="Haas 1999">Haas CN, Rose JB & Gerba CP (1999) Quantitative Microbial Risk Assessment. John Wiley & Sons, Inc.</ref> fitted beta-Poisson models to several pooled datasets describing the disease response from ETEC, EPEC and EIEC. Among these datasets were the EPEC strains O111<ref name="Ferguson et al. (1952)">Ferguson WW & June RC (1952) Experiments on feeding adult volunteers with Escherichia coli 111, B4, a coliform organism associated with infant diarrhea. American Journal of Hygiene. 55(2), pp.155-169. [http://aje.oxfordjournals.org/content/55/2/155.full.pdf+html Full text]</ref> and O55, as well as EIEC strains 4608 and 1624<ref name="DuPont et al. (1971)"></ref> with diarrhea as the end point. However, it mixed data from experiments in which bacteria were given with and without bicarbonate.

The best available dataset using infection as a response comes from an experiment (98) with 3 dose levels, feeding EIEC to adult humans.<ref name="DuPont et al. (1971)"></ref> 

Powell et al. (2000)<ref name="Powell 2000">Powell MR (2000) Dose-response envelope for Escherichia coli O157:H7. Quantitative Microbiology. 2, pp.141-163. [http://www.springerlink.com/content/k3t3768n75w16246/fulltext.pdf Full text]</ref> pooled 3 human trial datasets<ref name="Levine 1978">Levine MM, et al. (1978) Escherichia coli strains that cause diarrhoea but do not produce heat-labile or heat-stable enterotoxins and are non-invasive. Lancet. 1(8074), pp.1119-1122. [http://www.sciencedirect.com/science/article/pii/S0140673678902994 Abstract]</ref><ref name="Bieber 1998">Bieber D, et al. (1998) Type IV pili, transient bacterial aggregates, and virulence of enteropathogenic Escherichia coli. Science (New York, N.Y.). 280(5372), pp.2114-2118. [http://www.sciencemag.org/content/280/5372/2114.full Full text]</ref> for EPEC to produce a beta-Poisson model and a Weibull-gamma model.

Additional pooling analyses for this chapter were conducted on the basis of pathotype (ETEC or EPEC), whether the dose was given with bicarbonate, and the nature of the response (disease or infection), incorporating more data from the literature than the previous two published models. Since some combinations of these factors lacked data, analyses could only be done for ETEC disease (buffered or unbuffered), EPEC disease (buffered), ETEC infection (unbuffered), and EPEC infection (buffered). The pooled datasets for infection contained mostly positive responses, and therefore their behavior at low doses is very uncertain. For the pooled analyses describing disease, datasets were excluded if they contributed significantly (P < 0.05) to the -2 log likelihood of the model given the data.<ref name="Haas 1999"></ref> Two experiments<ref name="DuPont et al. (1971)"></ref> examining diarrhea from EIEC were also pooled.


{{DRSummaryTableStart|agent=''Escherichia coli''}}
{{DRSummaryTablePreferredModel|expID= 98 |refer=DuPont et al. (1971)|reference=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|host= human |agentStrain= EIEC 1624 |route= oral (in milk) |nDoses= 3 |doseUnits= CFU |response= positive stool isolation |bestFitModel=beta-Poisson|parameters=&alpha; =  1.55E-01 , N<sub>50</sub> =  2.11E+06  |N50= 2.11E+06}}
{{DRSummaryNonpreferredModel|expID= 39 |refer= DuPont et al. (1971)|reference=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|host= human |agentStrain= EIEC 4608 |route= oral (in milk) |nDoses= 3 |doseUnits= CFU |response= mild to severe diarrhea |bestFitModel=exponential|parameters=k =  9.7E-09 |N50= 7.14E+07 }}
{{DRSummaryNonpreferredModel|expID= 40 |refer= DuPont et al. (1971)|reference=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|host= human |agentStrain= EIEC 1624 |route= oral (in milk) |nDoses= 3 |doseUnits= CFU |response= mild to severe diarrhea |bestFitModel=exponential|parameters=k =  1.22E-08 |N50= 5.7E+07 }}
{{DRSummaryTableNonpreferredModel|expID= 42 |refer = June et al. (1953)|reference=June RC, Ferguson WW & Worfel MT (1953) Experiments in feeding adult volunteers with Escherichia coli 55, B5, a coliform organism associated with infant diarrhea. American Journal of Hygiene. 57(2), pp.222-236. [http://aje.oxfordjournals.org/content/57/2/222.full.pdf Full text]|host= human |agentStrain= ETEC O55 (in paper as “type 55, B5”) |route= oral |nDoses= 4 |doseUnits= CFU|response= slight to severe illness |bestFitModel=beta-Poisson|parameters=&alpha; =  8.7E-02 , N<sub>50</sub> =  2.05E+05 |N50= 2.05E+05 }}
{{DRSummaryTableNonpreferredModel|expID= 43 |refer = Ferguson et al. (1952)|reference=Ferguson WW & June RC (1952) Experiments on feeding adult volunteers with Escherichia coli 111, B4, a coliform organism associated with infant diarrhea. American Journal of Hygiene. 55(2), pp.155-169. [http://aje.oxfordjournals.org/content/55/2/155.full.pdf+html Full text]|host= human |agentStrain= ETEC O111 (in paper as "E. coli 111, B4") |route= oral |nDoses= 4 |doseUnits= CFU|response= slight to severe illness |bestFitModel=beta-Poisson|parameters=&alpha; =  2.63E-01 , N<sub>50</sub> =  3.56E+06 |N50= 3.56E+06 }}
{{DRSummaryTableNonpreferredModel|expID= 165 |refer= Levine et al. 1977|reference=Levine MM, et al. (1977) Diarrhea caused by Escherichia coli that produce only heat-stable enterotoxin. Infection and Immunity. 17(1), pp.78-82. [http://iai.asm.org/cgi/reprint/17/1/78 Full text]|host= human |agentStrain= ETEC 214-4 (ST) |route= oral (in milk) |nDoses= 3 |doseUnits= CFU|response= diarrhea or vomiting |bestFitModel=beta-Poisson|parameters=&alpha; =  2.5E-01 , N<sub>50</sub> =  9.1E+07|N50= 9.1E+07 }}
{{DRSummaryNonpreferredModelfourrefs|expID= 38, 39, 40, 42, 99, 144|refer1=DuPont et al. (1971)|reference1=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|refer2=June et al. (1953)|reference2=June, R.C., Ferguson, W.W. & Worfel, M.T., 1953. Experiments in feeding adult volunteers with Escherichia coli 55, B5, a coliform organism associated with infant diarrhea. ''American Journal of Hygiene'', 57(2), pp.222-236. [http://aje.oxfordjournals.org/content/57/2/222.full.pdf Full text]|refer3=Graham et al. (1983)|reference3=Graham DY, Estes MK & Gentry LO (1983) Double-blind comparison of bismuth subsalicylate and placebo in the prevention and treatment of enterotoxigenic Escherichia coli-induced diarrhea in volunteers. Gastroenterology 85(5), pp.1017-1022. [http://ukpmc.ac.uk/abstract/MED/6352386/reload=0;jsessionid=CFB7897160D474F82BB8E76CD3525EAA.jvm4 Abstract] |refer4=Haas 1999|reference4=Haas CN, Rose JB, and Gerba CP. 1999. Quantitative Microbial Risk Assessment. John Wiley & Sons. Inc| host= human |agentStrain= ETEC B7A |route= oral (in milk) |nDoses= 15 |doseUnits= CFU|response= mild to severe diarrhea |bestFitModel=beta-Poisson|parameters=&alpha; =  1.78E-01 , N<sub>50</sub> =  8.6E+07  |N50= 8.6E+07 }}
{{DRSummaryTableNonpreferredthreerefs|expID= 214, 216, 217 |refer1=Bieber 1998|reference1=COMPLETE REF HERE|refer2=Levine 1978 |reference2= Levine MM, et al. (1978). Escherichia coli strains that cause diarrhoea but do not produce heat-labile or heat-stable enterotoxins and are non-invasive. Lancet. 1(8074), pp.1119-1122. [http://www.sciencedirect.com/science/article/pii/S0140673678902994 Abstract]|refer3=Powell 2000|reference3= |host= human |agentStrain= EPEC B171-8 (serotype O11:NM) |route= oral (with NaHCO3) |nDoses= 8 |doseUnits= CFU |response= diarrhea |bestFitModel=beta-Poisson|parameters=&alpha; =  2.21E-01 , N<sub>50</sub> =  6.85E+07 |N50= 6.85E+07 }}
{{DRSummaryTableNonpreferredsixrefs|expID= 142, 143, 144, 145, 147, 151, 161, 162, 163, 164, 168, 169, 170, 172 |refer1=Coster TS 2007|reference1=Coster TS et al. (2007) Immune response, ciprofloxacin activity, and gender differences after human experimental challenge by two strains of enterotoxigenic Escherichia coli. Infection and Immunity. 75(1), pp.252-259. [http://iai.asm.org/cgi/reprint/75/1/252 Full text]|refer2=Graham et al. (1983)|reference2 = |refer3 = | Levine MM, et al. (1979)|reference3=Levine MM, et al. (1979) Immunity to enterotoxigenic Escherichia coli. Infection and Immunity. 23(3), pp.729-736. [http://iai.asm.org/cgi/reprint/23/3/729 Full text]|refer4= Clements ML, et al. (1981) |reference4 = Clements ML, et al. (1981) Lactobacillus prophylaxis for diarrhea due to enterotoxigenic Escherichia coli. Antimicrobial Agents and Chemotherapy 20(1), pp.104-108. [http://aac.asm.org/cgi/reprint/20/1/104 Full text] |refer5=Levine MM, et al. (1982)|reference5= Levine MM, et al. (1982) Reactogenicity, immunogenicity and efficacy studies of Escherichia coli type-1 somatic pili parenteral vaccine in man. Scandinavian Journal of Infectious Diseases. Suppl. 33, pp.83-95. [http://www.ncbi.nlm.nih.gov/pubmed/6127806 Abstract]|refer6=Levine 1980| reference6 = |host= human |agentStrain= ETEC B7A |route= oral (with NaHCO3) |nDoses= 19 |doseUnits= CFU |response= diarrhea |bestFitModel=beta-Poisson|parameters=&alpha; =  7.54E-02 , N<sub>50</sub> =  1.7E+06  |N50= 1.7E+06  }}
{{DRSummaryTableNonpreferredthreerefs|expID= 38, 42, 99, 165 |refer1=DuPont et al. (1971)|reference1=COMPLETE REF HERE|refer2= June et al. (1953)|reference2= |refer3=Levine et al. 1977|reference3= | host= human |agentStrain= ETEC B7A |route= oral (in milk) |nDoses= 11 |doseUnits= CFU |response= mild to severe diarrhea |bestFitModel=beta-Poisson|parameters=&alpha; =  2.06E-01 , N<sub>50</sub> =  1.28E+08 |N50= 1.28E+08}}
{{DRSummaryTableNonpreferredthreerefs|expID= 153, 157, 159, 214, 216, 217 |refer1=Tacket CO, et al. (2000)|reference1=Tacket CO, et al. (2000) Role of EspB in experimental human enteropathogenic Escherichia coli infection. Infection and Immunity. 68(6), pp.3689-3695. [http://iai.asm.org/cgi/reprint/68/6/3689 Full text]|refer2=Bieber 1998|reference2= |refer3=Levine 1978|reference3= |host= human |agentStrain= EPEC E2348/69 (O127:H6) |route= oral (w. 2g NaHCO3) |nDoses= 11 |doseUnits= CFU |response= diarrhea |bestFitModel=beta-Poisson|parameters=&alpha; =  1.62E-01 , N<sub>50</sub> =  9.98E+07  |N50= 9.98E+07 }}
{{DRSummaryTableNonpreferredthreerefs|expID= 154, 156, 158, 160, 219, 220, 221 |refer1=Tacket CO, et al. (2000)|reference1=COMPLETE REF HERE|refer2=Donnenberg MS, et al. (1993) |reference2=Donnenberg MS, et al. (1993) Role of the eaeA gene in experimental enteropathogenic Escherichia coli infection. The Journal of Clinical Investigation. 92(3), pp.1412-1417. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC288285/pdf/jcinvest00041-0308.pdf Full text]|refer3=Levine 1978|reference3= |host= human |agentStrain= EPEC E2348/69 (O127:H6) |route= oral (w. 2g NaHCO3) |nDoses= 13 |doseUnits= CFU |response= shedding in feces |bestFitModel=exponential|parameters=k =  1.95E-06 |N50= 3.56E+05 }}
{{DRSummaryNonpreferredModel|expID= 39, 40 |refer=DuPont et al. (1971)|reference=COMPLETE REF HERE|host= human |agentStrain= EIEC 4608 |route= oral (in milk) |nDoses= 6 |doseUnits= CFU|response= mild to severe diarrhea |bestFitModel=exponential|parameters=k =  1.07E-08 |N50= 6.5E+07 }}
{{DRSummaryTableNonpreferredModel|expID= 96, 100, 166 |refer=SHORT REF HERE|reference=COMPLETE REF HERE|host= human |agentStrain= ETEC B7A |route= oral (in milk) |nDoses= 7 |doseUnits= CFU|response= positive stool isolation |bestFitModel=beta-Poisson|parameters=&alpha; =  3.75E-01 , N<sub>50</sub> =  1.78E+05 |N50= 1.78E+05 }}
{{DRSummaryTableEnd}}


[[File:Exponential and betapoisson model.jpg|thumb|none|550px]]

==='''Optimization Output for experiment 98'''===

{{DRExperimentDataTable3|title=''Escherichia coli'' (EIEC 1624) in the human model data|refer= DuPont et al. (1971)|reference=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|pos=Positive stool isolation|neg=No positive stool isolation|d1=1E+04|p1=0|n1=5|t1=5|d2=1E+06|p2=5|n2=4|t2=9|d3=1E+08|p3=3|n3=2|t3=5}}


{{DRFit|title=Goodness of fit and model selection|devE=28.6|devB=1.38|delta=27.2|DFE=2|DFB=1|X2bPbetter=3.84|pbPbetter=1.82e-07|X2GOFe=5.99|pGOFe=6.18e-07|X2GOFb=3.84|pGOFb=0.24|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=1.55E-01|p5a=1.26E-03|p25a=1.26E-03|p50a=2.84E-02|p950a=1.84E+01|p975a=1.29E+02|p995a=1.90E+02|MLEN=2.11E+06|p5N= 1.73E+05|p25N= 2.95E+05|p50N= 2.95E+05|p950N= 7.85E+08|p975N=9.22E+140|p995N=9.22E+140}}


[[File:BPscatter ID98.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel ID98.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 39'''===

{{DRExperimentDataTable3|title=''Escherichia coli'' (EIEC 4608) in the human model data|refer = DuPont et al. (1971)|reference=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|pos=Mild to severe diarrhea|neg=No mild to severe diarrhea|d1=1E+04|p1=0|n1=5|t1=5|d2=1E+06|p2=0|n2=5|t2=5|d3=1E+08|p3=5|n3=3|t3=8}}


{{DRFit|title=Goodness of fit and model selection|devE=0.0986|devB=0.1|delta=-0.00188|DFE=2|DFB=1|X2bPbetter=3.84|pbPbetter=1|X2GOFe=5.99|pGOFe=0.952|X2GOFb=3.84|pGOFb=0.751|interpretation=Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.}}


{{DRConfidenceExponential|title=Optimized k parameter for the exponential model, from 10000 bootstrap iterations|MLEk=9.7E-09|p5k=2.85E-09|p25k=2.86E-09|p50k=4.66E-09|p950k=2.04E-08|p975k=2.04E-08|p995k=5.07E-08|N50type=ID50/LD50/ETC|MLEN=7.14E+07|p5N=1.37E+07|p25N=3.40E+07|p50N=3.40E+07|p950N=1.49E+08|p975N=2.43E+08|p995N=2.44E+08}}


[[File:ExpHisto ID39.png|thumb|left|500px|'''Parameter histogram for exponential model (uncertainty of the parameter)''']][[File:ExpModel ID39.png|thumb|none|500px|'''Exponential model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 40'''===

{{DRExperimentDataTable3|title=''Escherichia coli'' (EIEC 1624) in the human model data|refer = DuPont et al. (1971)|reference=DuPont HL, et al. (1971) Pathogenesis of Escherichia coli diarrhea. The New England Journal of Medicine. 285(1), pp.1-9. [http://www.nejm.org/doi/pdf/10.1056/NEJM197107012850101 Full text]|pos=Mild to severe diarrhea|neg=No mild to severe diarrhea|d1=1E+04|p1=0|n1=5|t1=5|d2=1E+06|p2=1|n2=8|t2=9|d3=1E+08|p3=3|n3=2|t3=5}}


{{DRFit|title=Goodness of fit and model selection|devE=2.99|devB=0.0156|delta=2.98|DFE=2|DFB=1|X2bPbetter=3.84|pbPbetter=0.0845|X2GOFe=5.99|pGOFe=0.224|X2GOFb=3.84|pGOFb=0.901|interpretation=Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.}}


{{DRConfidenceExponential|title=Optimized k parameter for the exponential model, from 10000 bootstrap iterations|MLEk=1.22E-08|p5k=1.97E-09|p25k=2.19E-09|p50k=4.40E-09|p950k=4.03E-08|p975k=1.17E-07|p995k=2.50E-07|N50type=ID50/LD50/ETC|MLEN=5.7E+07|p5N=2.77E+06|p25N=5.92E+06|p50N=1.72E+07|p950N=1.58E+08|p975N=3.17E+08|p995N=3.52E+08}}


[[File:ExpHisto ID40.png|thumb|left|500px|'''Parameter histogram for exponential model (uncertainty of the parameter)''']][[File:ExpModel ID40.png|thumb|none|500px|'''Exponential model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 42'''===

{{DRExperimentDataTable4|title=''Escherichia coli'' (ETEC O55 (in paper as “type 55, B5”)) in the human model data|refer = June et al. (1953)|reference=June, R.C., Ferguson, W.W. & Worfel, M.T., 1953. Experiments in feeding adult volunteers with Escherichia coli 55, B5, a coliform organism associated with infant diarrhea. ''American Journal of Hygiene'', 57(2), pp.222-236. [http://aje.oxfordjournals.org/content/57/2/222.full.pdf Full text]|pos=Slight to severe illness|neg=No slight to severe illness|d1=1.43E+08|p1=6|n1=2|t1=8|d2=1.73E+09|p2=5|n2=2|t2=7|d3=5.33E+09|p3=6|n3=2|t3=8|d4=1.6E+10|p4=7|n4=1|t4=8}}


{{DRFit|title=Goodness of fit and model selection|devE=35|devB=0.486|delta=34.5|DFE=3|DFB=2|X2bPbetter=3.84|pbPbetter=4.2e-09|X2GOFe=7.81|pGOFe=1.21e-07|X2GOFb=5.99|pGOFb=0.784|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=8.7E-02|p5a=9.87E-04|p25a=1.02E-03|p50a=1.67E-02|p950a=3.57E-01|p975a=4.67E-01|p995a=7.83E-01|MLEN=2.05E+05|p5N=3.40E-09|p25N=4.31E-06|p50N=2.31E-04|p950N=1.30E+08|p975N=2.09E+08|p995N=5.13E+08}}


[[File:BPscatter ID42.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel ID42.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 43'''===

{{DRExperimentDataTable4|title=''Escherichia coli'' (ETEC O111 (in paper as “E. coli 111, B4”)) in the human model data|refer = Ferguson et al. (1952)|reference=Ferguson WW & June RC (1952) Experiments on feeding adult volunteers with Escherichia coli 111, B4, a coliform organism associated with infant diarrhea. American Journal of Hygiene. 55(2), pp.155-169. [http://aje.oxfordjournals.org/content/55/2/155.full.pdf+html Full text]|pos=Slight to severe illness|neg=No slight to severe illness|d1=7E+06|p1=7|n1=4|t1=11|d2=5.31E+08|p2=8|n2=4|t2=12|d3=6.5E+09|p3=11|n3=0|t3=11|d4=9E+09|p4=12|n4=0|t4=12}}


{{DRFit|title=Goodness of fit and model selection|devE=39.8|devB=6.38|delta=33.4|DFE=3|DFB=2|X2bPbetter=3.84|pbPbetter=7.5e-09|X2GOFe=7.81|pGOFe=1.19e-08|X2GOFb=5.99|pGOFb=0.0412|interpretation=Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=2.63E-01|p5a=9.92E-04|p25a=7.95E-02|p50a=1.00E-01|p950a=4.71E-01|p975a=5.53E-01|p995a=1.48E+01|MLEN=3.56E+06|p5N=6.89E-01|p25N=1.15E+03|p50N=2.08E+03|p950N=1.85E+07|p975N=2.49E+07|p995N=4.18E+07}}


[[File:BPscatter ID43.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel ID43.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 165'''===

{{DRExperimentDataTable3|title=''Escherichia coli'' (ETEC 214-4 (ST)) in the human model data|refer=Levine et al. 1977|reference=Levine MM, et al. (1977) Diarrhea caused by Escherichia coli that produce only heat-stable enterotoxin. Infection and Immunity. 17(1), pp.78-82. [http://iai.asm.org/cgi/reprint/17/1/78 Full text]|pos=Diarrhea or vomiting|neg=No diarrhea or vomiting|d1=1E+06|p1=0|n1=4|t1=4|d2=1E+08|p2=3|n2=2|t2=5|d3=1E+10|p3=4|n3=1|t3=5}}


{{DRFit|title=Goodness of fit and model selection|devE=15.9|devB=0.531|delta=15.3|DFE=2|DFB=1|X2bPbetter=3.84|pbPbetter=9e-05|X2GOFe=5.99|pGOFe=0.000359|X2GOFb=3.84|pGOFb=0.466|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=2.5E-01|p5a=9.94E-04|p25a=9.94E-04|p50a=9.94E-04|p950a=1.76E+02|p975a=7.32E+02|p995a=7.32E+02|MLEN=9.1E+07|p5N=3.05E+04|p25N=4.09E+04|p50N=5.00E+04|p950N=3.20E+08|p975N=6.91E+08|p995N=6.91E+08}}


[[File:BPscatter ID165.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel ID165.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 38, 39, 40, 42, 99, 144'''===

{{DRexperimentDataTable15fourrefs|title=''E. coli'' disease (ETEC, EPEC, EIEC) in the human model data|pos=Mild to severe diarrhea|neg=No mild to severe diarrhea|d1=1E+04|p1=0|n1=5|t1=5|d2=1E+04|p2=0|n2=5|t2=5|d3=1E+06|p3=0|n3=5|t3=5|d4=1E+06|p4=1|n4=8|t4=9|d5=1E+08|p5=1|n5=4|t5=5|d6=1E+08|p6=5|n6=3|t6=8|d7=1E+08|p7=3|n7=2|t7=5|d8=1E+08|p8=2|n8=3|t8=5|d9=1.43E+08|p9=6|n9=2|t9=8|d10=2.7E+08|p10=9|n10=7|t10=16|d11=1.73E+09|p11=5|n11=2|t11=7|d12=5.33E+09|p12=6|n12=2|t12=8|d13=1E+10|p13=4|n13=1|t13=5|d14=1E+10|p14=3|n14=2|t14=5|d15=1.6E+10|p15=7|n15=1|t15=8}}


{{DRFit|title=Goodness of fit and model selection|devE=119|devB=6.56|delta=113|DFE=14|DFB=13|X2bPbetter=3.84|pbPbetter=0|X2GOFe=23.7|pGOFe=0|X2GOFb=22.4|pGOFb=0.924|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=1.78E-01|p5a=9.39E-02|p25a=1.09E-01|p50a=1.19E-01|p950a=3.21E-01|p975a=3.63E-01|p995a=4.77E-01|MLEN=8.6E+07|p5N=1.75E+07|p25N=2.62E+07|p50N=3.25E+07|p950N=2.63E+08|p975N=3.23E+08|p995N=5.21E+08}}


[[File:BPscatter_ID38_39_40_42_99_144.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel_ID38_39_40_42_99_144.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 214, 216, 217'''===

{{DRExperimentDataTable8noref|title=EPEC disease in the human model data|pos=Diarrhea |neg=No diarrhea |d1=1E+06|p1=0|n1=4|t1=4|d2=1E+06|p2=1|n2=4|t2=5|d3=1E+08|p3=1|n3=4|t3=5|d4=5E+08|p4=3|n4=2|t4=5|d5=2.5E+09|p5=6|n5=0|t5=6|d6=1E+10|p6=3|n6=2|t6=5|d7=1E+10|p7=5|n7=0|t7=5|d8=2E+10|p8=2|n8=0|t8=2}}


{{DRFit|title=Goodness of fit and model selection|devE=31.8|devB=11.2|delta=20.6|DFE=7|DFB=6|X2bPbetter=3.84|pbPbetter=5.69e-06|X2GOFe=14.1|pGOFe=4.37e-05|X2GOFb=12.6|pGOFb=0.0813|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=2.21E-01|p5a=9.31E-02|p25a=1.18E-01|p50a=1.27E-01|p950a=1.25E+00|p975a=7.41E+02|p995a=1.29E+04|MLEN=6.85E+07|p5N=6.14E+06|p25N=1.11E+07|p50N=1.52E+07|p950N=6.32E+08|p975N=7.69E+08|p995N=1.09E+09}}


[[File:BPscatter_ID214_216_217.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel_ID214_216_217.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 142, 143, 144, 145, 147, 151, 161, 162, 163, 164, 168, 169, 170, 172'''===

{{DRExperimentDataTable19norefs|title=EPEC disease in the human model data|pos=Diarrhea |neg=No diarrhea |d1=1E+06|p1=3|n1=3|t1=6|d2=1E+07|p2=6|n2=9|t2=15|d3=1E+08|p3=6|n3=1|t3=7|d4=1E+08|p4=7|n4=4|t4=11|d5=1E+08|p5=7|n5=5|t5=12|d6=1E+08|p6=9|n6=3|t6=12|d7=1E+08|p7=6|n7=3|t7=9|d8=1E+08|p8=4|n8=2|t8=6|d9=1E+08|p9=3|n9=1|t9=4|d10=1E+08|p10=4|n10=0|t10=4|d11=2.7E+08|p11=9|n11=7|t11=16|d12=5E+08|p12=19|n12=8|t12=27|d13=1E+09|p13=5|n13=3|t13=8|d14=1E+09|p14=7|n14=1|t14=8|d15=1E+09|p15=5|n15=5|t15=10|d16=1E+10|p16=8|n16=0|t16=8|d17=1E+10|p17=5|n17=4|t17=9|d18=1E+10|p18=9|n18=3|t18=12|d19=1E+10|p19=9|n19=5|t19=14}}


{{DRFit|title=Goodness of fit and model selection|devE=412|devB=19.1|delta=393|DFE=18|DFB=17|X2bPbetter=3.84|pbPbetter=0|X2GOFe=28.9|pGOFe=0|X2GOFb=27.6|pGOFb=0.322|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=7.54E-02|p5a=8.28E-03|p25a=1.11E-02|p50a=1.51E-02|p950a=1.46E-01|p975a=1.59E-01|p995a=1.84E-01|MLEN=1.7E+06|p5N=2.80E-11|p25N=1.91E-06|p50N=1.44E-03|p950N=2.34E+07|p975N=3.09E+07|p995N=4.67E+07}}


[[File:BPscatter ID142 143 144 145 147 151 161 162 163 164 168 169 170 172.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel_ID142 143 144 145 147 151 161 162 163 164 168 169 170 172.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 38, 42, 99, 165'''===

{{DRexperimentDataTable11norefs|title=ETEC disease, unbuffered, in the human model data|pos=Mild to severe diarrhea|neg=No mild to severe diarrhea|d1=1E+06|p1=0|n1=4|t1=4|d2=1E+08|p2=1|n2=4|t2=5|d3=1E+08|p3=2|n3=3|t3=5|d4=1E+08|p4=3|n4=2|t4=5|d5=1.43E+08|p5=6|n5=2|t5=8|d6=1.73E+09|p6=5|n6=2|t6=7|d7=5.33E+09|p7=6|n7=2|t7=8|d8=1E+10|p8=4|n8=1|t8=5|d9=1E+10|p9=3|n9=2|t9=5|d10=1E+10|p10=4|n10=1|t10=5|d11=1.6E+10|p11=7|n11=1|t11=8}}


{{DRFit|title=Goodness of fit and model selection|devE=68.4|devB=5.53|delta=62.9|DFE=10|DFB=9|X2bPbetter=3.84|pbPbetter=2.22e-15|X2GOFe=18.3|pGOFe=8.97e-11|X2GOFb=16.9|pGOFb=0.786|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=2.06E-01|p5a=1.75E-02|p25a=1.17E-01|p50a=1.32E-01|p950a=3.79E-01|p975a=4.29E-01|p995a=5.57E-01|MLEN=1.28E+08|p5N=3.53E+05|p25N=3.17E+07|p50N=4.09E+07|p950N=3.83E+08|p975N=4.65E+08|p995N=6.86E+08}}


[[File:BPscatter ID38 42 99 165.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel_ID38 42 99 165.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 153, 157, 159, 214, 216, 217'''===

{{DRexperimentDataTable11norefs|title=ETEC infection, unbuffered, in the human model data|pos=Diarrhea |neg=No diarrhea |d1=1E+06|p1=0|n1=4|t1=4|d2=1E+06|p2=1|n2=4|t2=5|d3=1E+08|p3=1|n3=4|t3=5|d4=5E+08|p4=3|n4=2|t4=5|d5=2.5E+09|p5=6|n5=0|t5=6|d6=1E+10|p6=9|n6=1|t6=10|d7=1E+10|p7=9|n7=5|t7=14|d8=1E+10|p8=3|n8=2|t8=5|d9=1E+10|p9=5|n9=0|t9=5|d10=2E+10|p10=2|n10=0|t10=2|d11=2.3E+10|p11=14|n11=5|t11=19}}


{{DRFit|title=Goodness of fit and model selection|devE=57.8|devB=14.4|delta=43.4|DFE=10|DFB=9|X2bPbetter=3.84|pbPbetter=4.51e-11|X2GOFe=18.3|pGOFe=9.36e-09|X2GOFb=16.9|pGOFb=0.108|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=1.62E-01|p5a=8.23E-02|p25a=9.98E-02|p50a=1.08E-01|p950a=3.69E-01|p975a=4.21E-01|p995a=5.36E-01|MLEN=9.98E+07|p5N=7.29E+06|p25N=1.55E+07|p50N=2.20E+07|p950N=8.50E+08|p975N=1.06E+09|p995N=1.57E+09}}


[[File:BPscatter ID153 157 159 214 216 217.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel_ID153 157 159 214 216 217.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 154, 156, 158, 160, 219, 220, 221'''===

{{DRExperimentDataTable13norefs|title=EPEC, infection, buffered, in the human model data|pos=Shedding in feces|neg=No shedding in feces|d1=1E+06|p1=3|n1=1|t1=4|d2=1E+06|p2=5|n2=0|t2=5|d3=1E+06|p3=4|n3=1|t3=5|d4=1E+08|p4=5|n4=0|t4=5|d5=1E+08|p5=5|n5=0|t5=5|d6=9E+08|p6=8|n6=0|t6=8|d7=1E+10|p7=10|n7=0|t7=10|d8=1E+10|p8=9|n8=0|t8=9|d9=1E+10|p9=14|n9=0|t9=14|d10=1E+10|p10=5|n10=0|t10=5|d11=1E+10|p11=5|n11=0|t11=5|d12=1E+10|p12=5|n12=0|t12=5|d13=2.3E+10|p13=19|n13=0|t13=19}}


{{DRFit|title=Goodness of fit and model selection|devE=1.98|devB=1.98|delta=2.71e-06|DFE=12|DFB=11|X2bPbetter=3.84|pbPbetter=0.999|X2GOFe=21|pGOFe=0.999|X2GOFb=19.7|pGOFb=0.999|interpretation=Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.}}


{{DRConfidenceExponential|title=Optimized k parameter for the exponential model, from 10000 bootstrap iterations|MLEk=1.95E-06|p5k=8.47E-07|p25k=1.03E-06|p50k=1.25E-06|p950k=2.64E-06|p975k=2.64E-06|p995k=2.64E-06|N50type=ID50/LD50/ETC|MLEN=3.56E+05|p5N=2.63E+05|p25N=2.63E+05|p50N=2.63E+05|p950N=5.53E+05|p975N=6.73E+05|p995N=8.18E+05}}


[[File:ExpHisto ID154 156 158 160 219 220 221.png|thumb|left|500px|'''Parameter histogram for exponential model (uncertainty of the parameter)''']][[File:ExpModel ID154 156 158 160 219 220 221.png|thumb|none|500px|'''Exponential model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 39, 40'''===

{{DRExperimentDataTable6norefs|title=EIEC disease, unbuffered, in the human model data|pos=Mild to severe diarrhea|neg=No mild to severe diarrhea|d1=1E+04|p1=0|n1=5|t1=5|d2=1E+04|p2=0|n2=5|t2=5|d3=1E+06|p3=0|n3=5|t3=5|d4=1E+06|p4=1|n4=8|t4=9|d5=1E+08|p5=5|n5=3|t5=8|d6=1E+08|p6=3|n6=2|t6=5}}


{{DRFit|title=Goodness of fit and model selection|devE=3.19|devB=0.951|delta=2.24|DFE=5|DFB=4|X2bPbetter=3.84|pbPbetter=0.134|X2GOFe=11.1|pGOFe=0.67|X2GOFb=9.49|pGOFb=0.917|interpretation=Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.}}


{{DRConfidenceExponential|title=Optimized k parameter for the exponential model, from 10000 bootstrap iterations|MLEk=1.07E-08|p5k=3.63E-09|p25k=4.79E-09|p50k=5.77E-09|p950k=2.04E-08|p975k=2.28E-08|p995k=3.21E-08|N50type=ID50/LD50/ETC|MLEN=6.5E+07|p5N=2.16E+07|p25N=3.04E+07|p50N=3.40E+07|p950N=1.20E+08|p975N=1.45E+08|p995N=1.91E+08}}


[[File:ExpHisto ID39 40.png|thumb|left|500px|'''Parameter histogram for exponential model (uncertainty of the parameter)''']][[File:ExpModel ID39 40.png|thumb|none|500px|'''Exponential model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 96, 100, 166'''===

{{DRExperimentDataTable7norefs|title=Dose response data|pos=Positive stool isolation|neg=No positive stool isolation|d1=1E+06|p1=3|n1=1|t1=4|d2=1E+08|p2=4|n2=1|t2=5|d3=1E+08|p3=5|n3=0|t3=5|d4=1E+08|p4=5|n4=0|t4=5|d5=1E+10|p5=5|n5=0|t5=5|d6=1E+10|p6=5|n6=0|t6=5|d7=1E+10|p7=5|n7=0|t7=5}}


{{DRFit|title=Goodness of fit and model selection|devE=64.1|devB=2.71|delta=61.4|DFE=6|DFB=5|X2bPbetter=3.84|pbPbetter=4.77e-15|X2GOFe=12.6|pGOFe=6.67e-12|X2GOFb=11.1|pGOFb=0.745|interpretation=Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.}}


{{DRConfidenceBetaPoisson|title=Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations|MLEa=3.75E-01|p5a=1.29E-01|p25a=1.34E-01|p50a=1.34E-01|p950a=9.97E+00|p975a=9.97E+00|p995a=1.07E+01|MLEN=1.78E+05|p5N=3.63E-01|p25N=3.63E-01|p50N=3.63E-01|p950N=2.46E+06|p975N=3.48E+06|p995N=6.09E+06}}


[[File:BPscatter ID96 100 166.png|thumb|left|500px|'''Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.''']][[File:BPmodel_ID96 100 166.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


===References===

<references />


[[Category:Completed Dose Response Models: Bacteria]][[Category:Dose Response Model]][[Category:Escherichia coli]]