View source for Shigella: Dose Response Models

==<center>'''''Shigella'' species'''</center>==
<center><big>'''(Shigellosis)'''</big></center>
<center><big>'''Kyle S. Enger'''</big></center>


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

''Shigella'' sp. are very closely related to ''E. coli'' and probably technically belong to that species; however, because of their disease significance, the distinct names are still used.<ref name="Kaper 2004">Kaper JB, Nataro JP, & Mobley HL, (2004) [http://www.nature.com/nrmicro/journal/v2/n2/pdf/nrmicro818.pdf Pathogenic Escherichia coli.] Nature Reviews. Microbiology, 2(2), pp.123-140. </ref> The most common types in developing countries are ''Shigella flexneri'' (~60% of cases) and ''Shigella sonnei'' (~15% of cases), with ''S. boydii'' and ''S. dysenteriae'' contributing ~6% each.<ref name="Kotloff 1999">Kotloff KL, et al., (1999) [http://www.who.int/bulletin/archives/77%288%29651.pdf Global burden of Shigella infections: implications for vaccine development and implementation of control strategies.] Bulletin of the World Health Organization, 77(8), pp.651-666.</ref> However, ''S. dysenteriae'' type 1 can spread in epidemics and tends to cause more severe and complicated disease.<ref name="Heymann 2004">Heymann DL, (2004) Control of Communicable Diseases Manual 18th ed., American Public Health Association.</ref> Nearly all cases occur in developing countries, with 69% of cases in children under 5 years of age.<ref name="Kotloff 1999"></ref>

''Shigella'' tends to cause dysentery (diarrhea with blood or mucus) by invading the mucosa of the colon, leading to ulceration and bleeding.<ref name="Niyogi 2005">Niyogi SK, (2005) [http://www.ncbi.nlm.nih.gov/pubmed/15880088/ Shigellosis.] ''Journal of Microbiology (Seoul, Korea)'', 43(2), pp.133-143. </ref> It is usually self-limited after 4-7 days<ref name="Heymann 2004"></ref>, but it tends to be more serious than watery diarrhea and is not effectively treated by oral rehydration solution.<ref name="Kotloff 1999"></ref> Pandemic waves of shigellosis have been described since the 1960s, and can cause high mortality, especially among refugees.<ref name="Kotloff 1999"></ref> Shigellosis is limited to human hosts.<ref name="AWWA 1999">American Water Works Association, (1999) Waterborne pathogens: manual of water supply practices, Denver, CO: American Water Works Association.</ref> Vaccines against ''Shigella'' are currently under development.<ref name="Niyogi 2005"></ref> 


http://www.cdc.gov/nczved/divisions/dfbmd/diseases/shigellosis/
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==='''Summary of data'''===


Levine et al. (1973)<ref name="Levine et al. (1973)"></ref> gave ''S. dysenteriae'' strains M 131 and A-1 in milk to healthy young adult male prisoners, and measured illness as the outcome. Four dose levels were used for strain M 131, but only 2 dose levels were used for strain A-1. Data for strain M 131<ref name="Levine et al. (1973)"></ref> are fit well by the beta-Poisson model, although the confidence intervals are wide.<ref name="Crockett et al. 1996">Crockett CS, et al., (1996) [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T7K-3W3NF3S-7&_user=1111158&_coverDate=06%2F30%2F1996&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1722657331&_rerunOrigin=scholar.google&_acct=C000051676&_version=1&_urlVersion=0&_userid=1111158&md5=bff3817b1ad23283b324c4af28734d6e&searchtype=a Prevalence of shigellosis in the U.S.: consistency with dose-response information.] International Journal of Food Microbiology, 30(1-2), pp.87-99. </ref><ref name="Haas et al. 1999">Haas CN, Rose JB, Gerba CP, (1999) Quantitative Microbial Risk Assessment, John Wiley & Sons, Inc.</ref> However, a poor fit is obtained if the data from strain A-1<ref name="Levine et al. (1973)"></ref> are pooled with M 131. Powell (2000)<ref name="Powell 2000">Powell MR, (2000) [http://www.springerlink.com/content/k3t3768n75w16246/fulltext.pdf Dose-response envelope for Escherichia coli O157:H7.] Quantitative Microbiology, 2, pp.141-163.</ref> reports a beta-Poisson model fit to the pooled data for strains M 131 and A-1.

DuPont et al. (1969 & 1972) conducted feeding studies of ''S. flexneri'' 2a (strain 2457T) in healthy male prisoners. A smaller study <ref name="DuPont et al. 1969">DuPont HL, et al., (1969) [http://www.jstor.org/stable/30102317 The response of man to virulent Shigella flexneri 2a.] The Journal of Infectious Diseases, 119(3), pp.296-299.</ref> used 5 doses in 31 subjects; a larger study <ref name="DuPont et al. 1972">DuPont HL, et al. (1972) [http://jid.oxfordjournals.org/content/125/1/5.short Immunity in shigellosis. I. Response of man to attenuated strains of Shigella.] ''The Journal of Infectious Diseases'', 125(1), pp.5-16.</ref> used 4 doses among 196 subjects. The smaller study only recorded illness as the response; however, the larger study recorded both illness and infection. The smaller study tested a wide dose range, from 10<sup>4</sup> to 10<sup>8</sup> CFU; however, the proportion ill did not change greatly over the range of 10<sup>5</sup> – 10<sup>8</sup> (68-88% ill). The beta-Poisson model fits better than the exponential model<ref name="Crockett et al. 1996"></ref> for each of these 3 datasets. It fits well for the two datasets using illness as a response (DuPont et al. 1969 & 1972), but fits poorly for the infection response.<ref name="DuPont et al. 1969"></ref><ref name="DuPont et al. 1972"></ref>

There have been two feeding studies<ref name="DuPont et al. 1989">DuPont HL, et al., (1989) [http://www.jstor.org/stable/30137443 Inoculum size in shigellosis and implications for expected mode of transmission.] The Journal of Infectious Diseases, 159(6), pp.1126-1128. </ref> in male prisoners of ''S. sonnei'' 53G; however, they both used a dose of 500 CFU in all subjects. However, 7/20 subjects became ill in one study, and 19/38 in the other, implying that this dose is close to the ID<sub>50</sub>.

There have been many additional feeding studies evaluating attenuated strains of ''Shigella'' for use in vaccines (e.g., DuPont et al. 1972a<ref name="DuPont et al. 1972a">DuPont HL, et al., (1972a) [http://jid.oxfordjournals.org/content/125/1/5.short Immunity in shigellosis. I. Response of man to attenuated strains of Shigella.] ''The Journal of Infectious Diseases'', 125(1), pp.5-11.</ref>, Levine et al. 1973<ref name="Levine et al. (1973)"></ref>, Kotloff et al. 1995<ref name="Kotloff et al. 1995">Kotloff KL, et al., (1995) [http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TD4-3Y44SK2-11-5&_cdi=5188&_user=1111158&_pii=0264410X95001027&_origin=gateway&_coverDate=12%2F31%2F1995&_sk=999869983&view=c&wchp=dGLzVtz-zSkzk&md5=d83bc555ae4859d05782081cdc6f5da2&ie=/sdarticle.pdf A modified Shigella volunteer challenge model in which the inoculum is administered with bicarbonate buffer: clinical experience and implications for Shigella infectivity.] Vaccine, 13(16), pp.1488-1494.</ref>). However, these are not included here since attenuated strains are deliberately intended to be less infectious or pathogenic than wild strains, and using dose response models based on such experiments might lead to underestimation of risk.

Pooling analysis of all datasets using illness as the response could not disprove the hypothesis that the datasets could be pooled (P > 0.05). However, separate pooled models are also provided for ''S. dysenteriae'' and ''S. flexneri''. A previously published pooling analysis<ref name="Crockett et al. 1996"></ref> excluded one dose level (1E7 CFU) from experiment 82. Although that dose level contributed disproportionately to the deviance, it was also the dose level with the largest sample size (19 volunteers; the next largest sample size was 8 volunteers); therefore, it was retained in all analyses conducted for this chapter.


{{DRSummaryTableStart|agent=''Shigella''}}
{{DRSummaryTablePreferredModel|expID= 83 |refer = DuPont et al. (1972b)|reference=DuPont HL, et al., (1972b) [http://jid.oxfordjournals.org/content/125/1/12.short Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection.] The Journal of Infectious Diseases, 125(1), pp.12-16. |host= human |agentStrain= 2a (strain 2457T) |route= oral (in milk) |nDoses= 4 |doseUnits= CFU |response= positive stool isolation |bestFitModel=beta-Poisson|parameters=&alpha;=  2.65E-01 , N<sub>50</sub> =  1.48E+03|N50= 1.48E+03 }}
{{DRSummaryTableNonpreferredModel|expID= 81 |refer= Levine et al. (1973)
|reference=Levine MM, et al., (1973) [http://jid.oxfordjournals.org/content/127/3/261.short Pathogenesis of Shigella dysenteriae 1 (Shiga) dysentery.] The Journal of Infectious Diseases, 127(3), pp.261-270. Available at: [Accessed 17:34:13].|host= human |agentStrain= M 131 |route= oral (in milk) |nDoses= 4 |doseUnits= CFU|response= illness |bestFitModel=beta-Poisson|parameters=&alpha; =  2.77E-01 , N<sub>50</sub> =  2.38E+02|N50= 2.38E+02 }}
{{DRSummaryTableNonpreferredModel|expID= 82 |refer =DuPont et al. 1969|reference=DuPont HL, et al., (1969) [http://www.jstor.org/stable/30102317 The response of man to virulent Shigella flexneri 2a.] The Journal of Infectious Diseases, 119(3), pp.296-299.|host= human |agentStrain= 2a (strain 2457T) |route= oral (in milk) |nDoses= 5 |doseUnits= CFU |response= illness |bestFitModel=beta-Poisson|parameters=&alpha; =  1.43E-01 , N<sub>50</sub> =  3.54E+04|N50= 3.54E+04 }}
{{DRSummaryTableNonpreferredModel|expID= 223 |refer=DuPont et al. (1972b)|reference=DuPont HL, et al., (1972b) [http://jid.oxfordjournals.org/content/125/1/12.short Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection.] The Journal of Infectious Diseases, 125(1), pp.12-16. |host= human |agentStrain= 2a (strain 2457T) |route= oral (in milk) |nDoses= 4 |doseUnits= CFU |response= illness |bestFitModel=beta-Poisson|parameters=&alpha; =  1.35E-01 , N<sub>50</sub> =  3.11E+03|N50= 3.11E+03 }}
{{DRSummaryNonpreferredModelManyrefs|expID= 81, 215 |refer1 = Levine et al. (1973) |reference1=Levine MM, et al., (1973) [http://jid.oxfordjournals.org/content/127/3/261.short Pathogenesis of Shigella dysenteriae 1 (Shiga) dysentery.] The Journal of Infectious Diseases, 127(3), pp.261-270. Available at: [Accessed 17:34:13].|refer2 = Powell 2000|reference2= |host= human |agentStrain= M 131 |route= oral (in milk) |nDoses= 6 |doseUnits= CFU|response= illness |bestFitModel=beta-Poisson|parameters=&alpha; =  4.93E-03 , N<sub>50</sub> =  3.64E-01|N50= 3.64E-01 }}
{{DRSummaryNonpreferredModelManyrefs|expID= 82, 223 |refer1 =DuPont et al. 1969|reference1=DuPont HL, et al., (1969) [http://www.jstor.org/stable/30102317 The response of man to virulent Shigella flexneri 2a.] The Journal of Infectious Diseases, 119(3), pp.296-299. |refer2=DuPont et al. (1972b)|reference2=DuPont HL, et al., (1972b) [http://jid.oxfordjournals.org/content/125/1/12.short Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection.] The Journal of Infectious Diseases, 125(1), pp.12-16. |host= human |agentStrain= 2a (strain 2457T) |route= oral (in milk) |nDoses= 9 |doseUnits= CFU |response= illness |bestFitModel=beta-Poisson|parameters=&alpha; =  1.17E-01 , N<sub>50</sub> =  3.64E+03|N50= 3.64E+03 }}
{{DRSummaryTableNonpreferredModelfourrefs|expID= 81, 215, 82, 223, 224, 225|refer1=Levine et al. (1973)|reference1= |refer2=DuPont et al. 1969|reference2= |refer3=DuPont et al. (1972b)|reference3= |refer4= DuPont et al. 1989|reference4= |host= human |agentStrain= M 131 |route= oral (in milk) |nDoses= 17 |doseUnits= CFU |response= illness |bestFitModel=beta-Poisson|parameters=&alpha; =  1.1E-01 , N<sub>50</sub> =  2.35E+03|N50= 2.35E+03 }}
{{DRSummaryTableEnd}}

==<sup>*</sup>Recommended Model==


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

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==='''Optimization Output for experiment 83 (''Shigella flexneri'')'''===

{{DRExperimentDataTable4|title=Model data for ''Shigella flexneri'' (2a, strain 2457T) in the human|refer = DuPont et al. (1972b)|reference=DuPont HL, et al., (1972b) [http://jid.oxfordjournals.org/content/125/1/12.short Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection.] The Journal of Infectious Diseases, 125(1), pp.12-16. |pos=Positive stool isolation|neg=No positive stool isolation|d1=180|p1=6|n1=30|t1=36|d2=5000|p2=33|n2=16|t2=49|d3=1E+04|p3=66|n3=21|t3=87|d4=1E+05|p4=15|n4=9|t4=24}}


{{DRFit|title=Goodness of fit and model selection|devE=169|devB=8.73|delta=160|DFE=3|DFB=2|X2bPbetter=3.84|pbPbetter=0|X2GOFe=7.81|pGOFe=0|X2GOFb=5.99|pGOFb=0.0127|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=2.65E-01|p5a=1.47E-01|p25a=1.74E-01|p50a=1.87E-01|p950a=3.82E-01|p975a=4.09E-01|p995a=4.70E-01|MLEN=1.48E+03|p5N=5.60E+02|p25N=7.33E+02|p50N=8.26E+02|p950N=2.55E+03|p975N=2.78E+03|p995N=3.38E+03}}


[[File:BPscatter ID83.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 ID83.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 81 (''Shigella dysenteriae'')'''===

{{DRExperimentDataTable4|title=Model data for ''Shigella dysenteriae'' (M 131) in the human|refer= Levine et al. (1973)
|reference=Levine MM, et al., (1973) [http://jid.oxfordjournals.org/content/127/3/261.short Pathogenesis of Shigella dysenteriae 1 (Shiga) dysentery.] The Journal of Infectious Diseases, 127(3), pp.261-270. Available at: [Accessed 17:34:13].|pos=Illness|neg=Not illness|d1=10|p1=1|n1=9|t1=10|d2=200|p2=2|n2=2|t2=4|d3=2000|p3=7|n3=3|t3=10|d4=1E+04|p4=5|n4=1|t4=6}}


{{DRFit|title=Goodness of fit and model selection|devE=13.2|devB=0.0315|delta=13.2|DFE=3|DFB=2|X2bPbetter=3.84|pbPbetter=0.000283|X2GOFe=7.81|pGOFe=0.0042|X2GOFb=5.99|pGOFb=0.984|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=2.77E-01|p5a=5.24E-03|p25a=1.10E-01|p50a=1.34E-01|p950a=1.63E+00|p975a=1.88E+01|p995a=1.72E+03|MLEN=2.38E+02|p5N=1.35E+01|p25N=4.73E+01|p50N=6.36E+01|p950N=1.42E+03|p975N=2.02E+03|p995N=5.89E+03}}


[[File:BPscatter ID81.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 ID81.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 82 (''Shigella flexneri'')'''===

{{DRExperimentDataTable5|title=Model data for Shigella flexneri (2a, strain 2457T) in the human|refer =DuPont et al. 1969|reference=DuPont HL, et al., (1969) [http://www.jstor.org/stable/30102317 The response of man to virulent Shigella flexneri 2a.] The Journal of Infectious Diseases, 119(3), pp.296-299.|pos=Illness|neg=Not illness|d1=1E+04|p1=1|n1=3|t1=4|d2=1E+05|p2=3|n2=1|t2=4|d3=1E+06|p3=7|n3=1|t3=8|d4=1E+07|p4=13|n4=6|t4=19|d5=1E+08|p5=7|n5=1|t5=8}}


{{DRFit|title=Goodness of fit and model selection|devE=73.6|devB=3.44|delta=70.2|DFE=4|DFB=3|X2bPbetter=3.84|pbPbetter=0|X2GOFe=9.49|pGOFe=3.89e-15|X2GOFb=7.81|pGOFb=0.329|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=1.43E-01|p5a=1.32E-02|p25a=2.12E-02|p50a=2.63E-02|p950a=2.90E-01|p975a=3.32E-01|p995a=4.27E-01|MLEN=3.54E+04|p5N=1.29E-11|p25N=8.16E-07|p50N=3.11E-04|p950N=3.34E+05|p975N=4.65E+05|p995N=9.68E+05}}


[[File:BPscatter ID82.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 ID82.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 223 (''Shigella flexneri'')'''===

{{DRExperimentDataTable4|title=Model data for Shigella flexneri (2a, strain 2457T) in the human|refer=DuPont et al. (1972b)|reference=DuPont HL, et al., (1972b) [http://jid.oxfordjournals.org/content/125/1/12.short Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection.] The Journal of Infectious Diseases, 125(1), pp.12-16. |pos=Illness|neg=Not illness|d1=180|p1=9|n1=27|t1=36|d2=5000|p2=28|n2=21|t2=49|d3=1E+04|p3=52|n3=36|t3=88|d4=1E+05|p4=14|n4=10|t4=24}}


{{DRFit|title=Goodness of fit and model selection|devE=154|devB=1.69|delta=153|DFE=3|DFB=2|X2bPbetter=3.84|pbPbetter=0|X2GOFe=7.81|pGOFe=0|X2GOFb=5.99|pGOFb=0.429|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=1.35E-01|p5a=9.86E-04|p25a=1.22E-02|p50a=6.85E-02|p950a=2.06E-01|p975a=2.22E-01|p995a=2.58E-01|MLEN=3.11E+03|p5N=5.09E+01|p25N=4.31E+02|p50N=9.64E+02|p950N=7.49E+03|p975N=9.14E+03|p995N=1.89E+04}}


[[File:BPscatter ID223.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 ID223.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 81, 215 (''Shigella dysenteriae'')'''===

{{DRExperimentDataTable6|title=Model data for Shigella dysenteriae in the human|refer = Levine et al. (1973) |reference=Levine MM, et al., (1973) [http://jid.oxfordjournals.org/content/127/3/261.short Pathogenesis of Shigella dysenteriae 1 (Shiga) dysentery.] The Journal of Infectious Diseases, 127(3), pp.261-270. Available at: [Accessed 17:34:13].|pos=Illness|neg=Not illness|d1=10|p1=1|n1=9|t1=10|d2=200|p2=2|n2=2|t2=4|d3=200|p3=1|n3=3|t3=4|d4=2000|p4=7|n4=3|t4=10|d5=1E+04|p5=5|n5=1|t5=6|d6=1E+04|p6=2|n6=4|t6=6}}


{{DRFit|title=Goodness of fit and model selection|devE=30.5|devB=13.6|delta=16.9|DFE=5|DFB=4|X2bPbetter=3.84|pbPbetter=3.94e-05|X2GOFe=11.1|pGOFe=1.2e-05|X2GOFb=9.49|pGOFb=0.00887|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=4.93E-03|p5a=9.85E-04|p25a=9.87E-04|p50a=9.88E-04|p950a=3.61E-01|p975a=4.26E-01|p995a=5.85E-01|MLEN=3.64E-01|p5N=2.07E-02|p25N=5.54E-02|p50N=7.42E-02|p950N=2.05E+03|p975N=4.61E+03|p995N=1.09E+28}}


[[File:BPscatter ID81 215.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 ID81 215.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 82, 223 (''Shigella flexneri'')'''===

{{DRExperimentDataTable9|title=Model data for Shigella flexneri (2a, strain 2457T) in the human|refer1=DuPont et al. 1969|reference1=DuPont HL, et al., (1969) [http://www.jstor.org/stable/30102317 The response of man to virulent Shigella flexneri 2a.] The Journal of Infectious Diseases, 119(3), pp.296-299.|refer2=DuPont et al. (1972b)|reference2= DuPont HL, et al., (1972b) [http://jid.oxfordjournals.org/content/125/1/12.short Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection.] The Journal of Infectious Diseases, 125(1), pp.12-16. |pos=Illness|neg=Not illness|d1=180|p1=9|n1=27|t1=36|d2=5000|p2=28|n2=21|t2=49|d3=1E+04|p3=1|n3=3|t3=4|d4=1E+04|p4=52|n4=36|t4=88|d5=1E+05|p5=3|n5=1|t5=4|d6=1E+05|p6=14|n6=10|t6=24|d7=1E+06|p7=7|n7=1|t7=8|d8=1E+07|p8=13|n8=6|t8=19|d9=1E+08|p9=7|n9=1|t9=8}}


{{DRFit|title=Goodness of fit and model selection|devE=677|devB=6.04|delta=671|DFE=8|DFB=7|X2bPbetter=3.84|pbPbetter=0|X2GOFe=15.5|pGOFe=0|X2GOFb=14.1|pGOFb=0.535|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=1.17E-01|p5a=4.86E-02|p25a=6.43E-02|p50a=7.25E-02|p950a=1.68E-01|p975a=1.78E-01|p995a=2.02E-01|MLEN=3.64E+03|p5N=3.32E+02|p25N=8.92E+02|p50N=1.22E+03|p950N=9.16E+03|p975N=1.12E+04|p995N=1.73E+04}}


[[File:BPscatter ID82 223.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 ID82 223.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


==='''Optimization Output for experiment 81, 215, 82, 223, 224, 225 (''Shigella'' spp.)'''===

{{DRExperimentDataTable17|title=Model data for Shigella spp. in the human|reference=ADDFULLREFERENCEHERE|pos=Illness|neg=Not illness|d1=10|p1=1|n1=9|t1=10|d2=180|p2=9|n2=27|t2=36|d3=200|p3=2|n3=2|t3=4|d4=200|p4=1|n4=3|t4=4|d5=500|p5=7|n5=13|t5=20|d6=500|p6=19|n6=19|t6=38|d7=2000|p7=7|n7=3|t7=10|d8=5000|p8=28|n8=21|t8=49|d9=1E+04|p9=5|n9=1|t9=6|d10=1E+04|p10=1|n10=3|t10=4|d11=1E+04|p11=2|n11=4|t11=6|d12=1E+04|p12=52|n12=36|t12=88|d13=1E+05|p13=3|n13=1|t13=4|d14=1E+05|p14=14|n14=10|t14=24|d15=1E+06|p15=7|n15=1|t15=8|d16=1E+07|p16=13|n16=6|t16=19|d17=1E+08|p17=7|n17=1|t17=8}}


{{DRFit|title=Goodness of fit and model selection|devE=836|devB=13.9|delta=822|DFE=16|DFB=15|X2bPbetter=3.84|pbPbetter=0|X2GOFe=26.3|pGOFe=0|X2GOFb=25|pGOFb=0.536|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=1.1E-01|p5a=6.09E-02|p25a=7.18E-02|p50a=7.78E-02|p950a=1.49E-01|p975a=1.58E-01|p995a=1.76E-01|MLEN=2.35E+03|p5N=6.00E+02|p25N=8.78E+02|p50N=1.03E+03|p950N=5.64E+03|p975N=6.91E+03|p995N=1.04E+04}}


[[File:BPscatter ID81 215 82 223 224 225.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 ID81 215 82 223 224 225.png|thumb|none|500px|'''beta Poisson model plot, with confidence bounds around optimized model''']]<br>


----

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[[Category:Completed Dose Response Models: Bacteria]][[Category:Dose Response Model]][[Category:Shigella]]