Shigella: Dose Response Models

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Shigella species

Kyle S. Enger


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 (Kaper 2004). 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 (Kotloff 1999). However, S. dysenteriae type 1 can spread in epidemics and tends to cause more severe and complicated disease (Heymann 2004). Nearly all cases occur in developing countries, with 69% of cases in children under 5 years of age (Kotloff 1999).

Shigella tends to cause dysentery (diarrhea with blood or mucus) by invading the mucosa of the colon, leading to ulceration and bleeding (Niyogi 2005). It is usually self-limited after 4-7 days (Heymann 2004), but it tends to be more serious than watery diarrhea and is not effectively treated by oral rehydration solution (Kotloff 1999). Pandemic waves of shigellosis have been described since the 1960s, and can cause high mortality, especially among refugees (Kotloff 1999). Shigellosis is limited to human hosts (AWWA 1999). Vaccines against Shigella are currently under development (Niyogi 2005).



Summary of data

Levine et al. (1973) 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 (Levine et al. 1973) are fit well by the beta-Poisson model, although the confidence intervals are wide (Crockett et al. 1996; Haas et al. 1999). However, a poor fit is obtained if the data from strain A-1 (Levine et al. 1973) are pooled with M 131. Powell (2000) 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 [1] used 5 doses in 31 subjects; a larger study [2] 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 104 to 108 CFU; however, the proportion ill did not change greatly over the range of 105 – 108 (68-88% ill). The beta-Poisson model fits better than the exponential model (Crockett et al. 1996) 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.[1][2]

There have been two feeding studies (DuPont et al. 1989) 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 ID50.

There have been many additional feeding studies evaluating attenuated strains of Shigella for use in vaccines (e.g., DuPont et al. 1972a[3], Levine et al. 1973, Kotloff et al. 1995). 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 (Crockett et al. 1996) 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.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
83* [4] human 2a (strain 2457T) oral (in milk) 4 CFU positive stool isolation beta-Poisson α= 2.65E-01 , N50 = 1.48E+03 1.48E+03
81 [5] human M 131 oral (in milk) 4 CFU illness beta-Poisson α = 2.77E-01 , N50 = 2.38E+02 2.38E+02
82 [1] human 2a (strain 2457T) oral (in milk) 5 CFU illness beta-Poisson α = 1.43E-01 , N50 = 3.54E+04 3.54E+04
223 [4] human 2a (strain 2457T) oral (in milk) 4 CFU illness beta-Poisson α = 1.35E-01 , N50 = 3.11E+03 3.11E+03
81, 215 [5] human M 131 oral (in milk) 6 CFU illness beta-Poisson α = 4.93E-03 , N50 = 3.64E-01 3.64E-01
82, 223 [6] human 2a (strain 2457T) oral (in milk) 9 CFU illness beta-Poisson α = 1.17E-01 , N50 = 3.64E+03 3.64E+03
81, 215, 82, 223, 224, 225 [1] human M 131 oral (in milk) 17 CFU illness beta-Poisson α = 1.1E-01 , N50 = 2.35E+03 2.35E+03
*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

Optimization Output for experiment 83

Model data for Shigella flexneri (2a, strain 2457T) in the human [4]
Dose Positive stool isolation No positive stool isolation Total
180 6 30 36
5000 33 16 49
1E+04 66 21 87
1E+05 15 9 24


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 169 160 3 3.84
0
7.81
0
Beta Poisson 8.73 2 5.99
0.0127
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.


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 2.65E-01 1.47E-01 1.74E-01 1.87E-01 3.82E-01 4.09E-01 4.70E-01
N50 1.48E+03 5.60E+02 7.33E+02 8.26E+02 2.55E+03 2.78E+03 3.38E+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


Optimization Output for experiment 81

Model data for Shigella dysenteriae (M 131) in the human [5]
Dose Illness Not illness Total
10 1 9 10
200 2 2 4
2000 7 3 10
1E+04 5 1 6


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 13.2 13.2 3 3.84
0.000283
7.81
0.0042
Beta Poisson 0.0315 2 5.99
0.984
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 2.77E-01 5.24E-03 1.10E-01 1.34E-01 1.63E+00 1.88E+01 1.72E+03
N50 2.38E+02 1.35E+01 4.73E+01 6.36E+01 1.42E+03 2.02E+03 5.89E+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


Optimization Output for experiment 82

Model data for Shigella flexneri (2a, strain 2457T) in the human [1]
Dose Illness Not illness Total
1E+04 1 3 4
1E+05 3 1 4
1E+06 7 1 8
1E+07 13 6 19
1E+08 7 1 8


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 73.6 70.2 4 3.84
0
9.49
3.89e-15
Beta Poisson 3.44 3 7.81
0.329
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 1.43E-01 1.32E-02 2.12E-02 2.63E-02 2.90E-01 3.32E-01 4.27E-01
N50 3.54E+04 1.29E-11 8.16E-07 3.11E-04 3.34E+05 4.65E+05 9.68E+05


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 223

Model data for Shigella flexneri (2a, strain 2457T) in the human [4]
Dose Illness Not illness Total
180 9 27 36
5000 28 21 49
1E+04 52 36 88
1E+05 14 10 24


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 154 153 3 3.84
0
7.81
0
Beta Poisson 1.69 2 5.99
0.429
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 1.35E-01 9.86E-04 1.22E-02 6.85E-02 2.06E-01 2.22E-01 2.58E-01
N50 3.11E+03 5.09E+01 4.31E+02 9.64E+02 7.49E+03 9.14E+03 1.89E+04


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 81, 215

Model data for Shigella dysenteriae in the human [5]
Dose Illness Not illness Total
10 1 9 10
200 2 2 4
200 1 3 4
2000 7 3 10
1E+04 5 1 6
1E+04 2 4 6


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 30.5 16.9 5 3.84
3.94e-05
11.1
1.2e-05
Beta Poisson 13.6 4 9.49
0.00887
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.


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 4.93E-03 9.85E-04 9.87E-04 9.88E-04 3.61E-01 4.26E-01 5.85E-01
N50 3.64E-01 2.07E-02 5.54E-02 7.42E-02 2.05E+03 4.61E+03 1.09E+28


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 82, 223

Model data for Shigella flexneri (2a, strain 2457T) in the human [6]
Dose Illness Not illness Total
180 9 27 36
5000 28 21 49
1E+04 1 3 4
1E+04 52 36 88
1E+05 3 1 4
1E+05 14 10 24
1E+06 7 1 8
1E+07 13 6 19
1E+08 7 1 8


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 677 671 8 3.84
0
15.5
0
Beta Poisson 6.04 7 14.1
0.535
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 1.17E-01 4.86E-02 6.43E-02 7.25E-02 1.68E-01 1.78E-01 2.02E-01
N50 3.64E+03 3.32E+02 8.92E+02 1.22E+03 9.16E+03 1.12E+04 1.73E+04


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 81, 215, 82, 223, 224, 225

Model data for Shigella spp. in the human [6]
Dose Illness Not illness Total
10 1 9 10
180 9 27 36
200 2 2 4
200 1 3 4
500 7 13 20
500 19 19 38
2000 7 3 10
5000 28 21 49
1E+04 5 1 6
1E+04 1 3 4
1E+04 2 4 6
1E+04 52 36 88
1E+05 3 1 4
1E+05 14 10 24
1E+06 7 1 8
1E+07 13 6 19
1E+08 7 1 8


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 836 822 16 3.84
0
26.3
0
Beta Poisson 13.9 15 25
0.536
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 1.1E-01 6.09E-02 7.18E-02 7.78E-02 1.49E-01 1.58E-01 1.76E-01
N50 2.35E+03 6.00E+02 8.78E+02 1.03E+03 5.64E+03 6.91E+03 1.04E+04


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

  1. 1.0 1.1 1.2 1.3 1.4 DuPont HL, et al., (1969) The response of man to virulent Shigella flexneri 2a. The Journal of Infectious Diseases, 119(3), pp.296-299.
  2. 2.0 2.1 DuPont HL, et al. (1972) Immunity in shigellosis. I. Response of man to attenuated strains of Shigella. The Journal of Infectious Diseases, 125(1), pp.5-16.
  3. DuPont HL, et al., (1972a) Immunity in shigellosis. I. Response of man to attenuated strains of Shigella. The Journal of Infectious Diseases, 125(1), pp.5-11.
  4. 4.0 4.1 4.2 4.3 DuPont HL, et al., (1972b) Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection. The Journal of Infectious Diseases, 125(1), pp.12-16.
  5. 5.0 5.1 5.2 5.3 Levine, M.M. et al., 1973. Pathogenesis of Shigella dysenteriae 1 (Shiga) dysentery. The Journal of Infectious Diseases, 127(3), pp.261-270. Available at: [Accessed 17:34:13]. Cite error: Invalid <ref> tag; name "Levine_et_al._.281973.29" defined multiple times with different content Cite error: Invalid <ref> tag; name "Levine_et_al._.281973.29" defined multiple times with different content
  6. 6.0 6.1 6.2 {{{reference}}} Cite error: Invalid <ref> tag; name ".7B.7B.7Brefer.7D.7D.7D" defined multiple times with different content Cite error: Invalid <ref> tag; name ".7B.7B.7Brefer.7D.7D.7D" defined multiple times with different content

Alam NH, et al. (2003) Efficacy and tolerability of racecadotril in the treatment of cholera in adults: a double blind, randomised, controlled clinical trial. Gut, 52(10), pp.1419-1423.

American Water Works Association, (1999) Waterborne pathogens: manual of water supply practices, Denver, CO: American Water Works Association.

Crockett CS, et al., (1996) Prevalence of shigellosis in the U.S.: consistency with dose-response information. International Journal of Food Microbiology, 30(1-2), pp.87-99.

DuPont HL, et al., (1969) The response of man to virulent Shigella flexneri 2a. The Journal of Infectious Diseases, 119(3), pp.296-299.

DuPont HL, et al., (1972a) Immunity in shigellosis. I. Response of man to attenuated strains of Shigella. The Journal of Infectious Diseases, 125(1), pp.5-11.

DuPont HL, et al., (1972b) Immunity in shigellosis. II. Protection induced by oral live vaccine or primary infection. The Journal of Infectious Diseases, 125(1), pp.12-16.

DuPont HL, et al., (1989) Inoculum size in shigellosis and implications for expected mode of transmission. The Journal of Infectious Diseases, 159(6), pp.1126-1128.

Haas CN, Rose JB, Gerba CP, (1999) Quantitative Microbial Risk Assessment, John Wiley & Sons, Inc.

Heymann DL, (2004) Control of Communicable Diseases Manual 18th ed., American Public Health Association.

Kaper JB, Nataro JP, & Mobley HL, (2004) Pathogenic Escherichia coli. Nature Reviews. Microbiology, 2(2), pp.123-140.

Kotloff KL, et al., (1995) 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.

Kotloff KL, et al., (1999) 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.

Levine MM, et al., (1973) Pathogenesis of Shigella dysenteriae 1 (Shiga) dysentery. The Journal of Infectious Diseases, 127(3), pp.261-270. Available at: [Accessed 17:34:13].

Niyogi SK, (2005) Shigellosis. Journal of Microbiology (Seoul, Korea), 43(2), pp.133-143.

Powell MR, (2000) Dose-response envelope for Escherichia coli O157:H7. Quantitative Microbiology, 2, pp.141-163.