Burkholderia pseudomallei: Dose Response Models

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Burkholderia pseudomallei

Author: Mark H. Weir

Overview

The bacterium Bukholderia pseudomallei (B. pseudomallei) is a gram negative bacterium and is present in numerous tropical regions such as Central and South America and Southeast Asia causes Melioidosis, typically infects horses, mules and donkeys but can also present a potentially life threatening disease in humans as well. Burkholderia mallei (B. mallei) is a close relative of B. pseudomallei both of which have been categorized as a B level bioterror agent by the CDC. No dose response models are currently available for B. mallei.

http://www.cdc.gov/melioidosis/

Liu et al. in 2002 examined infection through intranasal route to mimic infection through inhalation. C57BL/6 mice and BALB/c mice were inoculated intranasally to B. pseudomallei KHW strain and mortality was recorded as response (Liu, Koo et al. 2002). Miller et al.(1948) explored infection in guinea pigs via intraperitoneal route(Miller, Pannell et al. 1948). Similarly, Brett and Woods(1996) experimented infection in diabetic rats with B. pseuomallei 316c strain (Brett and Woods 1996.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
18,23* [1] C57BL/6 mice and diabetic rat KHW,316c intranasal,intraperitoneal 10 CFU death beta-Poisson α = 3.28E-01 , N50 = 5.43E+03 5.43E+03
21,23 [2] guinea pig and diabetic rat W294, 316c intraperitoneal 11 CFU death beta-Poisson α = 2.13E-01 , N50 = 4.77E+02 4.77E+02
18 [3] C57BL/6 mice KHW intranasal 5 CFU infection exponential k = 1.00E-04 6.92E+03
17 [3] BALB/c mice KHW intranasal 5 CFU infection exponential k = 1.04E-02 6.63E+01
21 [4] guinea pig W294 intraperitoneal 6 CFU death beta-Poisson α = 2.67E-01 , N50 = 2.55E+02 2.55E+02
23 [5] diabetic rat 316c intraperitoneal 5 CFU death beta-Poisson α = 2.65E-01 , N50 = 2.27E+03 2.27E+03
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

Recommended Model

Since the data of C57BL/6 mice and diabetic rat could be pooled and intranasal exposure is closer to inhalation which is the likeliest exposure route for humans, the pooled data sets and resulting models is preferred.

Exponential and betapoisson model.jpg
[edit]

Optimization Output for experiment 18 and 23 pooled (B. pseudomallei)

Pooled data of C57BL/6 mice and diabetic rat [6]
Dose DEATH NOT DEATH Total
150 0 6 6
450 1 5 6
1350 1 5 6
3000 6 4 10
4050 3 3 6
12200 3 3 6
3E+04 7 3 10
3E+05 7 3 10
3E+06 10 0 10
3E+07 10 0 10


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 63.3 56.6 9 3.84
5.42e-14
16.9
3.15e-10
Beta Poisson 6.68 8 15.5
0.571
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 3.28E-01 1.94E-01 2.16E-01 2.31E-01 5.15E-01 5.86E-01 8.32E-01
N50 5.43E+03 1.82E+03 2.37E+03 2.64E+03 1.23E+04 1.39E+04 1.68E+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 21 and 23 pooled (B. pseudomallei)

Pooled data of guinea pig and diabetic rat [6]
Dose DEATH NOT DEATH Total
44 1 4 5
440 3 2 5
3000 6 4 10
4400 4 1 5
3E+04 7 3 10
44000 5 0 5
3E+05 7 3 10
440000 5 0 5
3E+06 10 0 10
4.4E+06 4 1 5
3E+07 10 0 10


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 163 152 10 3.84
0
18.3
0
Beta Poisson 10.1 9 16.9
0.343
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 2.13E-01 9.14E-02 1.26E-01 1.39E-01 3.38E-01 3.76E-01 5.60E-01
N50 4.77E+02 3.04E+00 1.63E+01 7.19E+01 2.16E+03 2.75E+03 4.44E+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 18 (B. pseudomallei)

C57BL/6 Mice KHW Strain Data [3]
Dose Infected Non-infected Total
150 0 6 6
450 1 5 6
1350 1 5 6
4050 3 3 6
12200 3 3 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 3.36 2.17 4 3.84
0.141
9.49
0.499
Beta Poisson 1.19 3 7.81
0.755
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.


Optimized parameters for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1E-04 2.87E-05 4.15E-05 4.99E-05 1.89E-04 2.13E-04 2.70E-04
ID50/LD50/ETC* 6.92E+03 2.57E+03 3.26E+03 3.68E+03 1.39E+04 1.67E+04 2.41E+04
*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 17(B. pseudomallei)

BALB/c Mice KHW Strain Data [3]
Dose Infected Non-infected Total
5 0 6 6
15 0 6 6
45 3 1 4
135 4 2 6
405 6 0 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 5.25 -0.000362 4 3.84
1
9.49
0.263
Beta Poisson 5.25 3 7.81
0.154
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.


Optimized parameters for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.04E-02 4.94E-03 5.96E-03 6.60E-03 1.92E-02 2.45E-02 2.45E-02
ID50/LD50/ETC* 6.63E+01 2.82E+01 2.82E+01 3.61E+01 1.05E+02 1.16E+02 1.40E+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 21(B. pseudomallei)

Guinea Pigs W294 Strain Data [4]
Dose Dead Survived Total
44 1 4 5
440 3 2 5
4400 4 1 5
44000 5 0 5
440000 5 0 5
4.4E+06 4 1 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 70.3 66.1 5 3.84
4.44e-16
11.1
8.93e-14
Beta Poisson 4.14 4 9.49
0.387
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 2.67E-01 3.36E-02 8.80E-02 1.16E-01 1.05E+01 3.45E+02 3.55E+03
N50 2.55E+02 4.80E-07 2.49E+00 1.48E+01 1.35E+03 1.80E+03 3.22E+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 23 (B. pseudomallei)

diabetic rat and 316c strain [6]
Dose DEATH NOT DEATH Total
3000 6 4 10
3E+04 7 3 10
3E+05 7 3 10
3E+06 10 0 10
3E+07 10 0 10


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 43.4 39 4 3.84
4.25e-10
9.49
8.61e-09
Beta Poisson 4.39 3 7.81
0.222
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.


Optimized parameters for the beta-Poisson model, from 500 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 2.65E-01 7.56E-02 1.30E-01 1.54E-01 4.94E-01 5.69E-01 8.88E-01
N50 2.27E+03 7.58E-02 1.50E+01 5.32E+01 8.62E+03 1.11E+04 1.74E+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. Brett PJ and Woods DE (1996) Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates. Infection and Immunity 64(7), 2824-2828 and Liu B, Koo GC, Yap EH, Chua KL and Gan Y-H (2002) Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection. Infection and Immunity 70(2), 504-511.
  2. Miller WR, Pannell L, Cravitz L, Tanner WA and Rosebury T (1948) Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei: II. Virulence and Infectivity for Animals. Journal of Bacteriology 55(1), 127-135. and Brett PJ and Woods DE (1996) Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates. Infection and Immunity 64(7), 2824-2828
  3. 3.0 3.1 3.2 3.3 Liu B, Koo GC, Yap EH, Chua KL and Gan Y-H (2002) Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection. Infection and Immunity 70(2), 504-511. Cite error: Invalid <ref> tag; name "Liu.2C_Koo_et_al._2002" defined multiple times with different content Cite error: Invalid <ref> tag; name "Liu.2C_Koo_et_al._2002" defined multiple times with different content
  4. 4.0 4.1 Miller WR, Pannel I, Cravitz I, Tanner WA and Rosebury T (1947) Studies on Certain Biological Characteristics of Melleomyces mallei and Malleomyces pseudomallei II. Virulence and Infectivity for Animals Journal of Bacteriology 55: 127-135 Cite error: Invalid <ref> tag; name "Miller_1947" defined multiple times with different content
  5. Brett PJ and Woods DE (1996) Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates. Infection and Immunity 64(7), 2824-2828
  6. 6.0 6.1 6.2 Liu B, Koo GC, Yap EH, Chua KL and Gan Y-H (2002) Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection. Infection and Immunity 70(2), 504-511. and Brett PJ and Woods DE (1996) Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates. Infection and Immunity 64(7), 2824-2828. 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