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General 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 . Miller et al.(1948) explored infection in guinea pigs via intraperitoneal route . Similarly, Brett and Woods(1996) experimented infection in diabetic rats with B. pseuomallei 316c strain .

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.

 

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
17 intranasal 5.00 KHW CFU BALB/c mice exponential 6.63E+01 k = 1.04E-02 infection
Liu, B. ., Koo, G. C., Yap, E. H., Chua, K. L., & Y-h, G. . (2002). Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection. Infection and Immunity, 70, 2.
18 intranasal 5.00 KHW CFU C57BL/6 mice exponential 6.92E+03 k = 1.00E-04 infection
Liu, B. ., Koo, G. C., Yap, E. H., Chua, K. L., & Y-h, G. . (2002). Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection. Infection and Immunity, 70, 2.
18,23 10.00 KHW,316c CFU C57BL/6 mice and diabetic rat beta-Poisson 5.43E+03 a = 3.28E-01 N50 = 5.43E+03 death
Brett, P. J., & Woods, D. E. (1996). Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates. Infection and Immunity, 64, 2824–2828.
21 intraperitoneal 6.00 W294 CFU guinea pig beta-Poisson 2.55E+02 a = 2.67E-01 N50 = 2.55E+02 death
Miller, W. R., Pannell, L. ., Cravitz, L. ., Tanner, W. A., & Rosebury, T. . (1948). Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei. Journal of Bacteriology, 55, 1.
21,23 intraperitoneal 11.00 W294, 316c CFU guinea pig and diabetic rat beta-Poisson 4.77E+02 a = 2.13E-01 N50 = 4.77E+02 death
Miller, W. R., Pannell, L. ., Cravitz, L. ., Tanner, W. A., & Rosebury, T. . (1948). Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei. Journal of Bacteriology, 55, 1.
23 intraperitoneal 5.00 316c CFU diabetic rat beta-Poisson 2.27E+03 a = 2.65E-01 N50 = 2.27E+03 death
Brett, P. J., & Woods, D. E. (2000). Pathogenesis of and immunity to melioidosis. Acta Tropica, 74, 2.
Exposure Route:
intranasal
# of Doses:
5.00
Agent Strain:
KHW
Dose Units:
CFU
Host type:
BALB/c mice
Μodel:
exponential
LD50/ID50:
6.63E+01
Optimized parameters: k = 1.04E-02
Response type:
infection
Reference:
Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection
BALB/c Mice KHW Strain Data 
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)
Parameter histogram for exponential model (uncertainty of the parameter)

 

Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model

 

 

 

Exposure Route:
intranasal
# of Doses:
5.00
Agent Strain:
KHW
Dose Units:
CFU
Host type:
C57BL/6 mice
Μodel:
exponential
LD50/ID50:
6.92E+03
Optimized parameters: k = 1.00E-04
Response type:
infection
Reference:
Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection
C57BL/6 Mice KHW Strain Data 
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)
Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Exponential model plot, with confidence bounds around optimized model
Highest quality
Exposure Route:
# of Doses:
10.00
Agent Strain:
KHW,316c
Dose Units:
CFU
Host type:
C57BL/6 mice and diabetic rat
Μodel:
beta-Poisson
LD50/ID50:
5.43E+03
Optimized parameters: a = 3.28E-01 N50 = 5.43E+03
Response type:
death
Reference:
Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates.

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

Pooled data of C57BL/6 mice and diabetic rat 
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.
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
beta Poisson model plot, with confidence bounds around optimized model

 

Exposure Route:
intraperitoneal
# of Doses:
6.00
Agent Strain:
W294
Dose Units:
CFU
Host type:
guinea pig
Μodel:
beta-Poisson
LD50/ID50:
2.55E+02
Optimized parameters: a = 2.67E-01 N50 = 2.55E+02
Response type:
death
Reference:
Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei
Guinea Pigs W294 Strain Data 
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.
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
beta Poisson model plot, with confidence bounds around optimized model
Exposure Route:
intraperitoneal
# of Doses:
11.00
Agent Strain:
W294, 316c
Dose Units:
CFU
Host type:
guinea pig and diabetic rat
Μodel:
beta-Poisson
LD50/ID50:
4.77E+02
Optimized parameters: a = 2.13E-01 N50 = 4.77E+02
Response type:
death
Reference:
Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei
Pooled data of guinea pig and diabetic rat  
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.
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
beta Poisson model plot, with confidence bounds around optimized model
Exposure Route:
intraperitoneal
# of Doses:
5.00
Agent Strain:
316c
Dose Units:
CFU
Host type:
diabetic rat
Μodel:
beta-Poisson
LD50/ID50:
2.27E+03
Optimized parameters: a = 2.65E-01 N50 = 2.27E+03
Response type:
death
Reference:
Pathogenesis of and immunity to melioidosis
diabetic rat and 316c strain 
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.
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
beta Poisson model plot, with confidence bounds around optimized model

References

  • Liu, B. ., Koo, G. C., Yap, E. H., Chua, K. L., & Y-h, G. . (2002). Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection. Infection and Immunity, 70, 2.
  • Miller, W. R., Pannell, L. ., Cravitz, L. ., Tanner, W. A., & Rosebury, T. . (1948). Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei. Journal of Bacteriology, 55, 1.
  • Brett, P. J., & Woods, D. E. (1996). Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates. Infection and Immunity, 64, 2824–2828.