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 (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.

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 # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
17 5 KHW CFU BALB/c mice exponential
k = 1.04E-02
LD50/ID50 = 6.63E+01

infection Liu, B., et al. "Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection." Infection and Immunity. 70 (2002): 2.
18 5 KHW CFU C57BL/6 mice exponential
k = 1.00E-04
LD50/ID50 = 6.92E+03

infection Liu, B., et al. "Model of Differential Susceptibility to Mucosal Burkholderia pseudomallei Infection." Infection and Immunity. 70 (2002): 2.
18,23 10 KHW,316c CFU C57BL/6 mice and diabetic rat beta-Poisson a = 3.28E-01

LD50/ID50 = 5.43E+03
N50 = 5.43E+03
death Brett, Paul J., and Donald E. Woods. "Structural and immunological characterization of Burkholderia pseudomallei O-polysaccharide-flagellin protein conjugates." Infection and immunity. 64 (1996): 2824-2828.
21 6 W294 CFU guinea pig beta-Poisson a = 2.67E-01

LD50/ID50 = 2.55E+02
N50 = 2.55E+02
death Miller, W. R., et al. "Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei." Journal of Bacteriology. 55 (1948): 1.
21,23 11 W294, 316c CFU guinea pig and diabetic rat beta-Poisson a = 2.13E-01

LD50/ID50 = 4.77E+02
N50 = 4.77E+02
death Miller, W. R., et al. "Studies on Certain Biological Characteristics of Malleomyces mallei and Malleomyces pseudomallei." Journal of Bacteriology. 55 (1948): 1.
23 5 316c CFU diabetic rat beta-Poisson a = 2.65E-01

LD50/ID50 = 2.27E+03
N50 = 2.27E+03
death Brett, P. J., and D. E. Woods. "Pathogenesis of and immunity to melioidosis." Acta Tropica. 74 (2000): 2.
Experiment ID:
17
# of Doses:
5
Agent Strain:
KHW
Dose Units:
CFU
Host type:
BALB/c mice
Μodel:
exponential
Optimized parameters:
k = 1.04E-02
LD50/ID50 = 6.63E+01

Reference:
BALB/c Mice KHW Strain Data [1]
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

 

 

 


References

Experiment ID:
18
# of Doses:
5
Agent Strain:
KHW
Dose Units:
CFU
Host type:
C57BL/6 mice
Μodel:
exponential
Optimized parameters:
k = 1.00E-04
LD50/ID50 = 6.92E+03

Reference:
C57BL/6 Mice KHW Strain Data [1]
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


References

Best Fit
Experiment ID:
18,23
# of Doses:
10
Agent Strain:
KHW,316c
Dose Units:
CFU
Host type:
C57BL/6 mice and diabetic rat
Μodel:
beta-Poisson
Optimized parameters: a = 3.28E-01

LD50/ID50 = 5.43E+03
N50 = 5.43E+03
Reference:

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

Pooled data of C57BL/6 mice and diabetic rat [1]
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


References

Experiment ID:
21
# of Doses:
6
Agent Strain:
W294
Dose Units:
CFU
Host type:
guinea pig
Μodel:
beta-Poisson
Optimized parameters: a = 2.67E-01

LD50/ID50 = 2.55E+02
N50 = 2.55E+02
Reference:
Guinea Pigs W294 Strain Data [1]
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


References

Experiment ID:
21,23
# of Doses:
11
Agent Strain:
W294, 316c
Dose Units:
CFU
Host type:
guinea pig and diabetic rat
Μodel:
beta-Poisson
Optimized parameters: a = 2.13E-01

LD50/ID50 = 4.77E+02
N50 = 4.77E+02
Reference:
Pooled data of guinea pig and diabetic rat [1] 
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


References

Experiment ID:
23
# of Doses:
5
Agent Strain:
316c
Dose Units:
CFU
Host type:
diabetic rat
Μodel:
beta-Poisson
Optimized parameters: a = 2.65E-01

LD50/ID50 = 2.27E+03
N50 = 2.27E+03
Reference:
diabetic rat and 316c strain [1]
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