General Overview

Pseudomonas aeruginosa causes bacteremia primarily in immunocompromised and immunosupressed patients. Hematologic malignancies, immunodeficiency relating to AIDS, diabetes mellitus, and severe burns are some of the preexisting conditions (Todar 2012) [1]. Any route including intravascular, intraperitoneal or intranasal routes of bacterial administration can cause ocular infection. An exposure to almost any bacterium able to cause severe bacteremia can result in ocular infection [2].

http://www.cdc.gov/mmwr/preview/mmwrhtml/00001546.htm

Summary Data

Hazlett et al (1978) studied the susceptibility of newborn and infant mice to eye infection by P. aeruginosa. Inoculation of P. aeruginoa under the unopened eyelids of 5 and 10 day old mice resulted in acute infection and death of many animals due to severe bacteremia. [2]

Recommended Model

The pooled model of experiment number 281 and 282 was recommended model for bacteremia due to P. aeruginosa infection via eyes. The LD50 of the pooled model was lower than pooled model of experiment 283 and 284. Pooled model shows improvement in fitting than individual fits.

Exponential and betapoisson model.jpg


References

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
281,282 (pooled) 12 ATCC 19660 CFU Swiss webster mice (5day old) exponential
k = 1.05E-04
LD50/ID50 = 6.61E+03

death Hazlett, L. D., D. D. Rosen, and R. S. Berk. "Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice." Infection and Immunity. 20 (1978): 1.
281 6 ATCC 19660 CFU Swiss webster mice (5day old) exponential
k = 8.52E-05
LD50/ID50 = 8.13E+03

death Hazlett, L. D., D. D. Rosen, and R. S. Berk. "Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice." Infection and Immunity. 20 (1978): 1.
282 6 ATCC 19660 CFU Swiss webster mice (5day old) exponential
k = 1.39E-04
LD50/ID50 = 4.98E+03

death(after day 21) Hazlett, L. D., D. D. Rosen, and R. S. Berk. "Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice." Infection and Immunity. 20 (1978): 1.
283 6 ATCC 19660 CFU Swiss webster mice(10day old) beta-Poisson a = 6.73E-01

LD50/ID50 = 1.93E+04
N50 = 1.93E+04
death(after day 1) Hazlett, L. D., D. D. Rosen, and R. S. Berk. "Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice." Infection and Immunity. 20 (1978): 1.
284 6 ATCC 19660 CFU Swiss webster mice(10day old) beta-Poisson a = 5.49E-01

LD50/ID50 = 1.13E+04
N50 = 1.13E+04
death(after day 2-21) Hazlett, L. D., D. D. Rosen, and R. S. Berk. "Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice." Infection and Immunity. 20 (1978): 1.
283,284 12 ATCC 19660 CFU Swiss webster mice(10day old) beta-Poisson a = 6.01E-01

LD50/ID50 = 1.48E+04
N50 = 1.48E+04
death Hazlett, L. D., D. D. Rosen, and R. S. Berk. "Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice." Infection and Immunity. 20 (1978): 1.
Best Fit
Experiment ID:
281,282 (pooled)
# of Doses:
12
Agent Strain:
ATCC 19660
Dose Units:
CFU
Host type:
Swiss webster mice (5day old)
Μodel:
exponential
Optimized parameters:
k = 1.05E-04
LD50/ID50 = 6.61E+03

Reference:

mice (5day old, day 1-21 pooled) /  Pseudomonas aeruginosa [1]

Dose Dead Survived Total
2.5 0 13 13
2.5 0 13 13
25 0 14 14
25 0 14 14
250 0 12 12
250 0 12 12
2500 4 13 17
2500 4 13 17
25000 13 2 15
25000 15 0 15
250000 17 0 17
250000 17 0 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential

4.36 

 -0.000549

  3.84 
1
19.7
0.958
Beta Poisson

4.36

10 18.3 
0.93
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 500 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.05E-04 6.84E-05 7.49E-05 7.84E-05 1.48E-04 1.57E-04 1.73E-04
ID50/LD50/ETC* 6.61E+03 4.01E+03 4.40E+03 4.68E+03 8.84E+03 9.26E+03 1.01E+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

Experiment ID:
281
# of Doses:
6
Agent Strain:
ATCC 19660
Dose Units:
CFU
Host type:
Swiss webster mice (5day old)
Μodel:
exponential
Optimized parameters:
k = 8.52E-05
LD50/ID50 = 8.13E+03

Reference:
mice (5day old) /  Pseudomonas aeruginosa [1]
Dose Dead Survived Total
2.5 0 13 13
25 0 14 14
250 0 12 12
2500 4 13 17
25000 13 2 15
250000 17 0 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential

0.802

0.0885 5 3.84 
0.766
11.1 
0.977
Beta Poisson

0.713

4 9.49 
0.95
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 8.52E-05 4.21E-05 4.99E-05 5.50E-05 1.53E-04 1.57E-04 2.05E-04
ID50/LD50/ETC* 8.13E+03 3.38E+03 4.40E+03 4.54E+03 1.26E+04 1.39E+04 1.65E+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

Experiment ID:
282
# of Doses:
6
Agent Strain:
ATCC 19660
Dose Units:
CFU
Host type:
Swiss webster mice (5day old)
Μodel:
exponential
Optimized parameters:
k = 1.39E-04
LD50/ID50 = 4.98E+03

Reference:
mice (5day old) /  Pseudomonas aeruginosa [1]
Dose Dead Survived Total
2.5 0 13 13
25 0 14 14
250 0 12 12
2500 4 13 17
25000 15 0 15
250000 17 0 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential

2.17

-0.000196 

5 3.84 
1
11.1 
0.825
Beta Poisson

2.17

4 9.49 
0.704
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.39E-04 8.87E-05 9.90E-05 9.90E-05 2.05E-04 2.36E-04 2.73E-04
ID50/LD50/ETC* 4.98E+03 2.54E+03 2.94E+03 3.38E+03 7.00E+03 7.00E+03 7.82E+03
*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:
283
# of Doses:
6
Agent Strain:
ATCC 19660
Dose Units:
CFU
Host type:
Swiss webster mice(10day old)
Μodel:
beta-Poisson
Optimized parameters: a = 6.73E-01

LD50/ID50 = 1.93E+04
N50 = 1.93E+04
Reference:
mice (10day old, day1) /  Pseudomonas aeruginosa [1]
Dose Dead Survived Total
2.5 0 10 10
25 0 16 16
250 0 15 15
2500 0 13 13
25000 12 4 16
250000 14 3 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential

21.1

13.8 5 3.84 
0.000207
11.1 
0.000783
Beta Poisson

7.32

4 9.49 
0.12
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 6.73E-01 3.02E-01 3.62E-01 3.80E-01 1.55E+00 6.30E+03 1.06E+04
N50 1.93E+04 9.62E+03 1.12E+04 1.18E+04 3.42E+04 4.01E+04 5.18E+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:
284
# of Doses:
6
Agent Strain:
ATCC 19660
Dose Units:
CFU
Host type:
Swiss webster mice(10day old)
Μodel:
beta-Poisson
Optimized parameters: a = 5.49E-01

LD50/ID50 = 1.13E+04
N50 = 1.13E+04
Reference:
mice (10day old, day2-21) /  Pseudomonas aeruginosa [1]
Dose Dead Survived Total
2.5 0 10 10
25 0 16 16
250 0 15 15
2500 2 11 13
25000 13 3 16
250000 14 3 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential

27.3

23.1 5 3.84 
 1.54e-06
11.1
5.01e-05
Beta Poisson

4.19

4 9.49 
0.381
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 5.49E-01 2.38E-01 2.87E-01 3.17E-01 1.37E+00 1.13E+01 1.15E+04
N50 1.13E+04 4.53E+03 5.70E+03 6.34E+03 2.17E+04 2.46E+04 3.39E+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:
283,284
# of Doses:
12
Agent Strain:
ATCC 19660
Dose Units:
CFU
Host type:
Swiss webster mice(10day old)
Μodel:
beta-Poisson
Optimized parameters: a = 6.01E-01

LD50/ID50 = 1.48E+04
N50 = 1.48E+04
Reference:
mice (10day old, day1-21) /  Pseudomonas aeruginosa [1]
Dose Dead Survived Total
2.5 0 10 10
2.5 0 10 10
25 0 16 16
25 0 16 16
250 0 15 15
250 0 15 15
2500 0 13 13
2500 2 11 13
25000 12 4 16
25000 13 3 16
250000 14 3 17
250000 14 3 17

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential

48.6 

36.3 11 3.84 
 1.65e-09
19.7
1.09e-06
Beta Poisson

12.3

10 18.3 
0.265
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 6.01E-01 3.11E-01 3.69E-01 3.97E-01 1.04E+00 1.20E+00 2.01E+00
N50 1.48E+04 8.01E+03 9.07E+03 1.00E+04 2.29E+04 2.55E+04 2.83E+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