Pseudomonas aeruginosa (bacterimia): Dose Response Models

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) . 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 .

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.

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

ID	Exposure Route	# of Doses	Agent Strain	Dose Units	Host type	Μodel	LD50/ID50	Optimized parameters	Response type	Reference
281	injected in eyelids	6.00	ATCC 19660	CFU	Swiss webster mice (5day old)	exponential	8.13E+03	k = 8.52E-05	death	Hazlett, L. D., Rosen, D. D., & Berk, R. S. (1978). Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice. Infection and Immunity, 20, 1.
281,282 (pooled)	injected in eyelids	12.00	ATCC 19660	CFU	Swiss webster mice (5day old)	exponential	6.61E+03	k = 1.05E-04	death	Hazlett, L. D., Rosen, D. D., & Berk, R. S. (1978). Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice. Infection and Immunity, 20, 1.
282	injected in eyelids	6.00	ATCC 19660	CFU	Swiss webster mice (5day old)	exponential	4.98E+03	k = 1.39E-04	death(after day 21)	Hazlett, L. D., Rosen, D. D., & Berk, R. S. (1978). Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice. Infection and Immunity, 20, 1.
283	injected in eyelids	6.00	ATCC 19660	CFU	Swiss webster mice(10day old)	beta-Poisson	1.93E+04	a = 6.73E-01 N₅₀ = 1.93E+04	death(after day 1)	Hazlett, L. D., Rosen, D. D., & Berk, R. S. (1978). Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice. Infection and Immunity, 20, 1.
283,284	injected in eyelids	12.00	ATCC 19660	CFU	Swiss webster mice(10day old)	beta-Poisson	1.48E+04	a = 6.01E-01 N₅₀ = 1.48E+04	death	Hazlett, L. D., Rosen, D. D., & Berk, R. S. (1978). Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice. Infection and Immunity, 20, 1.
284	injected in eyelids	6.00	ATCC 19660	CFU	Swiss webster mice(10day old)	beta-Poisson	1.13E+04	a = 5.49E-01 N₅₀ = 1.13E+04	death(after day 2-21)	Hazlett, L. D., Rosen, D. D., & Berk, R. S. (1978). Age-Related Susceptibility to Pseudomonas aeruginosa Ocular Infections in Mice. Infection and Immunity, 20, 1.

Exposure Route:

injected in eyelids

# of Doses:

6.00

Agent Strain:

ATCC 19660

Dose Units:

CFU

Host type:

Swiss webster mice (5day old)

Μodel:

exponential

LD50/ID50:

8.13E+03

Optimized parameters: k = 8.52E-05

Response type:

death

Reference:

mice (5day old) / *Pseudomonas aeruginosa*
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	0.802	0.0885	5	3.84 0.766	11.1 0.977
Beta Poisson	0.713	0.0885	4	3.84 0.766	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
Parameter	MLE estimate	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

Highest quality

Exposure Route:

injected in eyelids

# of Doses:

12.00

Agent Strain:

ATCC 19660

Dose Units:

CFU

Host type:

Swiss webster mice (5day old)

Μodel:

exponential

LD50/ID50:

6.61E+03

Optimized parameters: k = 1.05E-04

Response type:

death

Reference:

mice (5day old, day 1-21 pooled) / *Pseudomonas aeruginosa*
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	4.36	-0.000549		3.84 1	19.7 0.958
Beta Poisson	4.36	-0.000549	10	3.84 1	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
Parameter	MLE estimate	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

Exposure Route:

injected in eyelids

# of Doses:

6.00

Agent Strain:

ATCC 19660

Dose Units:

CFU

Host type:

Swiss webster mice (5day old)

Μodel:

exponential

LD50/ID50:

4.98E+03

Optimized parameters: k = 1.39E-04

Response type:

death(after day 21)

Reference:

mice (5day old) / *Pseudomonas aeruginosa*
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	2.17	-0.000196	5	3.84 1	11.1 0.825
Beta Poisson	2.17	-0.000196	4	3.84 1	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
Parameter	MLE estimate	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

Exposure Route:

injected in eyelids

# of Doses:

6.00

Agent Strain:

ATCC 19660

Dose Units:

CFU

Host type:

Swiss webster mice(10day old)

Μodel:

beta-Poisson

LD50/ID50:

1.93E+04

Optimized parameters: a = 6.73E-01 N₅₀ = 1.93E+04

Response type:

death(after day 1)

Reference:

mice (10day old, day1) / *Pseudomonas aeruginosa*
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	21.1	13.8	5	3.84 0.000207	11.1 0.000783
Beta Poisson	7.32	13.8	4	3.84 0.000207	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
Parameter	MLE estimate	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

Exposure Route:

injected in eyelids

# of Doses:

12.00

Agent Strain:

ATCC 19660

Dose Units:

CFU

Host type:

Swiss webster mice(10day old)

Μodel:

beta-Poisson

LD50/ID50:

1.48E+04

Optimized parameters: a = 6.01E-01 N₅₀ = 1.48E+04

Response type:

death

Reference:

mice (10day old, day1-21) / *Pseudomonas aeruginosa*
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	48.6	36.3	11	3.84 1.65e-09	19.7 1.09e-06
Beta Poisson	12.3	36.3	10	3.84 1.65e-09	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
Parameter	MLE estimate	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

Exposure Route:

injected in eyelids

# of Doses:

6.00

Agent Strain:

ATCC 19660

Dose Units:

CFU

Host type:

Swiss webster mice(10day old)

Μodel:

beta-Poisson

LD50/ID50:

1.13E+04

Optimized parameters: a = 5.49E-01 N₅₀ = 1.13E+04

Response type:

death(after day 2-21)

Reference:

mice (10day old, day2-21) / *Pseudomonas aeruginosa*
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	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	27.3	23.1	5	3.84 1.54e-06	11.1 5.01e-05
Beta Poisson	4.19	23.1	4	3.84 1.54e-06	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
Parameter	MLE estimate	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

Pseudomonas aeruginosa (bacterimia): Dose Response Models Dose response experiments

General Overview

Summary Data

Recommended Model

References