Description
TITLE 
Dose INFECTION NOT

INFECTION || Total
0.05 0 4 4
0.15 1 4 5
0.5 3 14 17
1.5 4 10 14
5 4 11 15
50 28 14 42
Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 29.2 26.2 5 3.84 
{{{pbPbetter}}} 		11.1 
2.16e-05
Beta Poisson 2.93 4 9.49 
0

selection
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.
Optimized parameters for the beta-Poisson model, from 10000 bootstrapiterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 2E-01 7.86E-02 9.79E-02 1.11E-01 4.65E-01 5.58E-01 8.66E-01
N50 1.05E+01 3.00E+00 3.98E+00 4.65E+00 3.67E+01 5.32E+01 1.22E+02

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

# of Doses
6.00
Μodel
beta-Poisson
N50
1.05E+01
LD50/ID50
1.05E+01
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
2,00E-01
Agent Strain
type 39
Experiment ID
313
Host type
human
Description
TITLE 
Dose INFECTION NOT

INFECTION || Total
0.05 0 4 4
0.15 1 4 5
0.5 0 4 4
0.5 3 14 17
1.5 2 3 5
1.5 4 10 14
5 1 4 5
5 4 11 15
15 4 3 7
50 28 14 42
150 13 8 21
300 5 2 7

"

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 78.6 72.3 11 3.84 
{{{pbPbetter}}} 		19.7 
2.8e-12
Beta Poisson 6.22 10 18.3 
0.796
{{{interpretation}}}

"

Optimized parameters for the beta-Poisson model, from 10000 bootstrapiterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.82E-01 1.04E-03 1.03E-01 1.14E-01 3.04E-01 3.38E-01 4.09E-01
N50 1.38E+01 2.98E+00 5.64E+00 6.67E+00 3.77E+01 4.98E+01 1.32E+02

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

# of Doses
12.00
Μodel
beta-Poisson
N50
1.38E+01
LD50/ID50
1.38E+01
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
1.82E-01
Agent Strain
type 14
Experiment ID
312, 313
Host type
human
Description
TITLE 
Dose INFECTION NOT

INFECTION || Total
0.5 0 4 4
1.5 2 3 5
5 1 4 5
15 4 3 7
150 13 8 21
300 5 2 7
Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 24.3 21.5 5 3.84 
{{{pbPbetter}}} 		11.1 
0.000194
Beta Poisson 2.77 4 9.49 
0

selection
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.
Optimized parameters for the beta-Poisson model, from 10000 bootstrapiterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.81E-01 3.92E-02 7.30E-02 9.02E-02 4.00E-01 4.79E-01 7.28E-01
N50 2.22E+01 3.12E+00 5.01E+00 6.38E+00 1.22E+02 2.06E+02 1.26E+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

# of Doses
6.00
Μodel
beta-Poisson
N50
2.22E+01
LD50/ID50
2.22E+01
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
1.81E-01
Agent Strain
type 14
Experiment ID
312
Host type
human
Description

Optimization Output for experiment 311

TITLE 
Dose INFECTION NOT

INFECTION || Total
0.05 0 2 2
0.15 1 3 4
0.5 5 2 7
1.5 18 1 19
5 1 0 1
50 19 1 20
Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 61.7 56.8 5 3.84 
{{{pbPbetter}}} 		11.1 
5.32e-12
Beta Poisson 4.95 4 9.49 
0

selection
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.
Optimized parameters for the beta-Poisson model, from 10000 bootstrapiterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 7.01E-01 2.29E-01 3.14E-01 3.63E-01 1.81E+06 3.82E+06 1.41E+07
N50 1.9E-01 2.27E-02 5.85E-02 7.93E-02 4.20E-01 4.52E-01 5.56E-01

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

# of Doses
6.00
Μodel
beta-Poisson
N50
1.9E-01
LD50/ID50
1.9E-01
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
7.01E-01
Agent Strain
type 39
Experiment ID
311
Host type
human
Description
TITLE 
Dose INFECTION NOT

INFECTION || Total
0.5 1 4 5
1.5 2 3 5
5 3 2 5
15 2 1 3
150 14 5 19
300 5 0 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 29.7 27.3 5 3.84 
{{{pbPbetter}}} 		11.1 
1.71e-05
Beta Poisson 2.42 4 9.49 
0

selection
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.
Optimized parameters for the beta-Poisson model, from 10000 bootstrapiterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 2.52E-01 9.79E-04 9.14E-02 1.16E-01 5.50E-01 6.41E-01 1.06E+00
N50 3.83E+00 9.08E-03 3.23E-01 6.41E-01 1.48E+01 2.04E+01 8.86E+01

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

# of Doses
6.00
Μodel
beta-Poisson
N50
3.83E+00
LD50/ID50
3.83E+00
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
2.52E-01
Agent Strain
type 14
Experiment ID
310
Host type
human
Description
Humans/ type 4 Strain model data 
Dose Infected Non-infected Total
1 1 2 3
5 3 0 3
11 3 0 3
1000 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 0.487 -0.000723 3 3.84 
1 		7.81 
0.922
Beta Poisson 0.488 2 5.99 
0.784
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 6.07E-01 3.87E-01 3.87E-01 3.87E-01 1.13E+00 1.13E+00 1.13E+00
ID50/LD50/ETC* 1.14E+00 6.11E-01 6.11E-01 6.11E-01 1.79E+00 1.79E+00 1.79E+00
*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

# of Doses
4.00
Μodel
exponential
LD50/ID50
1.14E+00
Dose Units
TCID50
Response
infection
Exposure Route
inhalation
Contains Preferred Model
k
6.07E-01
Agent Strain
type 4
Experiment ID
31
Host type
human
Description
Human data( Rickettsia rickettsii) 
Dose CLINICAL SIGNS NOT CLINICAL SIGNS Total
13 2 4 6
126 6 1 7
1260 17 1 18

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 13.5 13.2 2 3.84 
0.000277		 5.99 
0.00119
Beta Poisson 0.248 1 3.84 
0.618
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 6.75E-01 1.17E-01 2.44E-01 3.31E-01 1.21E+03 3.74E+03 4.98E+03
N50 2.36E+01 2.56E-02 3.35E+00 7.30E+00 6.41E+01 8.91E+01 1.28E+02

 

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

# of Doses
3.00
Μodel
beta-Poisson
N50
2.36E+01
LD50/ID50
2.36E+01
Dose Units
CFU
Response
clinical signs
Exposure Route
intradermal
Contains Preferred Model
a
6.75E-01
Agent Strain
Sheila Smith
Experiment ID
301
Host type
human
Description
Pooled data (experiment no. 300 and 301) 
Dose MORBIDITY NOT MORBIDITY Total
13 2 4 6
25 1 3 4
66 2 0 2
83 2 0 2
99 2 0 2
126 6 1 7
182 7 0 7
1110 1 1 2
1260 17 1 18
1770 2 0 2
2290 2 0 2
2590 2 0 2
3170 2 0 2
5060 7 0 7
5520 2 0 2
5650 2 0 2
5670 1 0 1
7460 2 0 2
9200 2 0 2
10800 2 0 2
16800 2 0 2
41000 2 0 2
45500 3 0 3
53200 2 0 2
55200 2 0 2
132000 2 0 2
149000 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 42.2 30.5 26 3.84 
3.41e-08		 38.9 
0.0235
Beta Poisson 11.7 25 37.7 
0.989
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 7.77E-01 3.82E-01 4.41E-01 4.90E-01 4.24E+00 3.59E+03 3.25E+04
N50 2.13E+01 5.70E+00 8.34E+00 1.01E+01 4.00E+01 4.16E+01 5.10E+01

 

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

# of Doses
27.00
Μodel
beta-Poisson
N50
2.13E+01
LD50/ID50
2.13E+01
Dose Units
CFU
Response
morbidity
Contains Preferred Model
a
7.77E-01
Agent Strain
R1 and Sheila Smith
Experiment ID
300 and 301
Host type
pooled
Description
Rhesus monkey Data 
Dose MORBIDITY NOT MORBIDITY Total
25 1 3 4
66 2 0 2
83 2 0 2
99 2 0 2
182 7 0 7
1110 1 1 2
1770 2 0 2
2290 2 0 2
2590 2 0 2
3170 2 0 2
5060 7 0 7
5520 2 0 2
5650 2 0 2
5670 1 0 1
7460 2 0 2
9200 2 0 2
10800 2 0 2
16800 2 0 2
41000 2 0 2
45500 3 0 3
53200 2 0 2
55200 2 0 2
132000 2 0 2
149000 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value		 χ20.95,m-k 
p-value
Exponential 27.6 16.4 23 3.84 
5.12e-05		 35.2 
0.232
Beta Poisson 11.2 22 33.9 
0.972
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 8.58E-01 9.77E-04 9.77E-04 9.78E-04 5.70E+06 1.41E+08 1.62E+11
N50 1.88E+01 3.58E-01 1.81E+00 7.74E+00 1.02E+03 4.02E+03 3.71E+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

# of Doses
24.00
Μodel
beta-Poisson
N50
1.88E+01
LD50/ID50
1.88E+01
Dose Units
CFU
Response
morbidity
Exposure Route
aerosol
Contains Preferred Model
a
8.58E-01
Agent Strain
R1
Experiment ID
300
Host type
rhesus monkey
Description
Mouse/ CO92 model data 
Dose Dead Survived Total
2 0 20 20
8 5 15 20
26 13 7 20
74 9 1 10
257 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 3.12 -9.43e-05 4 3.84 
1 		9.49 
0.539
Beta Poisson 3.12 3 7.81 
0.374
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 3.45E-02 2.01E-02 2.28E-02 2.44E-02 4.89E-02 5.18E-02 5.79E-02
ID50/LD50/ETC* 2.01E+01 1.20E+01 1.34E+01 1.42E+01 2.84E+01 3.04E+01 3.44E+01
*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

# of Doses
5.00
Μodel
exponential
LD50/ID50
2.01E+01
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
k
3.45E-02
Agent Strain
CO92
Experiment ID
3
Host type
mice
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