$$P(response)=1-[1+dose\frac{2^{\frac{1}{a}}-1}{N^{50}} ]^{-a}$$

Description
human/H1N1 A/California/10/78 attenuated strain model data [2]
Dose Infected Non-infected Total
63095.73 0 15 15
630957.3 4 7 11
6309573 19 3 22
63095734 24 1 25

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 23.6 21.5 3 3.84 
3.47e-06 		7.81 
3.09e-05
Beta Poisson 2.02 2 5.99 
0.365
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 9.04E-01 4.20E-01 4.91E-01 5.45E-01 1.73E+03 2.57E+04 2.19E+05
N50 1.25E+06 5.27E+05 6.43E+05 7.19E+05 2.39E+06 2.74E+06 3.45E+06

 

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
4.00
Μodel
beta-Poisson
N50
1.25E+06
LD50/ID50
1.25E+06
Dose Units
TCID50
Response
infection
Exposure Route
intranasal
Contains Preferred Model
a
9.04E-01
Agent Strain
H1N1,A/California/10/78 attenuated strain
Experiment ID
257
Host type
human
Description
humans/ echovirus-12 strain 
Dose infected Non-infected Total
330 15 35 50
1000 9 11 20
3300 19 7 26
1E+04 12 0 12

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 7.39 4.18 3 3.84 
0.041 		7.81 
0.0605
Beta Poisson 3.21 2 5.99 
0.201
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 1.06E+00 3.07E-01 4.04E-01 4.69E-01 1.23E+01 6.22E+02 3.74E+04
N50 9.22E+02 4.68E+02 5.59E+02 6.15E+02 1.37E+03 1.49E+03 1.73E+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
4.00
Μodel
beta-Poisson
N50
9.22E+02
LD50/ID50
9.22E+02
Dose Units
PFU
Response
infection
Exposure Route
oral
Contains Preferred Model
a
1.06E+00
Agent Strain
strain 12
Experiment ID
256 (excluding the outliers of exp 112)
Host type
human
Description
hamsters/scrapie strain 263K model data 
Dose Dead Survived Total
200 0 40 40
2000 1 79 80
2E+04 9 71 80
2E+05 58 22 80
2E+06 29 1 30

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 14.5 12.6 4 3.84 
0.000382 		9.49 
0.00576
Beta Poisson 1.92 3 7.81 
0.589
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 1.76E+00 7.48E-01 8.76E-01 9.66E-01 1.44E+04 1.73E+04 2.08E+04
N50 1.04E+05 7.05E+04 7.83E+04 8.22E+04 1.34E+05 1.40E+05 1.55E+05

 

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
5.00
Μodel
beta-Poisson
N50
1.04E+05
LD50/ID50
1.04E+05
Dose Units
LD50 i.c.
Response
death
Exposure Route
oral
Contains Preferred Model
a
1.76E+00
Agent Strain
scrapie strain 263k
Experiment ID
250
Host type
hamsters
Description
Human Inaba Strain 569B  
Dose Infected Non-infected Total
10 0 2 2
1000 3 1 4
1E+04 11 2 13
1E+05 7 1 8
1E+06 21 2 23
1E+08 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 92.4 91.2 5 3.84 
0 		11.1 
0
Beta Poisson 1.16 4 9.49 
0.885
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 2.5E-01 1.14E-01 1.48E-01 1.66E-01 5.44E-01 6.55E-01 2.91E+00
N50 2.43E+02 1.88E+01 4.82E+01 6.35E+01 1.52E+03 2.08E+03 3.60E+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
2.43E+02
LD50/ID50
2.43E+02
Dose Units
CFU
Response
infection
Exposure Route
oral (with NaHCO3)
Contains Preferred Model
a
2.50E-01
Agent Strain
Inaba 569B
Experiment ID
249
Host type
human
Description
Mice/ Salmonella strain 533 data 
Dose Dead Survived Total
1E+04 20 180 200
1E+05 17 153 170
1E+06 11 29 40
3160000 6 24 30
1E+07 12 8 20
3.16E+07 17 3 20
1E+08 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 214 165 6 3.84 
0 		12.6 
0
Beta Poisson 48.7 5 11.1 
2.56e-09
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 1.08E-01 6.19E-02 7.06E-02 7.52E-02 1.79E-01 1.98E-01 2.44E-01
N50 9.66E+06 1.93E+06 2.43E+06 2.82E+06 5.38E+07 8.11E+07 2.13E+08

 

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
7.00
Μodel
beta-Poisson
N50
9.66E+06
LD50/ID50
9.66E+06
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
a
1.08E-01
Agent Strain
strain 533
Experiment ID
248
Host type
mice
Description
Mice/ Salmonella strain 533 data 
Dose Dead Survived Total
603 6 36 42
1910 3 39 42
6030 7 35 42
19100 5 42 47
60300 6 34 40
191000 3 29 32
603000 6 20 26
1910000 7 7 14
6030000 7 5 12
1.91E+07 10 2 12
6.03E+07 13 0 13

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 193 146 10 3.84 
0 		18.3 
0
Beta Poisson 47.5 9 16.9 
3.22e-07
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 6.21E-02 3.53E-02 4.06E-02 4.32E-02 1.09E-01 1.25E-01 1.80E-01
N50 3.46E+07 9.76E+05 1.69E+06 2.40E+06 9.41E+08 2.13E+09 1.34E+10

 

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
11.00
Μodel
beta-Poisson
N50
3.46E+07
LD50/ID50
3.46E+07
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
a
6.21E-02
Agent Strain
strain 533
Experiment ID
247
Host type
mice
Description
Mice/Salmonella strain 216 and 219 data 
Dose Dead Survived Total
5 7 8 15
25 4 11 15
125 7 8 15
630 9 6 15
3160 8 7 15
16000 13 2 15
8E+04 15 0 15
4E+05 15 0 15
2E+06 15 0 15
1E+07 15 0 15

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 133 113 9 3.84 
0 		16.9 
0
Beta Poisson 20.5 8 15.5 
0.00846
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 2.1E-01 1.45E-01 1.58E-01 1.65E-01 2.92E-01 3.14E-01 3.63E-01
N50 4.98E+01 8.10E+00 1.40E+01 1.72E+01 1.31E+02 1.62E+02 2.34E+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
10.00
Μodel
beta-Poisson
N50
4.98E+01
LD50/ID50
4.98E+01
Dose Units
CFU
Response
death
Exposure Route
intraperitoneal
Contains Preferred Model
a
2.1E-01
Agent Strain
strain 216 and 219
Experiment ID
246
Host type
mice
Description
Rhesus monkey Data 
Dose Dead Survived Total
25 1 3 4
66 2 0 2
83 2 0 2
99 1 1 2
182 3 4 7
1111 1 1 2
1774 1 1 2
2287 1 1 2
2586 2 0 2
3166 1 1 2
5055 6 1 7
5519 2 0 2
5652 2 0 2
5669 1 0 1
7459 2 0 2
9199 1 1 2
10774 2 0 2
16790 1 1 2
41023 2 0 2
45498 1 2 3
53206 2 0 2
55195 2 0 2
131771 1 1 2
149175 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 137 113 23 3.84 
0		 35.2 
0
Beta Poisson 24 22 33.9 
0.345
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 1.45E-01 1.82E-02 2.72E-02 4.15E-02 2.59E-01 2.87E-01 3.49E-01
N50 5.01E+01 6.71E-12 6.31E-07 2.86E-03 2.62E+02 3.28E+02 4.87E+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
24.00
Μodel
beta-Poisson
N50
5.01E+01
LD50/ID50
5.01E+01
Dose Units
CFU
Response
death
Exposure Route
aerosol
Contains Preferred Model
a
1.45E-01
Agent Strain
NA
Experiment ID
244
Host type
rhesus monkey
Description
Human/ S. meleagridis strain III data 
Dose Infected Non-infected Total
158000 1 5 6
1.5E+06 5 1 6
7680000 6 0 6
1E+07 5 1 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 7.81 5.51 3 3.84 
0.019 		7.81 
0.0501
Beta Poisson 2.3 2 5.99 
0.316
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 8.85E-01 1.78E-01 2.91E-01 3.68E-01 1.40E+03 1.71E+03 8.24E+03
N50 5.24E+05 4.71E+04 1.20E+05 1.92E+05 1.19E+06 1.39E+06 1.90E+06

 

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
4.00
Μodel
beta-Poisson
N50
5.24E+05
LD50/ID50
5.24E+05
Dose Units
CFU
Response
infection
Exposure Route
oral (with eggnog)
Contains Preferred Model
a
8.85E-01
Agent Strain
strain III
Experiment ID
240
Host type
human
Description
Human / S. meleagridis strain I data
Dose Infected Non-infected Total
12000 3 3 6
24000 4 2 6
52000 3 3 6
96000 3 3 6
155000 5 1 6
3E+05 6 0 6
720000 4 1 5
1150000 6 0 6
5.5E+06 5 1 6
2.4E+07 5 0 5
5E+07 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 71.8 63.8 10 3.84 
1.33e-15 		18.3 
1.98e-11
Beta Poisson 7.99 9 16.9 
0.535
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 3.89E-01 1.23E-01 1.74E-01 2.01E-01 1.12E+00 1.91E+00 3.82E+02
N50 1.68E+04 7.98E+01 1.08E+03 2.27E+03 4.78E+04 5.71E+04 7.49E+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
11.00
Μodel
beta-Poisson
N50
1.68E+04
LD50/ID50
1.68E+04
Dose Units
CFU
Response
infection
Exposure Route
oral (with eggnog)
Contains Preferred Model
a
3.89E-01
Agent Strain
strain I
Experiment ID
238
Host type
human
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