Pooled dose response model data [1]
| Dose |
Dead |
Survived |
Total |
| 5 |
0 |
5 |
5 |
| 50 |
1 |
4 |
5 |
| 240 |
1 |
2 |
3 |
| 500 |
3 |
2 |
5 |
| 800 |
3 |
0 |
3 |
| 2400 |
2 |
0 |
2 |
| 5000 |
5 |
0 |
5 |
| 12000 |
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 |
1.75 |
-0.00181 |
7 |
3.84
1 |
14.1
0.972 |
| Beta Poisson |
1.75 |
6 |
12.6
0.941 |
| 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 |
2.46E-03 |
1.07E-03 |
1.28E-03 |
1.35E-03 |
4.59E-03 |
5.27E-03 |
6.80E-03 |
| ID50/LD50/ETC* |
2.82E+02 |
1.02E+02 |
1.32E+02 |
1.51E+02 |
5.13E+02 |
5.43E+02 |
6.47E+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
QMRA