Guinea pig/ Josiah strain model data [1]
| Dose |
Dead |
Survived |
Total |
| 0.02 |
1 |
9 |
10 |
| 0.2 |
4 |
6 |
10 |
| 2 |
10 |
0 |
10 |
| 24 |
10 |
0 |
10 |
| 2400 |
15 |
0 |
15 |
| 240000 |
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 |
0.42 |
-0.000621 |
5 |
3.84
1 |
11.1
0.995 |
| Beta Poisson |
0.42 |
4 |
9.49
0.981 |
| 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 |
2.95E+00 |
1.35E+00 |
1.61E+00 |
1.65E+00 |
5.43E+00 |
5.90E+00 |
7.52E+00 |
| ID50/LD50/ETC* |
2.35E-01 |
9.21E-02 |
1.17E-01 |
1.28E-01 |
4.21E-01 |
4.32E-01 |
5.14E-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
References
QMRA