Mice/ Aa strain model data [1]
| Dose |
Dead |
Survived |
Total |
| 1E+04 |
0 |
22 |
22 |
| 1E+05 |
1 |
21 |
22 |
| 1E+06 |
1 |
10 |
11 |
| 1E+07 |
16 |
6 |
22 |
| 1E+08 |
22 |
0 |
22 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
1.27 |
0.0341 |
4 |
3.84
0.854 |
9.49
0.867 |
| Beta Poisson |
1.23 |
3 |
7.81
0.745 |
| 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 |
1.33E-07 |
6.86E-08 |
7.91E-08 |
8.83E-08 |
2.06E-07 |
2.24E-07 |
2.75E-07 |
| ID50/LD50/ETC* |
5.22E+06 |
2.52E+06 |
3.10E+06 |
3.37E+06 |
7.85E+06 |
8.76E+06 |
1.01E+07 |
| *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