Mice/Nine mile phase I model data [1]
| Dose |
Dead |
Survived |
Total |
| 0.05 |
0 |
10 |
10 |
| 0.5 |
0 |
10 |
10 |
| 5 |
0 |
10 |
10 |
| 50 |
0 |
10 |
10 |
| 501 |
0 |
10 |
10 |
| 5010 |
0 |
10 |
10 |
| 50100 |
0 |
10 |
10 |
| 501000 |
0 |
10 |
10 |
| 5010000 |
0 |
10 |
10 |
| 5.01E+07 |
0 |
10 |
10 |
| 5.01E+08 |
1 |
9 |
10 |
| 5.01E+09 |
3 |
7 |
10 |
| 5.01E+10 |
9 |
1 |
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 |
1.63 |
0.936 |
12 |
3.84
0.333 |
21
1 |
| Beta Poisson |
0.693 |
11 |
19.7
1 |
| 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 |
5.7E-11 |
2.31E-11 |
2.94E-11 |
3.33E-11 |
1.38E-10 |
1.61E-10 |
2.13E-10 |
| ID50/LD50/ETC* |
1.22E+10 |
3.25E+09 |
4.30E+09 |
5.02E+09 |
2.08E+10 |
2.36E+10 |
2.99E+10 |
| *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