TAMU data [1]
| Dose |
Infected |
Non-infected |
Total |
| 10 |
2 |
1 |
3 |
| 30 |
2 |
1 |
3 |
| 100 |
3 |
0 |
3 |
| 500 |
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 |
1.07 |
0.21 |
3 |
3.84
0.647 |
7.81
0.783 |
| Beta Poisson |
0.864 |
2 |
5.99
0.649 |
| 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 |
5.72E-02 |
1.80E-02 |
1.92E-02 |
2.46E-02 |
2.65E+00 |
2.65E+00 |
2.65E+00 |
| ID50/LD50/ETC* |
1.21E+01 |
2.61E-01 |
2.61E-01 |
2.61E-01 |
2.82E+01 |
3.61E+01 |
3.84E+01 |
| *Not a parameter of the exponential model; however, it facilitates comparison with other models. |
|
Exponential model plot, with confidence bounds around optimized model
Parameter histogram for exponential model (uncertainty of the parameter)
References
QMRA