Iowa strain data [1]
| Dose |
Infected |
Non-infected |
Total |
| 30 |
1 |
4 |
5 |
| 100 |
3 |
5 |
8 |
| 300 |
2 |
1 |
3 |
| 500 |
5 |
1 |
6 |
| 1000 |
2 |
0 |
2 |
| 1E+04 |
3 |
0 |
3 |
| 1E+05 |
1 |
0 |
1 |
| 1E+06 |
1 |
0 |
1 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
0.503 |
0.131 |
7 |
3.84
0.717 |
14.1
0.999 |
| Beta Poisson |
0.372 |
6 |
12.6
0.999 |
| 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 |
4.19E-03 |
1.80E-03 |
2.22E-03 |
2.46E-03 |
7.52E-03 |
8.52E-03 |
1.12E-02 |
| ID50/LD50/ETC* |
1.65E+02 |
6.17E+01 |
8.14E+01 |
9.22E+01 |
2.82E+02 |
3.12E+02 |
3.84E+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
References
QMRA 
