Iowa isolate data [1]
| Dose |
Infected |
Not infected |
Total |
| 30 |
2 |
3 |
5 |
| 100 |
4 |
4 |
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 |
3.07 |
2 |
7 |
3.84
0.157 |
14.1
0.879 |
| Beta Poisson |
1.07 |
6 |
12.6
0.983 |
| 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 |
5.26E-03 |
2.25E-03 |
2.75E-03 |
3.08E-03 |
1.03E-02 |
1.19E-02 |
1.60E-02 |
| ID50/LD50/ETC* |
1.32E+02 |
4.33E+01 |
5.80E+01 |
6.72E+01 |
2.25E+02 |
2.52E+02 |
3.08E+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