Mice/phase I Ohio strain model data [1]
| Dose |
Dead |
Survived |
Total |
| 0.7 |
0 |
30 |
30 |
| 7 |
0 |
20 |
20 |
| 70 |
0 |
30 |
30 |
| 7000 |
0 |
30 |
30 |
| 7E+05 |
0 |
30 |
30 |
| 7E+06 |
1 |
19 |
20 |
| 7E+07 |
6 |
24 |
30 |
| 7E+08 |
16 |
14 |
30 |
| 7E+09 |
23 |
7 |
30 |
| 7E+10 |
19 |
1 |
20 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
73.9 |
72.8 |
9 |
3.84
0 |
16.9
2.65e-12 |
| Beta Poisson |
1.11 |
8 |
15.5
0.997 |
| Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson. |
|
Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
| Parameter |
MLE estimate |
Percentiles |
| 0.5% |
2.5% |
5% |
95% |
97.5% |
99.5% |
| α |
3.57E-01 |
1.91E-01 |
2.20E-01 |
2.38E-01 |
6.34E-01 |
7.08E-01 |
9.84E-01 |
| N50 |
4.93E+08 |
1.89E+08 |
2.41E+08 |
2.73E+08 |
9.34E+08 |
1.06E+09 |
1.36E+09 |
|
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
References
QMRA