Human/ Salmonella anatum strain II data [4]
| Dose |
Positive stool culture |
No positive stool culture |
Total |
| 89000 |
5 |
1 |
6 |
| 448000 |
4 |
2 |
6 |
| 1040000 |
6 |
0 |
6 |
| 3.9E+06 |
4 |
2 |
6 |
| 1E+07 |
6 |
0 |
6 |
| 2.39E+07 |
5 |
1 |
6 |
| 4.45E+07 |
6 |
0 |
6 |
| 6.73E+07 |
8 |
0 |
8 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
62.8 |
54.2 |
7 |
3.84
1.84e-13 |
14.1
4.22e-11 |
| Beta Poisson |
8.6 |
6 |
12.6
0.198 |
| 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 |
2.3E-01 |
3.63E-02 |
5.29E-02 |
6.00E-02 |
5.51E-01 |
6.70E-01 |
1.40E+00 |
| N50 |
4.91E+03 |
2.59E-10 |
2.73E-08 |
4.91E-06 |
8.72E+04 |
1.23E+05 |
2.29E+05 |
|
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
QMRA