Human / Salmonella anatum strain I data[1]
| Dose |
Positive stool culture |
No positive stool culture |
Total |
| 12000 |
2 |
3 |
5 |
| 24000 |
3 |
3 |
6 |
| 66000 |
4 |
2 |
6 |
| 93000 |
1 |
5 |
6 |
| 141000 |
3 |
3 |
6 |
| 256000 |
5 |
1 |
6 |
| 587000 |
4 |
2 |
6 |
| 860000 |
6 |
0 |
6 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
20.5 |
11 |
7 |
3.84
0.000922 |
14.1
0.00457 |
| Beta Poisson |
9.53 |
6 |
12.6
0.146 |
| 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 |
2.91E-01 |
9.77E-04 |
9.77E-04 |
4.11E-02 |
1.68E+00 |
5.36E+00 |
1.20E+03 |
| N50 |
4.44E+04 |
6.74E-02 |
8.03E+02 |
4.15E+03 |
1.64E+05 |
6.89E+06 |
9.07E+07 |
|
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