Model data for S. Typhi (Quailes) in humans [3][4]
| Dose |
Disease |
No disease |
Total |
| 1000 |
0 |
14 |
14 |
| 1E+05 |
28 |
76 |
104 |
| 1E+05 |
32 |
84 |
116 |
| 1E+07 |
15 |
15 |
30 |
| 1E+07 |
16 |
16 |
32 |
| 1E+08 |
8 |
1 |
9 |
| 1E+09 |
4 |
0 |
4 |
| 1E+09 |
40 |
2 |
42 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
419 |
406 |
7 |
3.84
0 |
14.1
0 |
| Beta Poisson |
13.8 |
6 |
12.6
0.0321 |
| Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad. |
|
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 |
1.75E-01 |
1.21E-01 |
1.32E-01 |
1.39E-01 |
2.23E-01 |
2.34E-01 |
2.58E-01 |
| N50 |
1.11E+06 |
5.13E+05 |
6.10E+05 |
6.72E+05 |
2.00E+06 |
2.28E+06 |
2.95E+06 |
|
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