Table 2.
Type I error, power, sensitivity and positive predictive value obtained by the two methods according to the number of true signals and relative risk.
| True zero | True signal | RR | TreeScan-Poisson | TreeScan-ZIP | ||||
|---|---|---|---|---|---|---|---|---|
| Power* | Sensitivity | PPV | Power* | Sensitivity | PPV | |||
| 0 | 0 | 0.043 | 0.043 | |||||
| 2 | 3 | 0.061 | 0.144 | 0.275 | 0.061 | 0.144 | 0.275 | |
| 2 | 4 | 0.086 | 0.260 | 0.490 | 0.086 | 0.261 | 0.491 | |
| 2 | (3.8, 6) | 0.125 | 0.343 | 0.654 | 0.126 | 0.339 | 0.648 | |
| 6 | 3 | 0.833 | 0.176 | 0.976 | 0.833 | 0.176 | 0.976 | |
| 6 | 4 | 0.988 | 0.192 | 0.984 | 0.989 | 0.192 | 0.983 | |
| 6 | (3.8, 6) | 1.000 | 0.209 | 0.987 | 1.000 | 0.209 | 0.986 | |
| 7 | 3 | 1.000 | 0.379 | 0.995 | 1.000 | 0.380 | 0.995 | |
| 7 | 4 | 1.000 | 0.429 | 0.997 | 1.000 | 0.429 | 0.997 | |
| 7 | (3.8, 6) | 1.000 | 0.451 | 0.997 | 1.000 | 0.451 | 0.997 | |
| 13 | 3 | 1.000 | 0.234 | 0.996 | 1.000 | 0.235 | 0.996 | |
| 13 | 4 | 1.000 | 0.297 | 0.998 | 1.000 | 0.299 | 0.998 | |
| 13 | (3.8, 6) | 1.000 | 0.386 | 0.999 | 1.000 | 0.389 | 0.999 | |
| 10 | 0 | 0.052 | 0.046 | |||||
| 2 | 3 | 0.047 | 0.000 | 0.000 | 0.070 | 0.173 | 0.338 | |
| 2 | 4 | 0.042 | 0.000 | 0.000 | 0.104 | 0.304 | 0.581 | |
| 2 | (3.8, 6) | 0.040 | 0.000 | 0.000 | 0.159 | 0.388 | 0.732 | |
| 6 | 3 | 0.002 | 0.069 | 0.417 | 0.952 | 0.192 | 0.983 | |
| 6 | 4 | 0.085 | 0.166 | 0.993 | 1.000 | 0.241 | 0.988 | |
| 5 | (3.8, 6) | 0.901 | 0.200 | 1.000 | 1.000 | 0.388 | 0.992 | |
| 7 | 3 | 1.000 | 0.286 | 1.000 | 1.000 | 0.398 | 0.998 | |
| 7 | 4 | 1.000 | 0.286 | 1.000 | 1.000 | 0.434 | 0.999 | |
| 8 | (3.8, 6) | 1.000 | 0.276 | 1.000 | 1.000 | 0.389 | 0.999 | |
| 13 | 3 | 0.996 | 0.153 | 1.000 | 1.000 | 0.250 | 0.998 | |
| 13 | 4 | 1.000 | 0.154 | 1.000 | 1.000 | 0.318 | 0.999 | |
| 13 | (3.8, 6) | 1.000 | 0.164 | 1.000 | 1.000 | 0.404 | 1.000 | |
| 30 | 0 | 0.051 | 0.049 | |||||
| 2 | 3 | 0.044 | 0.000 | 0.000 | 0.071 | 0.205 | 0.390 | |
| 2 | 4 | 0.037 | 0.000 | 0.000 | 0.115 | 0.338 | 0.629 | |
| 2 | (3.8, 6) | 0.035 | 0.000 | 0.000 | 0.180 | 0.404 | 0.742 | |
| 6 | 3 | 0.002 | 0.000 | 0.000 | 0.982 | 0.242 | 0.986 | |
| 6 | 4 | 0.000 | 0.000 | 0.000 | 1.000 | 0.339 | 0.991 | |
| 5 | (3.8, 6) | 0.174 | 0.200 | 1.000 | 1.000 | 0.452 | 0.993 | |
| 8 | 3 | 0.830 | 0.232 | 1.000 | 1.000 | 0.359 | 0.998 | |
| 8 | 4 | 1.000 | 0.250 | 1.000 | 1.000 | 0.388 | 0.999 | |
| 8 | (3.8, 6) | 1.000 | 0.250 | 1.000 | 1.000 | 0.421 | 0.999 | |
| 14 | 3 | 0.733 | 0.128 | 1.000 | 1.000 | 0.258 | 0.998 | |
| 14 | 4 | 1.000 | 0.143 | 1.000 | 1.000 | 0.326 | 0.999 | |
| 14 | (3.8, 6) | 1.000 | 0.143 | 1.000 | 1.000 | 0.407 | 1.000 | |
| 50 | 0 | 0.052 | 0.051 | |||||
| 2 | 3 | 0.040 | 0.000 | 0.000 | 0.103 | 0.298 | 0.543 | |
| 2 | 4 | 0.033 | 0.000 | 0.000 | 0.184 | 0.423 | 0.761 | |
| 2 | (3.8, 6) | 0.023 | 0.000 | 0.000 | 0.313 | 0.519 | 0.875 | |
| 6 | 3 | 0.001 | 0.000 | 0.000 | 0.998 | 0.349 | 0.990 | |
| 6 | 4 | 0.000 | 0.167 | 1.000 | 1.000 | 0.397 | 0.993 | |
| 6 | (3.8, 6) | 0.258 | 0.167 | 1.000 | 1.000 | 0.404 | 0.995 | |
| 8 | 3 | 0.969 | 0.247 | 1.000 | 1.000 | 0.409 | 0.998 | |
| 8 | 4 | 1.000 | 0.250 | 1.000 | 1.000 | 0.464 | 0.999 | |
| 8 | (3.8, 6) | 1.000 | 0.250 | 1.000 | 1.000 | 0.529 | 1.000 | |
| 14 | 3 | 0.908 | 0.138 | 1.000 | 1.000 | 0.287 | 1.000 | |
| 14 | 4 | 1.000 | 0.143 | 1.000 | 1.000 | 0.362 | 1.000 | |
| 14 | (3.8, 6) | 1.000 | 0.143 | 1.000 | 1.000 | 0.466 | 1.000 | |
| 70 | 0 | 0.050 | 0.049 | |||||
| 2 | 3 | 0.040 | 0.000 | 0.000 | 0.226 | 0.499 | 0.826 | |
| 2 | 4 | 0.035 | 0.000 | 0.000 | 0.462 | 0.586 | 0.926 | |
| 2 | (3.8, 6) | 0.033 | 0.000 | 0.000 | 0.735 | 0.664 | 0.967 | |
| 6 | 3 | 0.000 | – | – | 1.000 | 0.417 | 0.996 | |
| 6 | 4 | 0.013 | 0.167 | 1.000 | 1.000 | 0.499 | 0.997 | |
| 6 | (3.8, 6) | 0.969 | 0.167 | 1.000 | 1.000 | 0.527 | 0.999 | |
| 7 | 3 | 1.000 | 0.286 | 1.000 | 1.000 | 0.429 | 0.999 | |
| 7 | 4 | 1.000 | 0.286 | 1.000 | 1.000 | 0.477 | 0.999 | |
| 7 | (3.8, 6) | 1.000 | 0.286 | 1.000 | 1.000 | 0.586 | 0.999 | |
| 13 | 3 | 1.000 | 0.154 | 1.000 | 1.000 | 0.249 | 0.999 | |
| 13 | 4 | 1.000 | 0.154 | 1.000 | 1.000 | 0.294 | 0.999 | |
| 13 | (3.8, 6) | 1.000 | 0.143 | 1.000 | 1.000 | 0.466 | 1.000 | |
* Type I error when the number of true signals is 0.