| |
N = 300 |
N = 1000 |
N = 3000 |
| |
Confounder |
P(Confounder|Exposure)† |
P(Confounder|Exposure)† |
P(Confounder|Exposure)† |
| OR* |
Effect^ |
0.25 |
0.50 |
0.67 |
0.75 |
0.25 |
0.50 |
0.67 |
0.75 |
0.25 |
0.50 |
0.67 |
0.75 |
| |
|
S |
FPR |
S |
S |
S |
FPR |
S |
S |
S |
FPR |
S |
S |
| 0.5 |
P(Y)x0.5 |
0.880 |
0.327 |
0.787 |
0.866 |
0.972 |
0.061 |
0.939 |
0.974 |
>0.999 |
0.003 |
0.998 |
>0.999 |
| 0.5 |
P(Y)x1‡ |
0.672 |
0.093 |
0.459 |
0.655 |
0.398 |
0.002 |
0.177 |
0.396 |
0.167 |
<0.001 |
0.029 |
0.183 |
| 0.5 |
P(Y)x2 |
0.948 |
0.327 |
0.858 |
0.916 |
>0.999 |
0.087 |
0.986 |
>0.999 |
>0.999 |
0.003 |
>0.999 |
>0.999 |
| 2 |
P(Y)x0.5 |
0.872 |
0.316 |
0.804 |
0.910 |
0.964 |
0.093 |
0.952 |
0.975 |
>0.999 |
0.008 |
0.999 |
>0.999 |
| 2 |
P(Y)x1‡ |
0.637 |
0.061 |
0.405 |
0.632 |
0.406 |
<0.001 |
0.184 |
0.410 |
0.129 |
<0.001 |
0.017 |
0.144 |
| 2 |
P(Y)x2 |
0.954 |
0.334 |
0.838 |
0.942 |
0.998 |
0.132 |
0.983 |
0.999 |
>0.999 |
0.023 |
>0.999 |
>0.999 |
| 3 |
P(Y)x0.5 |
0.872 |
0.312 |
0.826 |
0.866 |
0.983 |
0.109 |
0.962 |
0.986 |
0.999 |
0.014 |
0.999 |
>0.999 |
| 3 |
P(Y)x1‡ |
0.659 |
0.074 |
0.445 |
0.622 |
0.375 |
0.001 |
0.177 |
0.385 |
0.140 |
<0.001 |
0.013 |
0.163 |
| 3 |
P(Y)x2 |
0.949 |
0.400 |
0.815 |
0.939 |
>0.999 |
0.192 |
0.975 |
>0.999 |
>0.999 |
0.071 |
>0.999 |
>0.999 |
* OR is the odds ratio between exposure and outcome.
^ Confounder Effect is the influence of the presence of the confounder variable on the outcome. The confounder halves the probability of the outcome (P(Y)x0.5), has no effect on the outcome (P(Y)x1), or doubles the probability of the outcome (P(Y)x2).
† P(Confounder|Exposure) is the association between the possible confounder and exposure variable. The probability of the confounder among exposed subjects is 0.25, 0.50, 0.67, or 0.75. The probability of confounder among unexposed subjects is 0.75, 0.50, 0.33, and 0.25, respectively.
‡ Row displays False Positive Rate as there is no association between possible confounder and outcome, Y, and therefore no confounding. |
