Table 2.
Reduced models with correctly specified parameters for adjustment of collider-stratification bias in a cohort (N=100,000) defined by the DAGs in Figures 31 and 41
| Trial | P(S=1|Y=0,X=0,Z=0) | eβSX | eβSY | eβSYX | True ORYX|z |
Biased ORYX|z,S=1 |
Bias adjusted ORYX|z,S-adj |
Bias | RMSE |
|---|---|---|---|---|---|---|---|---|---|
| A1 | 0.10 | 5.0 | 5.0 | 1.0 | 1.01 (0.97, 1.04) | 0.59 (0.55, 0.63) | 1.01 (0.98, 1.05) | 0.0055 | 0.0182 |
| A2 | 0.20 | 5.0 | 5.0 | 1.0 | 1.01 (0.97, 1.04) | 0.62 (0.59, 0.65) | 1.01 (0.98, 1.05) | 0.0019 | 0.0175 |
| A3 | 0.50 | 5.0 | 5.0 | 1.0 | 1.01 (0.97, 1.04) | 0.75 (0.72, 0.78) | 1.01 (0.97, 1.04) | −0.0001 | 0.0174 |
| A4 | 0.70 | 5.0 | 5.0 | 1.0 | 1.01 (0.97, 1.04) | 0.83 (0.80, 0.87) | 1.01 (0.97, 1.04) | −0.0008 | 0.0174 |
| A5 | 0.10 | 0.7 | 0.7 | 1.0 | 1.01 (0.97, 1.04) | 1.00 (0.88, 1.14) | 1.02 (0.98, 1.05) | 0.0067 | 0.0187 |
| A6 | 0.10 | 10.0 | 0.5 | 1.0 | 1.00 (0.96, 1.03) | 1.25 (1.12, 1.39) | 0.99 (0.96, 1.03) | −0.0027 | 0.0183 |
| A7 | 0.10 | 10.0 | 5.0 | 1.0 | 1.00 (0.96, 1.03) | 0.44 (0.41, 0.48) | 0.99 (0.96, 1.03) | −0.0012 | 0.0181 |
| A8 | 0.10 | 10.0 | 10.0 | 1.0 | 1.00 (0.96, 1.03) | 0.33 (0.30, 0.35) | 0.99 (0.96, 1.03) | −0.0018 | 0.0182 |
| B1 | 0.10 | 5.0 | 5.0 | 1.0 | 1.97 (1.90, 2.05) | 1.16 (1.09, 1.24) | 1.98 (1.91, 2.05) | 0.0077 | 0.0203 |
| B2 | 0.20 | 5.0 | 5.0 | 1.0 | 1.97 (1.90, 2.05) | 1.22 (1.16, 1.29) | 1.98 (1.90, 2.05) | 0.0030 | 0.0190 |
| B3 | 0.50 | 5.0 | 5.0 | 1.0 | 1.97 (1.90, 2.05) | 1.47 (1.41, 1.53) | 1.97 (1.90, 2.05) | 0.0000 | 0.0188 |
| B4 | 0.70 | 5.0 | 5.0 | 1.0 | 1.97 (1.90, 2.05) | 1.63 (1.57, 1.70) | 1.97 (1.90, 2.05) | −0.0014 | 0.0188 |
| B5 | 0.10 | 0.7 | 0.7 | 1.0 | 1.97 (1.90, 2.05) | 1.99 (1.73, 2.29) | 2.01 (1.94, 2.09) | 0.0365 | 0.0410 |
| B6 | 0.10 | 10.0 | 0.5 | 1.0 | 1.97 (1.90, 2.04) | 2.54 (2.32, 2.78) | 1.97 (1.90, 2.05) | 0.0062 | 0.0199 |
| B7 | 0.10 | 10.0 | 5.0 | 1.0 | 1.97 (1.90, 2.04) | 0.92 (0.85, 0.98) | 1.97 (1.90, 2.04) | 0.0002 | 0.0189 |
| B8 | 0.10 | 10.0 | 10.0 | 1.0 | 1.97 (1.90, 2.04) | 0.82 (0.77, 0.87) | 1.97 (1.90, 2.04) | 0.0027 | 0.0191 |
| C1 | 0.20 | 5.0 | 5.0 | 0.4 | 1.97 (1.90, 2.05) | 1.05 (1.00, 1.11) | 1.98 (1.90, 2.05) | 0.0023 | 0.0189 |
| C2 | 0.20 | 5.0 | 5.0 | 0.8 | 1.97 (1.90, 2.05) | 1.19 (1.13, 1.25) | 1.98 (1.90, 2.05) | 0.0033 | 0.0191 |
| C3 | 0.20 | 5.0 | 5.0 | 2.0 | 1.97 (1.90, 2.05) | 1.29 (1.22, 1.36) | 1.98 (1.90, 2.05) | 0.0029 | 0.0190 |
| C4 | 0.20 | 5.0 | 5.0 | 5.0 | 1.97 (1.90, 2.05) | 1.34 (1.27, 1.41) | 1.98 (1.90, 2.05) | 0.0031 | 0.0190 |
1
Simulated prevalences in the hypothetical population were held constant as follows: P(X=1 | Z=0) = 0.3 and P(Y=1 | X=0, Z=0) = 0.5.