Table 2.
Results from simulation study in two‐sample setting with null causal effect
| Inverse‐variance weighted | Weighted median | Penalized weighted median | MR‐Egger regression | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Proportion of | Mean estimate | Mean estimate | Mean estimate | Mean estimate | |||||||
| N | invalid IVs | F | R 2 | (mean SE) | Power | (mean SE) | Power | (mean SE) | Power | (mean SE) | Power |
| Scenario 1. Balanced pleiotropy, InSIDE assumption satisfied | |||||||||||
| 10,000 | 0.1 | 10.7 | 2.6% | −0.001 (0.114) | 5.4 | −0.001 (0.093) | 3.2 | −0.001 (0.093) | 3.4 | −0.003 (0.287) | 6.3 |
| 10,000 | 0.2 | 10.7 | 2.6% | 0.001 (0.153) | 6.2 | 0.001 (0.098) | 4.5 | 0.001 (0.098) | 4.0 | −0.001 (0.386) | 6.2 |
| 10,000 | 0.3 | 10.7 | 2.6% | 0.003 (0.185) | 6.3 | 0.001 (0.103) | 6.2 | 0.001 (0.104) | 5.2 | 0.000 (0.467) | 6.0 |
| 20,000 | 0.1 | 20.5 | 2.5% | −0.001 (0.107) | 5.1 | 0.000 (0.067) | 3.4 | 0.000 (0.067) | 3.6 | 0.000 (0.305) | 6.0 |
| 20,000 | 0.2 | 20.5 | 2.5% | 0.002 (0.150) | 5.3 | 0.001 (0.071) | 4.4 | 0.001 (0.071) | 4.4 | −0.004 (0.426) | 6.1 |
| 20,000 | 0.3 | 20.5 | 2.5% | −0.004 (0.184) | 5.7 | −0.001 (0.075) | 6.4 | −0.001 (0.077) | 6.3 | −0.004 (0.523) | 6.2 |
| Scenario 2. Directional pleiotropy, InSIDE assumption satisfied | |||||||||||
| 10,000 | 0.1 | 10.7 | 2.6% | 0.126 (0.111) | 14.6 | 0.033 (0.093) | 4.9 | 0.024 (0.093) | 4.2 | 0.013 (0.279) | 6.3 |
| 10,000 | 0.2 | 10.7 | 2.6% | 0.256 (0.145) | 37.0 | 0.078 (0.100) | 10.7 | 0.071 (0.102) | 9.6 | 0.037 (0.363) | 6.5 |
| 10,000 | 0.3 | 10.7 | 2.6% | 0.384 (0.169) | 62.7 | 0.139 (0.109) | 21.8 | 0.149 (0.114) | 22.1 | 0.046 (0.421) | 6.3 |
| 20,000 | 0.1 | 20.5 | 2.5% | 0.134 (0.104) | 15.0 | 0.026 (0.067) | 4.9 | 0.026 (0.068) | 5.2 | 0.003 (0.295) | 6.1 |
| 20,000 | 0.2 | 20.5 | 2.5% | 0.271 (0.141) | 42.9 | 0.061 (0.072) | 11.9 | 0.080 (0.078) | 15.8 | 0.011 (0.398) | 6.2 |
| 20,000 | 0.3 | 20.5 | 2.5% | 0.404 (0.166) | 70.4 | 0.115 (0.080) | 25.4 | 0.177 (0.095) | 35.9 | 0.016 (0.467) | 6.0 |
| Scenario 3. Directional pleiotropy, InSIDE assumption not satisfied | |||||||||||
| 10,000 | 0.1 | 13.5 | 3.3% | 0.182 (0.092) | 48.0 | 0.145 (0.095) | 29.9 | 0.062 (0.094) | 12.6 | 0.363 (0.195) | 50.9 |
| 10,000 | 0.2 | 16.3 | 3.9% | 0.318 (0.105) | 77.2 | 0.303 (0.097) | 61.3 | 0.186 (0.097) | 37.9 | 0.555 (0.204) | 72.5 |
| 10,000 | 0.3 | 19.2 | 4.6% | 0.421 (0.110) | 91.1 | 0.435 (0.092) | 82.5 | 0.335 (0.095) | 65.9 | 0.651 (0.204) | 83.2 |
| 20,000 | 0.1 | 26.0 | 3.1% | 0.189 (0.084) | 53.5 | 0.131 (0.072) | 32.4 | 0.059 (0.070) | 13.2 | 0.412 (0.184) | 57.5 |
| 20,000 | 0.2 | 31.7 | 3.8% | 0.327 (0.100) | 81.0 | 0.290 (0.075) | 63.8 | 0.176 (0.077) | 40.5 | 0.607 (0.198) | 77.1 |
| 20,000 | 0.3 | 37.2 | 4.4% | 0.427 (0.105) | 93.5 | 0.428 (0.072) | 83.9 | 0.321 (0.077) | 68.4 | 0.697 (0.197) | 86.9 |
Mean estimates, mean standard errors, and power of 95% confidence interval to reject null hypothesis of inverse‐variance weighted, weighted median, and MR‐Egger regression methods in simulation study for two‐sample Mendelian randomization with a null () causal effect.
Abbreviations: IV, instrumental variable; SE, standard error.