Table 1.
Validation simulation to compare estimates of power in a Mendelian randomization analysis with a continuous risk factor and a binary outcome from analytical formula and simulation study with a 5% significance level varying the size of causal effect (β1), the IV strength (
), the sample size and the ratio of cases to controls
| Case:control ratio = 1:1 | 10000 cases |
20000 cases |
30000 cases |
||||
|---|---|---|---|---|---|---|---|
| Formula | Simulation | Formula | Simulation | Formula | Simulation | ||
 = 0.01 |
β1 = 0.1 | 10.5% | 10.2% | 16.9% | 16.6% | 23.1% | 22.4% |
| β1 = 0.2 | 29.3% | 28.4% | 51.6% | 51.2% | 68.8% | 69.5% | |
| β1 = 0.3 | 56.4% | 56.4% | 85.1% | 85.0% | 95.7% | 95.7% | |
 = 0.02 |
β1 = 0.1 | 16.9% | 17.2% | 29.3% | 28.9% | 41.0% | 41.1% |
| β1 = 0.2 | 51.6% | 51.0% | 80.7% | 80.2% | 93.4% | 93.6% | |
| β1 = 0.3 | 85.1% | 84.9% | 98.9% | 98.9% | 99.9% | 100.0% | |
 = 0.03 |
β1 = 0.1 | 23.1% | 22.9% | 41.0% | 40.8% | 56.4% | 57.0% |
| β1 = 0.2 | 68.8% | 68.5% | 93.4% | 93.3% | 98.9% | 99.0% | |
| β1 = 0.3 | 95.7% | 95.5% | 99.9% | 99.9% | 100.0% | 100.0% | |
| Case:control ratio = 1:2 | 10000 cases |
20000 cases |
30000 cases |
||||
|---|---|---|---|---|---|---|---|
| Formula | Simulation | Formula | Simulation | Formula | Simulation | ||
 = 0.01 |
β1 = 0.1 | 12.6% | 12.9% | 21.0% | 21.4% | 29.3% | 28.9% |
| β1 = 0.2 | 37.2% | 37.5% | 63.7% | 64.4% | 80.7% | 81.1% | |
| β1 = 0.3 | 68.8% | 68.2% | 93.4% | 93.3% | 98.9% | 98.8% | |
 = 0.02 |
β1 = 0.1 | 21.0% | 21.2% | 37.2% | 37.8% | 51.6% | 51.6% |
| β1 = 0.2 | 63.7% | 63.9% | 90.4% | 90.7% | 97.9% | 97.9% | |
| β1 = 0.3 | 93.4% | 93.2% | 99.8% | 99.8% | 100.0% | 100.0% | |
 = 0.03 |
β1 = 0.1 | 29.3% | 29.0% | 51.6% | 51.4% | 68.8% | 68.8% |
| β1 = 0.2 | 80.7% | 80.8% | 97.9% | 97.7% | 99.8% | 99.9% | |
| β1 = 0.3 | 98.9% | 98.9% | 100.0% | 100.0% | 100.0% | 100.0% | |