Table 4 Summary measures for a strong direct effect (β6 = 0.5). Confounding and strength of IV remained as in the baseline scenario with α1 = 0.5, α2 = 0.3, β5 = 1.0. The causal treatment effect was β1 = 3.0. Results are across 200 simulated data sets; values are: sample mean (Monte Carlo SD) unless otherwise stated
From: Assessing causal treatment effect estimation when using large observational datasets
|  | N = 2000 | N = 20,000 | N = 200,000 |
|---|---|---|---|
Adjusted Linear Model and Propensity score IPTW | |||
 Effect Estimate | 3.55 (0.05) | 3.55 (0.02) | 3.55 (0.01) |
 Bias | 0.55 (0.05) | 0.55 (0.02) | 0.55 (0.01) |
 Mean Square Error | 0.30 (0.05) | 0.30 (0.02) | 0.30 (0.01) |
 Z Statistic | 10.76 (0.94) | 34.18 (1.04) | 108.28 (1.07) |
 Coverage: n (%) | 0 (0.00) | 0 (0.00) | 0 (0.00) |
 Power: n (%) | 200 (100.00) | 200 (100.00) | 200 (100.00) |
2SLS IV | |||
 Effect Estimate | 5.67 (2.52) | 6.10 (0.72) | 6.01 (0.25) |
 Bias | 2.67 (2.52) | 3.10 (0.72) | 3.01 (0.25) |
 Mean Square Error | 19.83 (17.89) | 10.65 (4.41) | 9.17 (1.49) |
 Z Statistic | 0.99 (0.89) | 3.69 (0.84) | 11.39 (0.90) |
 Coverage: n (%) | 177 (88.50) | 8 (4.00) | 0 (0.00) |
 Power: n (%) | 118 (59.00) | 200 (100.00) | 200 (100.00) |
Adjusted 2SLS IV | |||
 Effect Estimate | 6.07 (0.44) | 6.04 (0.16) | 6.02 (0.05) |
 Bias | 3.07 (0.44) | 3.04 (0.16) | 3.02 (0.05) |
 Mean Square Error | 9.82 (2.81) | 9.32 (0.97) | 9.15 (0.30) |
 Z Statistic | 6.03 (0.65) | 18.93 (0.73) | 60.01 (0.66) |
 Coverage: n (%) | 0 (0.00) | 0 (0.00) | 0 (0.00) |
 Power: n (%) | 200 (100.00) | 200 (100.00) | 200 (100.00) |