Table 3 Summary measures for the initial parameter values: 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 | 3.47 (0.05) | 3.47 (0.02) | 3.47 (0.01) |
 Bias | 0.47 (0.05) | 0.47 (0.02) | 0.47 (0.01) |
 Mean Square Error | 0.23 (0.04) | 0.22 (0.02) | 0.22 (0.00) |
 Z Statistic | 9.41 (0.92) | 29.97 (1.05) | 94.92 (1.06) |
 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 | 2.62 (2.53) | 3.06 (0.73) | 2.98 (0.24) |
 Bias | −0.38 (2.53) | 0.06 (0.73) | −0.02 (0.24) |
 Mean Square Error | 12.90 (10.63) | 1.06 (0.84) | 0.12 (0.07) |
 Z Statistic | −0.12 (0.90) | 0.08 (0.87) | −0.07 (0.93) |
 Coverage: n (%) | 192 (96.00) | 194 (97.00) | 197 (98.50) |
 Power: n (%) | 27 (13.50) | 191 (95.50) | 200 (100.00) |
Adjusted 2SLS IV | |||
 Effect Estimate | 3.03 (0.30) | 3.00 (0.10) | 3.00 (0.03) |
 Bias | 0.03 (0.30) | 0.00 (0.10) | 0.00 (0.03) |
 Mean Square Error | 0.18 (0.16) | 0.02 (0.01) | 0.00 (0.00) |
 Z Statistic | 0.15 (0.87) | 0.04 (1.00) | −0.07 (1.04) |
 Coverage: n (%) | 194 (97.00) | 192 (96.00) | 187 (93.50) |
 Power: n (%) | 200 (100.00) | 200 (100.00) | 200 (100.00) |