Table 2.
Beta | Pool size |
Naïve Standardization | Covariate-adjusted standardization using our pooling protocols |
||||
---|---|---|---|---|---|---|---|
95% CI coverage |
Bias (SE) | 95% CI coverage |
Mean 95% CI width |
Power | Bias (SE) | ||
Scenario A | |||||||
0 | 1a | 0.95 | −0.003 (0.003) | 0.95 | 0.42 | 0.05 | −0.003 (0.003) |
0 | 2 | 0.96 | 0.000 (0.003) | 0.95 | 0.42 | 0.05 | 0.003 (0.004) |
0 | 5 | 0.95 | −0.006 (0.003) | 0.96 | 0.43 | 0.04 | −0.008 (0.004) |
0 | 10 | 0.95 | −0.002 (0.003) | 0.95 | 0.43 | 0.05 | 0.006 (0.004) |
0.26 | 1a | 0.95 | 0.003 (0.004) | 0.95 | 0.44 | 0.97 | 0.003 (0.004) |
0.26 | 2 | 0.93 | −0.037 (0.003) | 0.96 | 0.44 | 0.97 | 0.003 (0.004) |
0.26 | 5 | 0.92 | −0.036 (0.004) | 0.95 | 0.46 | 0.96 | 0.008 (0.004) |
0.26 | 10 | 0.93 | −0.029 (0.004) | 0.96 | 0.50 | 0.97 | 0.016 (0.004) |
0.69 | 1a | 0.95 | 0.008 (0.004) | 0.95 | 0.50 | 1.00 | 0.008 (0.004) |
0.69 | 2 | 0.81 | −0.113 (0.004) | 0.95 | 0.54 | 1.00 | 0.013 (0.004) |
0.69 | 5 | 0.86 | −0.102 (0.005) | 0.96 | 0.66 | 1.00 | 0.031 (0.005) |
0.69 | 10 | 0.88 | −0.068 (0.007) | 0.96 | 0.92 | 1.00 | 0.077 (0.008) |
Scenario B | |||||||
0 | 1a | 0.95 | 0.001 (0.004) | 0.95 | 0.44 | 0.06 | 0.001 (0.004) |
0 | 2 | 0.95 | −0.008 (0.003) | 0.96 | 0.45 | 0.04 | 0.003 (0.004) |
0 | 5 | 0.95 | 0.004 (0.004) | 0.96 | 0.49 | 0.04 | 0.003 (0.004) |
0 | 10 | 0.95 | 0.003 (0.004) | 0.95 | 0.58 | 0.06 | −0.010 (0.005) |
0.26 | 1a | 0.95 | 0.005 (0.004) | 0.95 | 0.45 | 0.96 | 0.005 (0.004) |
0.26 | 2 | 0.93 | −0.047 (0.003) | 0.95 | 0.47 | 0.96 | 0.005 (0.004) |
0.26 | 5 | 0.93 | −0.028 (0.004) | 0.94 | 0.53 | 0.91 | 0.010 (0.005) |
0.26 | 10 | 0.92 | −0.016 (0.005) | 0.96 | 0.65 | 0.84 | 0.031 (0.005) |
0.69 | 1a | 0.94 | 0.009 (0.004) | 0.94 | 0.51 | 1.00 | 0.009 (0.004) |
0.69 | 2 | 0.83 | −0.123 (0.004) | 0.97 | 0.56 | 1.00 | 0.013 (0.004) |
0.69 | 5 | 0.87 | −0.089 (0.006) | 0.96 | 0.74 | 1.00 | 0.046 (0.006) |
0.69 | 10 | 0.92 | −0.021 (0.009) | 0.96 | 1.15 | 1.00 | 0.118 (0.011) |
Scenario B’ | |||||||
0 | 1a | 0.95 | −0.003 (0.003) | 0.95 | 0.42 | 0.05 | −0.003 (0.003) |
0 | 2 | 0.95 | 0.000 (0.003) | 0.95 | 0.42 | 0.05 | 0.003 (0.003) |
0 | 5 | 0.95 | −0.007 (0.003) | 0.95 | 0.43 | 0.06 | −0.002 (0.004) |
0 | 10 | 0.95 | 0.002 (0.003) | 0.96 | 0.43 | 0.04 | 0.000 (0.004) |
0.26 | 1a | 0.95 | 0.004 (0.004) | 0.95 | 0.44 | 0.97 | 0.004 (0.004) |
0.26 | 2 | 0.77 | −0.110 (0.003) | 0.95 | 0.44 | 0.97 | 0.009 (0.004) |
0.26 | 5 | 0.8 | −0.101 (0.003) | 0.95 | 0.46 | 0.97 | 0.012 (0.004) |
0.26 | 10 | 0.81 | −0.087 (0.004) | 0.95 | 0.50 | 0.96 | 0.017 (0.004) |
0.69 | 1a | 0.95 | 0.001 (0.004) | 0.95 | 0.50 | 1.00 | 0.001 (0.004) |
0.69 | 2 | 0.2 | −0.311 (0.003) | 0.96 | 0.54 | 1.00 | 0.010 (0.004) |
0.69 | 5 | 0.39 | −0.284 (0.004) | 0.96 | 0.65 | 1.00 | 0.011 (0.005) |
0.69 | 10 | 0.57 | −0.256 (0.006) | 0.96 | 0.92 | 1.00 | 0.071 (0.008) |
Pool size of 1 means no pooling; analysis used individual observations. In each “pool size 1” row, entries are the same for both naïve standardization and for our proposed methods and are repeated only for convenience.