Table 2 Scenario (II): performance of the estimated propensity score (PS) model
From: Treatment effect estimation using the propensity score in clinical trials with historical control
Performance measurement | PS model | Outcome event rate | Odds ratio | |||
|---|---|---|---|---|---|---|
1.0 | 2.0 | 5.0 | 10.0 | |||
Bias | \(\pi\) (without \(X_\textit{r}\)) | 50% | 0.169 | 0.151 | 0.135 | 0.128 |
10% | 0.154 | 0.155 | 0.151 | 0.151 | ||
5% | 0.135 | 0.153 | 0.172 | 0.190 | ||
\({\pi }^{*}\) (with \(X_\textit{r}\)) | 50% | 0.044 | 0.026 | 0.010 | 0.006 | |
10% | 0.029 | 0.034 | 0.035 | 0.038 | ||
5% | 0.007 | 0.032 | 0.062 | 0.091 | ||
MSE | \(\pi\) | 50% | 0.053 | 0.049 | 0.052 | 0.065 |
10% | 0.090 | 0.079 | 0.080 | 0.092 | ||
5% | 0.154 | 0.132 | 0.140 | 0.212 | ||
\({\pi }^{*}\) | 50% | 0.036 | 0.038 | 0.050 | 0.070 | |
10% | 0.094 | 0.080 | 0.084 | 0.103 | ||
5% | 0.183 | 0.150 | 0.161 | 0.248 | ||
Coverage (%) | \(\pi\) | 50% | 81.5 | 85.6 | 90.4 | 92.7 |
10% | 89.6 | 89.6 | 90.6 | 92.6 | ||
5% | 91.8 | 92.1 | 93.2 | 94.9 | ||
\({\pi }^{*}\) | 50% | 94.4 | 95.1 | 94.7 | 94.3 | |
10% | 94.5 | 94.1 | 94.1 | 94.1 | ||
5% | 94.1 | 94.2 | 93.7 | 93.8 | ||
Type I error and power (%) | \(\pi\) | 50% | 18.5 | 99.9 | 100.0 | 100.0 |
10% | 10.4 | 94.2 | 100.0 | 100.0 | ||
5% | 8.2 | 74.7 | 100.0 | 100.0 | ||
\({\pi }^{*}\) | 50% | 5.6 | 96.1 | 100.0 | 100.0 | |
10% | 5.5 | 74.9 | 99.9 | 100.0 | ||
5% | 5.8 | 52.5 | 98.8 | 99.9 | ||