Table 1 Scenario (I): 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% | 0.004 | -0.016 | -0.034 | -0.032 |
10% | -0.026 | -0.022 | -0.018 | -0.013 | ||
5% | -0.060 | -0.031 | -0.009 | 0.017 | ||
\({\pi }^{*}\) (with \(X_\textit{r}\)) | 50% | 0.035 | 0.014 | -0.005 | -0.007 | |
10% | 0.019 | 0.020 | 0.023 | 0.030 | ||
5% | 0.000 | 0.023 | 0.045 | 0.074 | ||
MSE | \(\pi\) | 50% | 0.045 | 0.050 | 0.069 | 0.097 |
10% | 0.117 | 0.092 | 0.086 | 0.097 | ||
5% | 0.228 | 0.175 | 0.160 | 0.201 | ||
\({\pi }^{*}\) | 50% | 0.037 | 0.039 | 0.052 | 0.074 | |
10% | 0.097 | 0.080 | 0.084 | 0.100 | ||
5% | 0.187 | 0.154 | 0.160 | 0.217 | ||
Coverage (%) | \(\pi\) | 50% | 95.0 | 94.6 | 94.0 | 93.2 |
10% | 93.9 | 94.3 | 94.8 | 94.7 | ||
5% | 93.2 | 93.9 | 94.3 | 94.4 | ||
\({\pi }^{*}\) | 50% | 94.9 | 94.8 | 94.8 | 94.3 | |
10% | 94.7 | 94.9 | 94.6 | 94.4 | ||
5% | 94.3 | 94.1 | 94.5 | 94.1 | ||
Type I error and power (%) | \(\pi\) | 50% | 5.0 | 86.6 | 99.8 | 100.0 |
10% | 6.1 | 63.7 | 100.0 | 100.0 | ||
5% | 6.8 | 41.7 | 98.5 | 100.0 | ||
\({\pi }^{*}\) | 50% | 5.0 | 94.1 | 99.9 | 100.0 | |
10% | 5.2 | 72.4 | 99.8 | 100.0 | ||
5% | 5.7 | 50.7 | 98.4 | 99.8 | ||