Table 2 Simulation results
From: A systematic comparison of recurrent event models for application to composite endpoints
Simulation parameters | Mean (SD) | \(\hat \theta \) (\(sd(\hat \theta)\)), power | |||||||
|---|---|---|---|---|---|---|---|---|---|
Sc. | \(\lambda _{0}^{MI}(t,t_{prev})\) | \(\lambda _{0}^{D}(t,t_{prev})\) | exp(βMI(t prev )) | exp(βD(t prev )) | # events | \(\hat \theta _{MixAG}\) | \(\hat \theta _{MixPWP1}\) | \(\hat \theta _{MixPWP2}\) | \(\hat \theta _{MixWLW}\) |
1a | 0.25 | 0.25 | 0.5 | 0.5 | 2.93 (0.65) | 0.50 (0.13), 0.83 | 0.50 (0.13), 0.83 | 0.51 (0.13), 0.83 | 0.46 (0.14), 0.82 |
1b | 0.25 | 0.25 | 0.5 | 0.7 | 2.93 (0.65) | 0.50 (0.13), 0.83 | 0.50 (0.13), 0.82 | 0.51 (0.13), 0.82 | 0.46 (0.14), 0.82 |
1c | 0.25 | 0.25 | 0.7 | 0.5 | 3.02 (0.63) | 0.70 (0.16), 0.39 | 0.71 (0.16), 0.38 | 0.71 (0.16), 0.39 | 0.68 (0.19), 0.37 |
1d | 0.25 | 0.25 | 0.7 | 1.5 | 3.00 (0.64) | 0.72 (0.17), 0.35 | 0.72 (0.17), 0.34 | 0.72 (0.17), 0.34 | 0.68 (0.19), 0.36 |
1e | 0.25 | 0.25 | 1.5 | 0.7 | 3.66 (0.73) | 1.53 (0.30), 0.57 | 1.52 (0.30), 0.56 | 1.52 (0.29), 0.56 | 1.71 (0.41), 0.59 |
2a | \(0.25\cdot 1/\sqrt {t_{prev}}\) | \(0.25\cdot 1/\sqrt {t_{prev}}\) | 0.5 | 0.5 | 2.15 (0.43) | 0.52 (0.13), 0.81 | 0.51 (0.13), 0.81 | 0.51 (0.13), 0.81 | 0.48 (0.14), 0.80 |
2b | \(0.25\cdot 1/\sqrt {t_{prev}}\) | \(0.25\cdot 1/\sqrt {t_{prev}}\) | 0.5 | 0.7 | 2.15 (0.43) | 0.52 (0.13), 0.81 | 0.51 (0.13), 0.81 | 0.51 (0.13), 0.81 | 0.48 (0.14), 0.80 |
2c | \(0.25\cdot 1/\sqrt {t_{prev}}\) | \(0.25\cdot 1/\sqrt {t_{prev}}\) | 0.7 | 0.5 | 2.20 (0.46) | 0.71 (0.16), 0.37 | 0.71 (0.17), 0.36 | 0.71 (0.17), 0.37 | 0.69 (0.18), 0.35 |
2d | \(0.25\cdot 1/\sqrt {t_{prev}}\) | \(0.25\cdot 1/\sqrt {t_{prev}}\) | 0.7 | 1.5 | 2.18 (0.44) | 0.73 (0.17), 0.32 | 0.72 (0.17), 0.32 | 0.72 (0.17), 0.32 | 0.70 (0.19), 0.34 |
2e | \(0.25\cdot 1/\sqrt {t_{prev}}\) | \(0.25\cdot 1/\sqrt {t_{prev}}\) | 1.5 | 0.7 | 2.44 (0.65) | 1.45 (0.29), 0.57 | 1.52 (0.31), 0.53 | 1.51 (0.30), 0.53 | 1.64 (0.33), 0.54 |
3a | t 0.3 | t 0.3 | 0.5 | 0.5 | 5.69 (0.99) | 0.47 (0.07), 1 | 0.48 (0.07), 1 | 0.48 (0.07), 1 | 0.38 (0.08), 0.99 |
3b | t 0.3 | t 0.3 | 0.5 | 0.7 | 5.69 (0.99) | 0.48 (0.07), 1 | 0.49 (0.07), 0.99 | 0.49 (0.07), 0.99 | 0.39 (0.08), 0.99 |
3c | t 0.3 | t 0.3 | 0.7 | 0.5 | 5.83 (0.95) | 0.66 (0.09), 0.91 | 0.66 (0.09), 0.92 | 0.66 (0.05), 0.93 | 0.60 (0.12), 0.78 |
3d | t 0.3 | t 0.3 | 0.7 | 1.5 | 5.75 (0.97) | 0.74 (0.10), 0.63 | 0.76 (0.10), 0.56 | 0.77 (0.10), 0.54 | 0.63 (0.12), 0.69 |
3e | t 0.3 | t 0.3 | 1.5 | 0.7 | 7.60 (1.12) | 1.43 (0.16), 0.89 | 1.40 (0.15), 0.87 | 1.39 (0.15), 0.87 | 1.77 (0.33), 0.85 |
3f | 1.5·t0.3 | t 0.3 | 0.5 | 0.5 | 7.52 (1.12) | 0.48 (0.06), 1 | 0.48 (0.06), 0.99 | 0.48 (0.06), 1 | 0.35 (0.07), 0.99 |
4a | 0.25 | 0.25 | 0.5exp(0.05ln(0.5)·t prev ) | 0.5exp(0.05ln(0.5)·t prev ) | 2.91 (0.65) | 0.49 (0.13), 0.85 | 0.49 (0.13), 0.85 | 0.49 (0.13), 0.85 | 0.45 (0.13), 0.84 |
4b | 0.25 | 0.25 | 0.5exp(0.05ln(0.5)·t prev ) | 0.7exp(0.05ln(0.7)·t prev ) | 2.92 (0.65) | 0.49 (0.13) 0.84 | 0.50 (0.13), 0.84 | 0.50 (0.13), 0.84 | 0.46 (0.13), 0.84 |
4c | 0.25 | 0.25 | 0.7exp(0.05ln(0.7)·t prev ) | 0.5exp(0.05ln(0.5)·t prev ) | 3.01 (0.63) | 0.70 (0.16), 0.41 | 0.70 (0.16), 0.40 | 0.70 (0.16), 0.41 | 0.67 (0.18), 0.38 |
4d | 0.25 | 0.25 | 0.7exp(0.05ln(0.7)·t prev ) | 1.5exp(0.05ln(1.5)·t prev ) | 2.99 (0.64) | 0.71 (0.17), 0.37 | 0.71 (0.17), 0.36 | 0.72 (0.17), 0.36 | 0.67 (0.18), 0.37 |
4e | 0.25 | 0.25 | 1.5exp(0.05ln(1.5)·t prev ) | 0.7exp(0.05ln(0.7)·t prev ) | 3.69 (0.73) | 1.55 (0.30), 0.61 | 1.54 (0.30), 0.59 | 1.54 (0.30), 0.60 | 1.73 (0.42), 0.60 |
5a | 0.25 | 0.25 | 0.5exp(−0.05ln(0.5)·t prev ) | 0.5exp(−0.05ln(0.5)·t prev ) | 2.95 (0.65) | 0.52 (0.13), 0.80 | 0.52 (0.14), 0.79 | 0.52 (0.13), 0.79 | 0.48 (0.14), 0.79 |
5b | 0.25 | 0.25 | 0.5exp(−0.05ln(0.5)·t prev ) | 0.7exp(−0.05ln(0.7)·t prev ) | 2.95 (0.65) | 0.52 (0.13), 0.79 | 0.52 (0.14), 0.78 | 0.52 (0.14), 0.78 | 0.48 (0.14), 0.79 |
5c | 0.25 | 0.25 | 0.7exp(−0.05ln(0.7)·t prev ) | 0.5exp(−0.05ln(0.5)·t prev ) | 3.03 (0.62) | 0.71 (0.17), 0.37 | 0.72 (0.17), 0.37 | 0.72 (0.17), 0.37 | 0.69 (0.19), 0.35 |
5d | 0.25 | 0.25 | 0.7exp(−0.05ln(0.7)·t prev ) | 1.5exp(−0.05ln(1.5)·t prev ) | 3.01 (0.63) | 0.72 (0.17), 0.33 | 0.73 (0.17), 0.33 | 0.73 (0.17), 0.32 | 0.69 (0.19), 0.35 |
5e | 0.25 | 0.25 | 1.5exp(−0.05ln(1.5)·t prev ) | 0.7exp(−0.05ln(0.7)·t prev ) | 3.61 (0.72) | 1.48 (0.44), 0.62 | 1.47 (0.44), 0.61 | 1.47 (0.44), 0.61 | 1.65 (0.55), 0.62 |
5f | 0.25 | 0.25 | 0.5exp(−0.5ln(0.5)·t prev ) | 0.5exp(−0.5ln(0.5)·t prev ) | 3.09 (0.60) | 0.67 (0.24), 0.44 | 0.81 (0.30), 0.40 | 0.77 (0.33), 0.40 | 0.61 (0.24), 0.48 |