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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
  1. \(\hat \theta \) estimated mean treatment effect; \(sd(\hat \theta)\) mean standard deviation of estimated treatment effect; power empirical power values for the Andersen-Gill model (AG), the Prentice-Williams-Peterson total time model (PWP1), the Prentice-Williams-Peterson gap time model (PWP2), the Wei-Lin-Weissfeld model (WLW); \(\lambda _{0}^{MI}(t,t_{prev})\) baseline hazard function for the recurrent event (myocaridal infarction); \(\lambda _{0}^{D}(t,t_{prev})\) baseline hazard function for the fatal event (death); exp(βMI(t prev )) hazard ratio for the recurrent event (myocaridal infarction); exp(βD(t prev )) hazard ratio for the fatal event (death)