Table 2.
Simulation results, values are estimated hazard ratio (percentage power). H R COMP: hazard ratio from the Cox proportional‐hazards model for the composite of first heart failure hospitalisation and cardiovascular death. H R WLW, H R GL, H R JFM1: hazard ratios from WLW, Ghosh and Lin and joint frailty models respectively for recurrent heart failure hospitalisations. H R CPH, H R JFM2: hazard ratios from Cox proportional‐hazards and joint frailty models respectively for time to cardiovascular death. θ, α, r 0, λ 0, λ C: frailty variance, frailty exponent, baseline annual recurrent event rate, baseline annual terminal event rate and annual independent censoring rate respectively.
| Simulation parameters | Composite | Recurrent events | Terminal event | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| θ | α | r 0 | λ 0 | λ C | H R r | H R λ | H R COMP | H R WLW | H R GL | HRJFM1 | H R CPH | HRJFM2 |
| 3.5 | 3 | 0.9 | 31% | 5% | 0.67 | 0.67 | 0.87 (23) | 0.87 (35) | 0.76 (49) | 0.68 (53) | 0.91 (8) | 0.68 (12) |
| 3.5 | 3 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.87 (26) | 0.87 (38) | 0.76 (53) | 0.70 (48) | 0.91 (8) | 0.69 (10) |
| 3.5 | 1 | 0.9 | 31% | 5% | 0.67 | 0.67 | 0.84 (29) | 0.83 (46) | 0.81 (28) | 0.69 (54) | 0.79 (36) | 0.66 (44) |
| 3.5 | 1 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.84 (33) | 0.83 (50) | 0.81 (32) | 0.69 (55) | 0.77 (37) | 0.65 (39) |
| 3.5 | 0.5 | 0.9 | 31% | 5% | 0.67 | 0.67 | 0.81 (40) | 0.80 (62) | 0.79 (35) | 0.71 (52) | 0.72 (54) | 0.67 (57) |
| 3.5 | 0.5 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.82 (40) | 0.80 (67) | 0.79 (37) | 0.71 (53) | 0.71 (55) | 0.67 (58) |
| 1.45 | 3 | 0.9 | 25% | 5% | 0.67 | 0.67 | 0.80 (52) | 0.83 (62) | 0.72 (73) | 0.68 (77) | 0.86 (15) | 0.67 (16) |
| 1.45 | 3 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.82 (48) | 0.85 (62) | 0.73 (81) | 0.67 (83) | 0.86 (15) | 0.66 (17) |
| 1.45 | 1 | 0.9 | 25% | 5% | 0.67 | 0.67 | 0.77 (66) | 0.77 (80) | 0.72 (69) | 0.68 (80) | 0.71 (50) | 0.66 (50) |
| 1.45 | 1 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.80 (63) | 0.82 (85) | 0.76 (77) | 0.70 (87) | 0.72 (54) | 0.65 (56) |
| 1.45 | 0.5 | 0.9 | 25% | 5% | 0.67 | 0.67 | 0.76 (68) | 0.76 (88) | 0.71 (72) | 0.69 (77) | 0.68 (57) | 0.67 (58) |
| 1.45 | 0.5 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.77 (72) | 0.80 (92) | 0.72 (75) | 0.69 (84) | 0.68 (66) | 0.67 (67) |
| 1 | 3 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.79 (69) | 0.83 (74) | 0.72 (88) | 0.67 (91) | 0.84 (23) | 0.66 (23) |
| 1 | 3 | 1.2 | 31% | 5% | 0.67 | 0.75 | 0.79 (64) | 0.83 (74) | 0.70 (91) | 0.67 (91) | 0.88 (14) | 0.75 (14) |
| 1 | 1 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.76 (77) | 0.78 (93) | 0.72 (85) | 0.68 (91) | 0.71 (58) | 0.67 (57) |
| 1 | 1 | 1.2 | 31% | 5% | 0.67 | 0.75 | 0.77 (70) | 0.80 (90) | 0.70 (89) | 0.68 (90) | 0.78 (37) | 0.75 (35) |
| 1 | 0.5 | 1.2 | 31% | 5% | 0.67 | 0.67 | 0.75 (83) | 0.77 (95) | 0.70 (88) | 0.68 (93) | 0.68 (67) | 0.66 (68) |
| 1 | 0.5 | 1.2 | 31% | 5% | 0.67 | 0.75 | 0.76 (77) | 0.79 (92) | 0.70 (88) | 0.68 (92) | 0.76 (42) | 0.75 (42) |