Table 2 Simulation scenarios
Scen. | \(\lambda _{M,j}^{I}(t)\) | \(\lambda _{D,j}^{I}(t)\) | \(\lambda _{M,j}^{C}(t)\) | \(\lambda _{D,j}^{C}(t)\) | Weight for fatal event | Weight for non-fatal event | ||
|---|---|---|---|---|---|---|---|---|
Wei-Lachin | Rauch and Bakal | Wei-Lachin | Rauch and Bakal | |||||
1a | 0.25·0.5 | 0.25·0.5 | 0.25 | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
1b | proportional time independent hazards for event type | 0.5882 | 1 | 0.4118 | 0.7 | |||
1c | assumptions for approaches by Wei-Lachin and Rauch fulfilled | 0.6667 | 1 | 0.3333 | 0.5 | |||
1d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
1e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
2a | 0.25·0.5 | 0.25·0.7 | 0.25 | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
2b | see Scenario 1 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
2c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
2d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
2e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
3a | 0.25·0.7 | 0.25·0.5 | 0.25 | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
3b | see Scenario 1 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
3c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
3d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
3e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
4a | 0.25·1.5 | 0.25·0.7 | 0.25 | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
4b | see Scenario 1 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
4c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
4d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
4e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
5a | 0.25·0.7 | 0.25·1.5 | 0.25 | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
5b | see Scenario 1 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
5c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
5d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
5e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
6a | 0.25·0.5 | 0.1t·0.7 | 0.25 | 0.1t | 0.5263 | 1 | 0.4737 | 0.9 |
6b | proportional hazards for each event type | 0.5882 | 1 | 0.4118 | 0.7 | |||
6c | time dependent hazards for one event type | 0.6667 | 1 | 0.3333 | 0.5 | |||
6d | assumptions for approaches by Wei-Lachin and Rauch fulfilled | 0.7692 | 1 | 0.2308 | 0.3 | |||
6e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
7a | 0.25·0.7 | 0.1t·0.5 | 0.25 | 0.1t | 0.5263 | 1 | 0.4737 | 0.9 |
7b | see Scenario 6 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
7c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
7d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
7e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
8a | 0.1t·0.5 | 0.25·0.7 | 0.1t | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
8b | see Scenario 6 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
8c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
8d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
8e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
9a | 0.1t·0.7 | 0.25·0.5 | 0.1t | 0.25 | 0.5263 | 1 | 0.4737 | 0.9 |
9b | see Scenario 6 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
9c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
9d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
9e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
10a | 0.192t−0.2 | 0.084t−0.3 | 0.28t−0.3 | 0.32t−0.2 | 0.5263 | 1 | 0.4737 | 0.9 |
10b | non-proportional hazards for both event types (Weibull distributions) | 0.5882 | 1 | 0.4118 | 0.7 | |||
10c | assumptions for approach by Wei-Lachin not fulfilled | 0.6667 | 1 | 0.3333 | 0.5 | |||
10d | assumptions for approach by Rauch et al. fulfilled | 0.7692 | 1 | 0.2308 | 0.3 | |||
10e | 0.9091 | 1 | 0.0909 | 0.1 | ||||
11a | 0.084t−0.3 | 0.192t−0.2 | 0.32t−0.2 | 0.28t−0.3 | 0.5263 | 1 | 0.4737 | 0.9 |
11b | see Scenario 10 for underlying assumptions | 0.5882 | 1 | 0.4118 | 0.7 | |||
11c | 0.6667 | 1 | 0.3333 | 0.5 | ||||
11d | 0.7692 | 1 | 0.2308 | 0.3 | ||||
11e | 0.9091 | 1 | 0.0909 | 0.1 | ||||