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Table 2 Simulation scenarios

From: Weighted composite time to event endpoints with recurrent events: comparison of three analytical approaches

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
  1. Scen. =Scenario; \(\lambda _{M,j}^{I}(t), \lambda _{D,j}^{I}(t), \lambda _{M,j}^{C}(t)\), and \(\lambda _{D,j}^{C}(t)\) are the hazards for the non-fatal (M) and fatal event (D) in the intervention (I) and control (C) group for all strata j, respectively