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Table 1 Investigated simulation scenarios

From: Introducing a new estimator and test for the weighted all-cause hazard ratio

Scenario \(\lambda ^{I}_{EP_{1}}(t)\) \(\lambda ^{C}_{EP_{1}}(t)\) \(\lambda ^{I}_{EP_{2}}(t)\) \({\lambda ^{C}_{EP_{2}}(t)}\) Description Assumptions for original parametric estimator Assumptions for new non-parametric estimator #
1 0.24 0.4 0.24t 0.8t Weibull distributed; \(\checkmark \)
      PH assumption only fulfilled for components;   
      unequal cause-specific baseline hazards   
2 0.192t−0.2 0.28t−0.3 0.084t−0.3 0.32t−0.2 Weibull distributed;
      PH assumption not fulfilled for components and composite;   
      unequal cause-specific baseline hazards   
3 0.24t 0.8t 1.2t2 0.72t2 Weibull distributed; \(\checkmark \)
      PH assumption only fulfilled for components;   
      unequal cause-specific baseline hazards   
4 0.2t−0.4 0.3t−0.3 0.1t 0.1t1.5 Weibull distributed;
      PH assumption not fulfilled for components and composite;   
      unequal cause-specific baseline hazards   
5 0.5t−0.4 0.9t−0.5 0.25 0.22t0.1 Weibull distributed;
      PH assumption not fulfilled for components and composite;   
      unequal cause-specific baseline hazards   
6 0.24 0.24 0.24t 0.24t Weibull distributed; \(\checkmark \)
      PH assumption fulfilled for components and composite;   
      unequal cause-specific baseline hazards   
7 0.05 0.1 1 0.5 Weibull distributed; \(\checkmark \) \(\checkmark \)
      PH assumption fulfilled for components and composite;   
      equal cause-specific baseline hazards   
8 0.42e0.7t−0.42 0.7e0.7t−0.7 0.21e0.7t−0.21 0.7e0.7t−0.7 Gompertz distributed; \(\checkmark \)
      PH assumption fulfilled for components and composite;   
      equal cause-specific baseline hazards   
9 0.42e2t−0.42 0.7e2t−0.7 0.21e0.7t−0.21 0.7e0.7t−0.7 Gompertz distributed;
      PH assumption only fulfilled for components;   
      unequal cause-specific baseline hazards   
10 0.42e0.7t 0.7e0.8t 0.21e0.8t 0.7e0.6t Gompertz distributed;
      PH assumption not fulfilled for components and composite;   
      unequal cause-specific baseline hazards   
  1. \(\lambda ^{I}_{EP_{1}}(t),\lambda ^{C}_{EP_{1}}(t),\lambda ^{I}_{EP_{2}}(t),\lambda ^{C}_{EP_{2}}(t)\): cause-specific hazard functions for EP1 and EP2 in the intervention and the control group, respectively; PH: proportional hazards;
  2. *It is assumed that the Weibull model used to estimate the cause-specific hazards is the correct one and the PH assumption is fulfilled for the components;
  3. #It is assumed that the cause-specific baseline hazards are equal.