Table 4.

Results of the simulation study with n = 2000

Event			Naive estimator (β̂)					Robust estimator with Cox PH censoring (β̂CRC)					Robust estimator with Sur- vival Trees (β̂CR)					Avg
Scenario	Rate	Truth	Bias	ESE	MSE	SE/ESE	CP	Bias	ESE	MSE	SE/ESE	CP	Bias	ESE	MSE	SE/ESE	CP	Groups
n = 2000
Null
C: 1	0.819	0.000	− 0.001	0.055	0.298	1.024	0.954	− 0.001	0.056	0.313	1.000	0.957	− 0.001	0.055	0.298	1.024	0.954	1.000
C: 2	0.548	0.000	− 0.002	0.069	0.472	1.003	0.957	− 0.001	0.101	1.010	0.874	0.914	− 0.003	0.086	0.733	0.979	0.943	27.084
C: 3	0.606	0.000	− 0.001	0.062	0.389	1.035	0.963	0.010	0.156	2.441	0.754	0.926	− 0.001	0.077	0.595	0.994	0.941	22.101
C: 4	0.678	0.000	− 0.001	0.059	0.346	1.025	0.951	0.041	1.143	130.607	0.389	0.831	− 0.003	0.067	0.451	1.008	0.945	19.191
C: 5	0.416	0.000	− 0.000	0.081	0.654	1.000	0.953	− 0.001	0.087	0.759	0.984	0.940	− 0.001	0.106	1.118	0.976	0.947	40.183
C: 6	0.374	0.000	− 0.001	0.090	0.806	1.026	0.952	− 0.001	0.098	0.957	0.979	0.948	0.007	0.123	1.515	0.992	0.948	46.701
C: 7	0.380	0.000	− 0.002	0.082	0.674	1.019	0.958	− 0.004	0.143	2.035	0.919	0.934	0.001	0.127	1.602	0.943	0.944	39.311
PH
C: 1	0.766	− 0.401	0.000	0.057	0.327	1.028	0.954	− 0.000	0.060	0.355	0.986	0.948	− 0.000	0.057	0.327	1.028	0.954	1.000
C: 2	0.494	− 0.401	− 0.001	0.073	0.539	1.002	0.953	0.001	0.102	1.039	0.950	0.949	− 0.001	0.091	0.832	1.001	0.954	30.884
C: 3	0.549	− 0.401	− 0.000	0.066	0.434	1.044	0.963	0.002	0.162	2.631	0.761	0.946	− 0.001	0.081	0.658	1.024	0.955	26.256
C: 4	0.618	− 0.401	0.001	0.063	0.398	1.016	0.947	− 0.029	1.207	145.633	0.337	0.825	− 0.003	0.074	0.554	0.989	0.946	22.798
C: 5	0.370	− 0.401	0.000	0.084	0.702	1.031	0.953	− 0.003	0.094	0.892	0.986	0.943	0.000	0.113	1.266	1.005	0.956	43.059
C: 6	0.342	− 0.401	− 0.000	0.096	0.926	1.030	0.953	− 0.001	0.109	1.195	0.947	0.934	0.010	0.135	1.841	0.998	0.947	49.230
C: 7	0.332	− 0.401	− 0.002	0.090	0.813	0.998	0.950	0.004	0.154	2.377	0.947	0.940	− 0.008	0.140	1.977	0.935	0.935	42.194
Non-PH
C: 1	0.885	− 0.646	0.000	0.058	0.335	0.954	0.945	− 0.004	0.056	0.319	0.980	0.947	− 0.000	0.058	0.335	0.954	0.945	1.000
C: 2	0.664	− 0.646	0.136	0.065	2.265	0.974	0.420	− 0.002	0.078	0.604	0.946	0.938	0.005	0.074	0.548	0.969	0.942	17.648
C: 3	0.723	− 0.646	0.098	0.063	1.367	0.963	0.622	− 0.029	0.085	0.816	0.883	0.929	0.003	0.070	0.493	0.950	0.931	14.312
C: 4	0.784	− 0.646	0.048	0.060	0.596	0.963	0.861	− 0.042	0.381	14.682	0.370	0.888	− 0.011	0.065	0.429	0.960	0.931	12.588
C: 5	0.508	− 0.646	0.202	0.073	4.636	0.989	0.210	0.096	0.080	1.574	0.947	0.737	0.016	0.086	0.759	1.008	0.945	33.533
C: 6	0.486	− 0.646	0.204	0.087	4.904	0.985	0.334	0.151	0.089	3.072	0.981	0.574	0.028	0.109	1.266	0.986	0.940	38.197
C: 7	0.500	− 0.646	0.263	0.073	7.475	0.983	0.051	− 0.032	0.129	1.769	0.855	0.906	0.027	0.096	0.999	0.968	0.937	30.439

Each scenario is repeated 1000 times. Event rate refers to the average proportion of the sample with an observed event. Truth refers to the Monte Carlo average of β̂ at n = 2000 and under censoring scenario 1. ESE refers to the empirical standard error as calculated through the replicated datasets. MSE refers to the mean squared error times 1000. SE/ESE refers to the average ratio of analytically calculated sandwich standard error to the ESE. CP refers to the coverage probability of the 95 % confidence intervals. Avg Groups refer to the average number of censoring-specific groups derived from the chosen tree used to obtain β̂_CR