. Author manuscript; available in PMC: 2021 Sep 29.

Published in final edited form as: Biometrics. 2020 Aug 25;77(3):1024–1036. doi: 10.1111/biom.13356

Table 3.

Simulation results (all the entries are multiplied by 100) under setting 3. PL, the standard Cox regression with the partial likelihood; DEL and DEL-E, the double empirical likelihood method and its extension by Huang et al. (2016); ADEL, the proposed adaptive double empirical likelihood method.

PC	Method	β ₁						β ₂
PC	Method	Bias	SD	SE	RMSE	CP	RE	Bias	SD	SE	RMSE	CP	RE
Sample Size=100
0%	PL	−1.27	11.09	11.56	11.15	95.4	–	1.93	21.69	21.25	21.76	95.4	–
	DEL	3.79	4.58	4.57	5.94	79.4	0.53	−8.54	16.84	17.20	18.86	94.2	0.87
	DEL-E	3.40	4.74	4.67	5.83	81.4	0.52	0.88	20.86	21.00	20.86	96.2	0.96
	ADEL	−1.06	10.17	9.94	10.21	92.8	0.92	−1.25	18.75	19.69	18.77	95.8	0.86
15%	PL	−1.53	12.28	12.43	12.36	95.2	–	1.17	26.29	23.05	26.29	92.0	–
	DEL	4.23	4.65	4.52	6.28	77.0	0.51	−9.11	19.41	18.42	21.42	92.4	0.81
	DEL-E	3.93	4.73	4.60	6.15	78.2	0.50	0.05	25.67	22.78	25.64	92.2	0.98
	ADEL	−1.62	11.47	11.01	11.57	93.2	0.94	−1.62	22.23	21.44	22.27	95.0	0.85
30%	PL	−1.97	13.27	13.69	13.40	95.4	–	2.11	29.04	25.44	29.08	92.2	–
	DEL	4.29	4.69	4.57	6.36	76.2	0.47	−9.52	20.49	19.88	22.58	92.6	0.78
	DEL-E	4.02	4.77	4.64	6.23	78.2	0.46	0.86	28.35	25.12	28.33	92.4	0.97
	ADEL	−1.95	12.08	12.22	12.23	94.4	0.91	−0.85	23.50	23.66	23.49	95.4	0.81
Sample Size=200
0%	PL	−0.18	8.15	8.00	8.15	95.4	–	0.44	15.17	14.78	15.16	95.2	–
	DEL	4.07	3.24	3.21	5.20	70.6	0.64	−8.79	11.92	12.06	14.80	91.2	0.98
	DEL-E	3.75	3.30	3.26	4.99	73.6	0.61	−0.48	14.72	14.66	14.71	95.8	0.97
	ADEL	−0.57	7.89	7.54	7.90	93.0	0.97	−1.98	13.59	14.11	13.72	95.4	0.91
15%	PL	−1.10	8.87	8.66	8.92	95.0	–	−0.76	15.84	15.99	15.84	94.2	–
	DEL	4.14	3.26	3.26	5.27	72.2	0.59	−9.09	12.01	12.93	15.05	90.8	0.95
	DEL-E	3.89	3.29	3.30	5.10	75.4	0.57	−1.77	15.42	15.87	15.51	94.6	0.98
	ADEL	−1.12	8.31	7.74	8.38	92.2	0.94	−2.82	13.95	14.89	14.21	95.2	0.90
30%	PL	−1.12	9.60	9.49	9.66	95.4	–	−0.71	18.11	17.59	18.11	93.6	–
	DEL	4.23	3.32	3.29	5.37	71.2	0.56	−9.79	13.64	13.95	16.78	89.0	0.93
	DEL-E	4.01	3.35	3.33	5.22	74.4	0.54	−1.73	17.65	17.46	17.72	94.6	0.98
	ADEL	−1.12	9.03	8.57	9.09	92.4	0.94	−2.75	15.83	16.38	16.05	95.4	0.89