Table 1.

Simulation summary statistics

		Point estimation									Interval estimation
cen		One-step, ${\widehat{\beta }}^{\left(1\right)}$(1)			Proposed, $\widehat{\beta }$			Jin et al.			SW		TI
	(%)	B	SD	Ω	B	SD	Ω	B	SD	Ω	SE	C	SE	C
size=100, 2 covariates
0	G	−2	124	5764	0	124	37	0	124	68	121	93.6	120	93.3
	L	−7	108	106970	−1	107	1105	−1	107	3328	113	94.2	104	93.6
25	G	5	151	6121	6	151	36	6	151	68	159	96.1	150	95.4
	L	0	138	59858	5	136	800	4	136	2767	146	95.1	132	94.8
50	G	2	206	39234	10	201	45	10	201	97	230	96.7	204	95.3
	L	4	180	51839	10	179	1123	10	179	3839	204	96.3	177	94.6
size=100, 4 covariates
0	G	−5	117	19449	−3	117	93	−3	117	235	123	95.3	119	94.8
	L	−8	107	317532	−2	103	3608	−2	103	10735	119	97.1	103	94.8
25	G	−6	153	20245	−4	153	107	−4	153	273	159	95.1	148	94.2
	L	−7	137	240739	−2	136	9496	−2	136	10739	160	95.6	127	93.3
50	G	−9	206	81991	1	200	173	1	200	435	227	95.3	198	94.2
	L	−4	177	218665	4	175	11634	4	176	22207	217	96.4	166	93.2
size=200, 2 covariates
0	G	−3	83	1789	−3	83	5	−3	83	9	83	94.5	83	94.2
	L	−5	73	38260	−3	72	314	−3	72	1031	75	95.1	72	94.6
25	G	3	103	1446	4	103	4	4	103	9	107	95.9	104	95.7
	L	4	91	20787	6	91	235	6	91	721	96	96.5	92	95.9
50	G	−4	141	14739	−1	138	5	−1	138	11	150	95.8	138	94.6
	L	−1	120	22293	2	120	292	2	120	1548	131	96.4	120	95.8
size=200, 4 covariates
0	G	2	87	4329	2	87	12	2	87	29	84	93.7	83	93.6
	L	−4	75	123051	−1	75	890	−1	75	2824	79	94.9	73	94.2
25	G	2	101	4717	2	100	14	2	100	35	107	96.0	103	95.6
	L	1	89	111116	5	88	1146	5	88	3957	98	96.8	89	95.0
50	G	−1	136	18448	2	134	19	2	134	51	147	96.7	136	95.1
	L	−1	113	112253	4	112	1592	4	112	5194	132	96.6	115	95.0

cen: censoring rate.

G: Gehan estimating function; L: log-rank estimating function.

With the log-rank function, Jin et al. was the estimator with 10 iterations.

For interval estimation, SW: the sandwich variance estimation; TI: the test inversion.

B, SD, SE, and C are all for the first coefficient, where B is bias (×10³), SD standard deviation (×10³),

SE mean standard error (×10³), and C coverage (%) of the 95% confidence interval.

Ω: Mean quadratic score statistic (×10⁶).