Table 1.

Simulation summary statistics of $\widehat{S}(t)$,${\widehat{S}}_{\mathit{PPL}}(t)$ and ${\widehat{S}}_{\mathit{PL}}(t)$

			$\widehat{S}(t)$			${\widehat{S}}_{\mathrm{PPL}}(t)$			${\widehat{S}}_{\mathrm{PL}}(t)$
n	Cen	S(t)	Bias	SE	ESMSE	Bias	SE	ESMSE	Bias	SE	ESMSE
						Scenario I
100	25%	0.75	6	55	55	5	56	56	1	60	60
		0.5	5	56	56	4	56	56	2	60	60
		0.25	3	47	47	3	46	47	4	49	49
	50%	0.75	5	57	58	6	58	58	0.4	62	62
		0.5	−1	61	60	3	61	61	1	64	64
		0.25	−10	55	56	5	56	56	7	59	60
400	25%	0.75	1	28	28	1	28	28	−0.3	30	30
		0.5	1	28	28	0.3	28	28	0.1	29	29
		0.25	0.4	23	23	1	23	23	2	24	24
	50%	0.75	0.4	29	29	1	29	29	−1	31	31
		0.5	−2	30	30	0.3	30	30	0.2	32	32
		0.25	−6	27	28	2	28	28	4	29	30
						Scenario II
100	25%	0.75	61	70	93	33	92	97	17	108	109
		0.5	48	69	84	27	79	84	16	91	93
		0.25	25	47	53	10	50	51	10	56	57
	50%	0.75	59	74	94	45	91	101	17	111	112
		0.5	45	72	85	37	83	91	16	95	96
		0.25	20	54	58	13	59	60	12	65	66
400	25%	0.75	30	42	51	12	55	56	2	64	64
		0.5	22	36	42	10	43	44	3	50	50
		0.25	10	23	25	2	25	25	1	30	30
	50%	0.75	30	43	52	19	56	59	2	65	65
		0.5	22	38	44	15	45	48	4	52	52
		0.25	8	25	27	1	28	28	1	33	33

Note: Cen is the censoring rate; Bias is the empirical bias (×1000); SE is the empirical standard error (×1000); ESMSE is the square root of empirical mean square error (×1000). $\widehat{S}(t)$ is the proposed estimator; ${\widehat{S}}_{\mathit{PPL}}(t)$ is the pseudo partial likelihood estimator; ${\widehat{S}}_{\mathit{PL}}(t)$ is the partial likelihood estimator.