Table 2.

Relative bias (RB), standard error (SE) and mean squared error (MSE) of the estimated quantile coefficients under Model (4) at quantile levels of 0.5, and 0.9. In Model (4), x_i ~ N(0, 1), z_i ~ N(0, 1), and $e_i\sim {\chi }_1^2/\sqrt{2}$. “QR_controls” stands for unadjusted quantile regression using controls only. “QR_cases” stands for unadjusted quantile regression using cases only. “QR_controls” are unadjusted quantile regression using both case and control samples. IPW is the estimates using inverse probability weighting; “KS” is the KS estimates using kernel smoothing. SICO(m) is the SICO estimates with m replicate.

n	Methods	τ = 0.5			τ = 0.9
		RB (%)	SE	MSE × n	RB (%)	SE	MSE × n
2000	QR_controls	1.7	0.017	0.6	−26.7	0.072	14.0
	QR_cases	6.9	0.069	14.4	−127.5	0.126	113.2
	QR_case-control	2.5	0.025	7.3	51.4	0.101	33.4
	IPW	2.5	0.025	1.3	0.5	0.096	18.5
	KS	2.0	0.020	0.8	−1.6	0.077	11.9
	SICO (m=1)	1.9	0.019	0.8	−3.4	0.079	12.4
	SICO (m=10)	1.8	0.018	0.6	−3.1	0.073	10.7
	SICO (m=100)	1.7	0.017	0.6	−3.1	0.071	10.0
500	QR_controls	−5.5	0.036	0.7	−27.2	0.146	11.6
	QR_cases	−36.0	0.140	10.9	−114.3	0.259	49.8
	QR_case-control	41.9	0.052	2.8	59.0	0.210	26.4
	IPW	−1.4	0.036	0.7	−0.1	0.150	11.2
	KS	−1.2	0.039	0.7	0.0	0.165	13.6
	SICO (m=1)	−1.1	0.039	0.8	−3.1	0.157	12.4
	SICO (m=10)	−1.2	0.035	0.6	−1.6	0.144	10.4
	SICO (m=100)	−1.4	0.035	0.6	−1.5	0.143	10.3