Application of Seemingly Unrelated Regression in Medical Data with Intermittently Observed Time-Dependent Covariates

Table 3

Simulation results (summary of estimated parameters, bias, and MSE) for intermittent observation of time-dependent covariates (situation 1 from Table 1) with different sample sizes (𝑛=20,60,120, and 240).

Parameter; (true value)	Method	Sample size = 20			Sample size = 60			Sample size = 120			Sample size = 240
		^↼𝛽	Bias	MSE	^↼𝛽	Bias	MSE	^↼𝛽	Bias	MSE	^↼𝛽	Bias	MSE
𝛽2; (−1.13)	SURCC	−.94	.19	7.25	−1.15	−.02	1.87	−1.12	.008	.83	−1.13	−.006	.43
	MRMCC	−1.003	.13	6.39	−1.14	−.01	1.86	−1.12	.009	.84	−1.14	−.01	.43
	SURBOCF	−.99	.13	7.26	−1.14	−.01	1.89	−1.12	.01	.83	−1.14	−.007	.42
	MRMBOCF	−1.01	.12	6.05	−1.16	−.03	1.83	−1.12	.007	.82	−1.14	−.009	.42
	SURLOCF	−.98	.14	7.40	−1.14	−.01	1.88	−1.12	.01	.83	−1.14	−.007	.42
	MRMLOCF	−1.01	.12	6.18	−1.16	−.03	1.82	−1.12	.009	.83	−1.14	−.01	.42
𝛽3; (.23)	SURCC	.20	−.03	7.22	.15	−.08	1.90	.20	−.03	.87	.24	.009	.43
	MRMCC	.17	−.06	6.08	.14	−.09	1.90	.20	−.03	.87	.24	.01	.43
	SURBOCF	.21	−.02	7.29	.14	−.09	1.90	.21	−.02	.86	.24	.01	.42
	MRMBOCF	.12	−.11	5.88	.12	−.11	1.83	.20	−.03	.85	.24	.01	.42
	SURLOCF	.21	−.02	7.37	.12	−.10	1.85	.21	−.02	.85	.24	.01	.42
	MRMLOCF	.13	−.1	5.91	.12	−.11	1.82	.19	−.04	.85	.24	.01	.42
𝛽4; (−.01)	SURCC	.002	.01	3.42	−.02	−.006	.82	−.02	−.01	.39	−.02	.39	.18
	MRMCC	−.02	−.01	3.24	−.05	−.04	.91	−.03	−.02	.43	−.02	−.009	.18
	SURBOCF	.03	.04	3.39	−.01	−.001	.83	−.02	−.01	.39	−.02	−.01	.18
	MRMBOCF	−.03	−.02	2.67	−.02	−.007	.77	−.02	−.01	.37	−.02	−.01	.17
	SURLOCF	.02	.02	3.39	−.009	.0004	.83	−.02	−.008	.39	−.02	−.01	.18
	MRMLOCF	−.03	−.02	2.68	−.02	−.0006	.76	−.02	−.01	.37	−.02	−.01	.17
𝛽5; (−1.12)	SURCC	−.45	.67	1.56	−.49	.63	.66	−.45	.67	.58	−.46	.66	.51
	MRMCC	−1.16	−.04	2.20	−1.13	−.009	.61	−1.08	.04	.28	−1.10	.02	.14
	SURBOCF	−1.03	.09	2.37	−1.03	.09	.60	−.99	.13	.29	−1.02	.10	.14
	MRMBOCF	−.97	.15	1.81	−.98	.14	.55	−.95	.17	.29	−.97	.14	.14
	SURLOCF	−1.06	.06	2.48	−1.05	−.07	.58	−1.006	.11	.27	−1.02	.09	.14
	MRMLOCF	−1.06	.06	1.96	−1.03	−.09	.54	−.99	.13	.27	−1.01	.10	.14

*Note: SUR_CC,MRM_CC,SUR_BOCF,MRM_BOCF,SUR_LOCF,  and MRM_LOCF represent the estimated parameters from MRM and SUR models under complete case (CC) analysis, baseline observation carried forward (BOCF), and last observation carried forward (LOCF) method, respectively.