Table 3.

Bias, coverage, average width of 95% confidence interval (CI), and means square error (MSE) for the regression coefficient estimate for x under the correct assumption that the underlying distribution for x is bivariate normal

		Simple substitution of LOD			Distribution-based MI			Bayesian MI
sample size	% <LOD (x1, x2)	bias	CI coverage	CI width	bias	CI coverage	CI width	bias	CI coverage	CI width	MSEs	MSEs/MSEd	MSEs/MSEb
50	(10,20)	0.0157	94.42	0.88	0.0021	95.10	0.80	0.0004	95.34	0.79	0.06	1.32	1.37
	(20,30)	0.0227	94.62	0.97	−0.0031	96.34	0.82	−0.0057	96.42	0.81	0.07	1.66	1.76
	(30,40)	0.0327	94.32	1.08	−0.0079	97.42	0.85	−0.0118	97.62	0.83	0.09	2.17	2.38
	(40,50)	0.0457	94.12	1.23	−0.0144	98.20	0.89	−0.0203	98.40	0.85	0.12	3.01	3.46
	(50,60)	0.0624	94.00	1.43	−0.0204	99.00	0.93	−0.0272	98.98	0.87	0.16	4.43	5.31
	(60,70)	0.0905	93.76	1.73	.*	. *	. *	−0.0362	99.34	0.89	0.27	. *	9.72
200	(10,20)	0.0140	94.80	0.44	0.0004	95.60	0.39	−0.0002	95.48	0.39	0.01	1.35	1.36
	(20,30)	0.0218	94.64	0.48	−0.0032	96.34	0.40	−0.0043	96.52	0.40	0.02	1.69	1.73
	(30,40)	0.0304	94.54	0.54	−0.0078	97.10	0.41	−0.0093	97.24	0.41	0.02	2.22	2.27
	(40,50)	0.0405	94.38	0.60	−0.0140	97.86	0.43	−0.0153	97.58	0.43	0.03	2.96	3.08
	(50,60)	0.0523	94.12	0.70	−0.0216	98.02	0.45	−0.0234	98.02	0.44	0.04	4.07	4.22
	(60,70)	0.0673	94.18	0.83	−0.0307	98.62	0.47	−0.0335	98.66	0.46	0.05	6.15	6.43

Note: The true regression coefficient for x is 0.1. MSE_s is the MSE for the estimate based on simple substitution of LOD; MSE_s/MSE_d is the relative efficiency of distribution-based MI and simple substitution methods; MSE_s/MSE_b is the relative efficiency of Bayesian MI and simple substitution methods. The correct underlying distributional assumption for x is bivariate normal.

^*The results are not presented due to convergence problems in the estimation process when sample size is small and the degree of left-censoring is high.