Table I.

Empirical means of β̂_X (with empirical standard deviations in parentheses) in 1000 simulations where the disease model is linear, estimated by naïve linear regression of Y on W, regression calibration for W in the main study (RC1), regression calibration for M̄ in the calibration study (RC2), efficient regression calibration (ERC), moment reconstruction (MR) and multiple imputation (IM); main study sample size= 1000, calibration sample size= 100.

βX	γX	${\sigma }_{\delta }^2$	ρXW*	Naïve	RC1	RC2	ERC	MR	IM
0.3	1	1	0.71	0.150 (0.022)	0.307 (0.071)	0.312 (0.135)	0.303 (0.061)	0.310 (0.129)	0.301 (0.115)
0.3	0.75	1	0.60	0.144 (0.025)	0.309 (0.077)		0.299 (0.068)	0.301 (0.127)	0.298 (0.118)
0.3	0.5	1	0.45	0.119 (0.028)	0.323 (0.131)		0.293 (0.084)	0.301 (0.125)	0.296 (0.122)
0.3	0.5	2	0.33	0.067 (0.022)	0.363 (0.422)		0.285 (0.100)	0.300 (0.122)	0.294 (0.121)
0.3	0.5	4	0.24	0.036 (0.015)	0.563 (3.498)		0.279 (0.106)	0.297 (0.118)	0.287 (0.121)
0.6	1	1	0.71	0.300 (0.020)	0.614 (0.104)	0.605 (0.138)	0.595 (0.083)	0.604 (0.124)	0.590 (0.121)
0.6	0.75	1	0.60	0.289 (0.023)	0.621 (0.121)		0.600 (0.095)	0.609 (0.127)	0.596 (0.126)
0.6	0.5	1	0.45	0.239 (0.027)	0.654 (0.252)		0.593 (0.115)	0.612 (0.122)	0.599 (0.124)
0.6	0.5	2	0.33	0.133 (0.020)	0.745 (0.909)		0.585 (0.119)	0.609 (0.124)	0.594 (0.125)
0.6	0.5	4	0.24	0.071 (0.016)	0.984 (4.524)		0.581 (0.130)	0.610 (0.124)	0.594 (0.125)

^*ρ_XW is the correlation of X and W.