Table 2.

Biases and (RMSEs) for the naive approach that ignores existence of measurement error and our proposed method. The results are based on a simulation study with 500 replications for 1000 cases and 1000 controls, where disease status (D) is binary, environmental variables (X, W) are continuous, and the genetic variant h₃ is in the form of diplotype with a multiplicative interaction. The environmental variable is measured with error and the error variance is 0.25. Two cases are considered: (a) genotype known for all subjects and (b) genotype missing for 50% of the subjects.

			Naive approach		Proposed method
	Parameter	True value	Bias	RMSE	Bias	RMSE
Complete data	β0	−5.000	1.207	1.459	0.230	0.086
	βg	0.693	0.080	0.011	−0.001	0.007
	βx	1.099	−0.797	0.645	0.001	0.137
	βxg	0.693	−0.478	0.235	0.006	0.088
	pr(h3)	0.250	0.005	0.000	0.000	0.000
	pr(D = 1)	0.046	−0.032	0.001	0.008	0.000
	η1	0.000			0.003	0.001
	η2	0.100			−0.001	0.000
50% of genetic information is missing	β0	−5.000	1.206	1.460	0.228	0.084
	βg	0.693	0.082	0.015	−0.002	0.007
	βx	1.099	−0.794	0.647	0.013	0.161
	βxg	0.693	−0.477	0.243	0.011	0.102
	pr(h3)	0.250	0.004	0.000	0.000	0.000
	pr(D = 1)	0.046	−0.032	0.001	0.008	0.000
	η1	0.000			0.003	0.001
	η2	0.100			−0.002	0.000