The impact of imprecisely measured covariates on estimating gene-environment interactions

Table 1 Scenario 1: The effect of measurement error σ _v ² in a confounding variable on estimated exposure effects $β^MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqcaaaa@2E64@$ ₂. The exposure is measured without error.

Coefficient for true effect of confounder (β ₄)	Correlation between true value of confounder and exposure	$β^MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqcaaaa@2E64@$ ₂ (sd of estimate)
		σ _v ² = 0	σ _v ² = 1	σ _v ² = 2	σ _v ² = 4	σ _v ² = 9
1.0	0.2	1.001 (0.073)	1.103 (0.076)	1.136 (0.077)	1.162 (0.078)	1.182 (0.079)
	0.5	1.001 (0.081)	1.287 (0.079)	1.365 (0.079)	1.422 (0.078)	1.463 (0.078)
	-0.5	1.000 (0.080)	0.715 (0.079)	0.637 (0.079)	0.580 (0.078)	0.539 (0.078)
-1.0	0.2	1.001 (0.073)	0.898 (0.077)	0.865 (0.078)	0.839 (0.078)	0.819 (0.079)
	0.5	1.001 (0.081)	0.715 (0.079)	0.637 (0.079)	0.579 (0.078)	0.539 (0.078)
	-0.5	1.000 (0.080)	1.286 (0.080)	1.364 (0.079)	1.421 (0.079)	1.462 (0.078)

True values of coefficients β ₁ = 1 (binary genotype), β ₂ = 1 (continuous exposure), β ₃ = 1 (interaction term), β ₄ (confounder) given in first column. Simulations based on 10,000 simulations of 1000 observations. Monte Carlo error is 1% of the empirical standard deviation of the estimates for $β^MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqcaaaa@2E64@$ ₂; approximately 0.0008.