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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.

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

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)
  1. 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.