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Unmodeled GxE and r GE [Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 5(6), 554-571.] How do unmodeled GxE and r GE bias parameter estimates in standard twin models?

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  1. Unmodeled GxE and rGE[Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 5(6), 554-571.] How do unmodeled GxE and rGE bias parameter estimates in standard twin models? E.g.: If the additive genotype (A) interacts with common environment (C; environmental influences that increase phenotypic similarity between family members), then the phenotypic value may be decomposed as follows: P = aA + cC + iAC + eE, and its expected variance is VP = a2 + c2 + i2 + e2 (assuming the variances of the latent variables are scaled to 1). The expected twin covariances are Cov(P1,P2)= a2Cov(A1, A2) + c2Cov(C1, C2) + e2Cov(E1, E2) + i2Cov(A1C1, A2C2) = a2 + c2 + i2 for MZ twins = a2/2 + c2 + i2/2 for DZ twins as Cov(A1, A2) is 1 for MZ twins and 0.5 for DZ twins; Cov(C1,C2)=1 and Cov(E1, E2)=0 for all twins; also Cov(A1C1,A2C2)=Cov(A1, A2)Cov(C1, C2)=Cov(A1, A2). Similar covariance algebra can show that AxE interaction contributes to the E component. rA=0.5/1 rC=1 A1C1 A1 C1 E1 A2C2 A2 C2 E2 i a c e i a c e P1 P2 Twin 1 Twin 2

  2. Unmodeled GxE and rGE[Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 5(6), 554-571.] How do unmodeled GxE and rGE bias parameter estimates in standard twin models? If A is correlated with an environmental variable, say C, then the expected phenotypic variance is VP = a2 + c2 + 2ac * rAC+ e2 and the expected twin covariances are Cov(P1,P2) = a2Cov(A1, A2) + c2Cov(C1, C2) + e2Cov(E1, E2) + acCov(A1, C2) + acCov(A2, C1) = a2 + c2 + 2ac * rAC for MZ twins = a2/2 + c2 + 2ac * rAC for DZ twins as Cov(A1, C2) = Cov(A2, C1) = rAC . Similarly, if A and E are non-independent then Cov(P1, P2) = a2 + c2 + 2ae * rAEforMZtwins = a2/2 + c2 + ae x rAE for DZ twins Thus: Interaction between A and C acts in the same way as A; interaction between A and E acts like E. Correlation between A and C acts like C; correlation between A and E acts like A. rAC rA=0.5/1 rC=1 rAC A1 C1 E1 A2 C2 E2 a c e a c e P1 P2 Twin 1 Twin 2

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