The assumption in the twin model that genotypic and environmental variables are uncorrelated is primarily made to ensure parameter identification, not because researchers necessarily think that these variables are uncorrelated. Although the biasing effects of such correlations are well understood, it would be useful to be able to estimate these parameters in the twin model. Here we consider the possibility of relaxing this assumption by adding polygenic score to the (univariate) twin model. We demonstrated numerically and analytically this extension renders the additive genetic (A) – unshared environmental correlation (E) and the additive genetic (A) - shared environmental (C) correlations simultaneously identified. We studied the statistical power to detect A-C and A-E correlations in the ACE model, and to detect A-E correlation in the AE model. The results showed that the power to detect these covariance terms, given 1000 MZ and 1000 DZ twin pairs (α=0.05), depends greatly on the parameter settings of the model. We show fixing the estimated percentage of variance in the outcome trait that is due to the polygenic scores greatly increases statistical power.
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