Incorporating Polygenic Risk Scores in the ACE Twin Model to Estimate A-C Covariance

Abstract

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, a method to estimate these parameters in the twin model would be useful. Here we explore the possibility of relaxing this assumption by adding polygenic scores to the (univariate) twin model. We demonstrate that this extension renders the additive genetic (A)-common environmental (C) covariance (σ_AC) identified. We study the statistical power to reject σ_AC = 0 in the ACE model and present the results of simulations.

Keywords: A–C covariance; Classical twin design; Identification; Polygenic risk scores; Statistical power.

Fig. 1

The covariance between C and A_p and A_q are derived as σ_ACγ_p and σ_ACγ_q, respectively, where γ_p = σ²_Ap/σ²_A and γ_q = σ²_Aq/σ²_A

Fig. 2

ACE twin model with PRSs, including A–C covariances σ_ApC and σ_AqC (dashed double headed arrows). This is the model in DZ twins (i.e., r_z = 0.5). The covariance between A_p and A_q is fixed to zero, but, as demonstrated in the text, this has no bearing on the derived estimate of the total A, C covarianc (σ_A,C)

Fig. 3

Power of the LLR test to reject σ_AC = 0 given positive and negative σ_AC. The parameter settings are given in Table 1. The only difference is the sign of σ_AC. The power to reject σ_AC = 0 given positive σ_AC is given in Table 1

Fig. 4

Distribution of estimates of σ²_F (left) and σ_AF (right) given positive definiteness constraints (simulation 2). The true values are σ²_F = 0.091 and σ_AF = 0.125