Bias and Precision of Parameter Estimates from Models Using Polygenic Scores to Estimate Environmental and Genetic Parental Influences

Abstract

In a companion paper Balbona et al. (Behav Genet, in press), we introduced a series of causal models that use polygenic scores from transmitted and nontransmitted alleles, the offspring trait, and parental traits to estimate the variation due to the environmental influences the parental trait has on the offspring trait (vertical transmission) as well as additive genetic effects. These models also estimate and account for the gene-gene and gene-environment covariation that arises from assortative mating and vertical transmission respectively. In the current study, we simulated polygenic scores and phenotypes of parents and offspring under genetic and vertical transmission scenarios, assuming two types of assortative mating. We instantiated the models from our companion paper in the OpenMx software, and compared the true values of parameters to maximum likelihood estimates from models fitted on the simulated data to quantify the bias and precision of estimates. We show that parameter estimates from these models are unbiased when assumptions are met, but as expected, they are biased to the degree that assumptions are unmet. Standard errors of the estimated variances due to vertical transmission and to genetic effects decrease with increasing sample sizes and with increasing [Formula: see text] values of the polygenic score. Even when the polygenic score explains a modest amount of trait variation ([Formula: see text]), standard errors of these standardized estimates are reasonable ([Formula: see text]) for [Formula: see text] trios, and can even be reasonable for smaller sample sizes (e.g., down to 4K) when the polygenic score is more predictive. These causal models offer a novel approach for understanding how parents influence their offspring, but their use requires polygenic scores on relevant traits that are modestly predictive (e.g., [Formula: see text] as well as datasets with genomic and phenotypic information on parents and offspring. The utility of polygenic scores for elucidating parental influences should thus serve as additional motivation for large genomic biobanks to perform GWAS's on traits that may be relevant to parenting and to oversample close relatives, particularly parents and offspring.

Keywords: Assortative mating (AM); Nature of nurture; OpenMx; Structural equation modeling (SEM); Vertical transmission (VT).

Fig. 1

Comparison of estimates across models when there is VT but no AM. For each simulation, $h_{t0}^2=.50$, $r_{\mathit{mate}}=0$, $V_{F,t0}=.15$, and $n_{\mathit{fam}}=16K$. a $r_{PGS,t0}^2=.50$. b $r_{PGS,t0}^2=.05$. Boxplots show first quartile, median, and third quartile of estimates, with whiskers at the 2.5% and 97.5% quantiles. Equilibrium values of parameters are grey dashed lines. *Models where assumptions about AM and $r_{PGS,t0}^2$ are met

Fig. 2

Comparison of estimates across models when there is VT and equilibrium AM. For each simulation, $h_{t0}^2=.50$, $r_{\mathit{mate}}=.25$, $V_{F,t0}=.15$, and $n_{\mathit{fam}}=16K$. a $r_{PGS,t0}^2=.50$. b $r_{PGS,t0}^2=.05$. See Fig. 1 note for additional details

Fig. 3

Comparison of estimates across models when there is VT and disequilibrium AM. For each simulation, $h_{t0}^2=.50$, $r_{\mathit{mate}}=.25$, $V_{F,t0}=.15$, and $n_{\mathit{fam}}=16K$. a $r_{PGS,t0}^2=.50$. b $r_{PGS,t0}^2=.05$. See Fig. 1 note for additional details

Fig. 4

Scatter plots between Model 2e estimates. Estimates are from 1K simulations where $r_{PGS,t0}^2=.05$, $r_{\mathit{mate}}=0.25$, and AM is at equilibrium

Fig. 5

The standard errors (SE’s) of standardized estimates from Models 2e and 2e-NP a as a function of $n_{\mathit{fam}}$ when $r_{PGS,t0}^2=.05$ and b as a function of $r_{PGS,t0}^2$ when $n_{\mathit{fam}}=16K$. Estimates are from 1K simulations where $r_{\mathit{mate}}=0.25$ and AM is at equilibrium