Estimating indirect parental genetic effects on offspring phenotypes using virtual parental genotypes derived from sibling and half sibling pairs

Abstract

Indirect parental genetic effects may be defined as the influence of parental genotypes on offspring phenotypes over and above that which results from the transmission of genes from parents to their children. However, given the relative paucity of large-scale family-based cohorts around the world, it is difficult to demonstrate parental genetic effects on human traits, particularly at individual loci. In this manuscript, we illustrate how parental genetic effects on offspring phenotypes, including late onset conditions, can be estimated at individual loci in principle using large-scale genome-wide association study (GWAS) data, even in the absence of parental genotypes. Our strategy involves creating "virtual" mothers and fathers by estimating the genotypic dosages of parental genotypes using physically genotyped data from relative pairs. We then utilize the expected dosages of the parents, and the actual genotypes of the offspring relative pairs, to perform conditional genetic association analyses to obtain asymptotically unbiased estimates of maternal, paternal and offspring genetic effects. We apply our approach to 19066 sibling pairs from the UK Biobank and show that a polygenic score consisting of imputed parental educational attainment SNP dosages is strongly related to offspring educational attainment even after correcting for offspring genotype at the same loci. We develop a freely available web application that quantifies the power of our approach using closed form asymptotic solutions. We implement our methods in a user-friendly software package IMPISH (IMputing Parental genotypes In Siblings and Half Siblings) which allows users to quickly and efficiently impute parental genotypes across the genome in large genome-wide datasets, and then use these estimated dosages in downstream linear mixed model association analyses. We conclude that imputing parental genotypes from relative pairs may provide a useful adjunct to existing large-scale genetic studies of parents and their offspring.

Fig 1. Diagram showing the relationship between mother’s, father’s and offspring’s genotypes and phenotypes.

In this manuscript we refer to the path from the offspring genotype to offspring phenotype as the (direct) offspring genetic effect. We refer to the path from mother’s genotype to mother’s phenotype to offspring phenotype as an indirect maternal genetic effect (indirect because the effect of the mother’s genotype is mediated through a maternal phenotype). Likewise, we refer to the path from father’s genotype to father’s phenotype to the offspring phenotype as an example of an indirect paternal genetic effect (indirect because the effect of the father’s genotype is mediated through the paternal phenotype). Indirect maternal and paternal genetic effects are both instances of indirect parental genetic effects on offspring phenotypes. The parental phenotypes mediating these relationships may be known or unknown, may involve one or several phenotypes, and may be modelled or not in the analysis strategy. In this manuscript, we do not model the mother’s or father’s phenotype explicitly, merely the association between mother’s/father’s genotype and offspring phenotype.

Fig 2. Illustration showing the intuition behind why the genotypes of relative pairs such as siblings and half siblings provide information on parental genotypes.

In the case of sibling pairs at autosomal loci, sibling genotypes provide information on parental genotypes. However, mothers and fathers have the same expected genotypes and so separate genotypes for mothers and fathers cannot be imputed given only genotype information from sibling pairs. However, mothers and fathers have different expected genotypes given sibling pair genotypes at non-autosomal X chromosome loci, and so different parental genotypes can be imputed at these loci. Likewise, in the case of half sibling pairs, mothers and fathers have different expectations for their genotypes given half sibling genotypes, and so different dosages for the parents can be imputed at loci. Male individuals are uninformative for the genotypes of their fathers at (non-pseudoautosomal) X chromosome loci.

Fig 3. Power of locus detection in sibling pairs assuming directionally concordant maternal and offspring genetic effects (red lines: d² = 0.1%; b² = 0.1%), directionally discordant maternal and offspring genetic effects (blue lines: d² = 0.1%; b² = 0.1%), or offspring genetic effects only (black lines: d² = 0%; b² = 0.1%).

Shown are results of a one degree of freedom test using sibling genotypes only (lines with circles), an omnibus two degree of freedom test using observed genotypes in siblings and their mothers (lines with triangles), and an omnibus two degree of freedom test of association when parental genotypes need to be imputed from sibling genotypes (lines with open boxes). For all calculations we assume an autosomal locus, shared residual variance φ² = 0.2, a type 1 error rate α = 5x10^-8, and where relevant, a decreasing allele frequency of p = 0.1. The graph shows that when observed genotypes in mothers are available, power to detect loci may be greatest when employing a two degree of freedom test, providing maternal effects are present, and particularly when maternal and offspring genetic effects are directionally discordant. In contrast, when maternal effects are absent, simply fitting a one degree of freedom model using sibling genotypes alone is often the best strategy. When parental genotypes are unavailable, there appears to be little gained from imputing genotypes in mothers in terms of power to detect loci. Note that power is similar for two conditions shown in this graph (i.e. in the case of discordant maternal and offspring genetic effects for the Siblings only one degree of freedom test and the two degrees of freedom test when mothers have to be imputed). For simplicity, we do not show results for the two degree of freedom test when mothers are imputed and there is no maternal effect (i.e. this condition has identical power to when mothers are genotyped).

Fig 4. Power to resolve an autosomal maternal genetic effect (d² = 0.1%; f ² = 0%; b² = 0%;) at a known genetic locus, using a conditional one degree of freedom test of association in sibling pairs (green lines), maternal half sibling pairs who share the same mother (red lines) and paternal half sibling pairs who share the same father (blue lines).

All calculations assume p = 0.3 frequency of the trait decreasing allele; shared variance φ² = 0.2; type 1 error rate α = 0.05). The red dashed vertical line in the figure indicates the approximate number of sibling pairs in the UK Biobank (N = 20,000). This figure highlights the advantage of having actual parental genotypes in the statistical model.