Interpreting population and family-based genome-wide association studies in the presence of confounding

Examining intergenerational risk factors for conduct problems using polygenic scores in the Norwegian Mother, Father and Child Cohort Study

The aetiology of conduct problems involves a combination of genetic and environmental factors, many of which are inherently linked to parental characteristics given parents' central role in children's lives across development. It is important to disentangle to what extent links between parental heritable characteristics and children's behaviour are due to transmission of genetic risk or due to parental indirect genetic influences via the environment (i.e., genetic nurture). We used 31,290 genotyped mother-father-child trios from the Norwegian Mother, Father and Child Cohort Study (MoBa), testing genetic transmission and genetic nurture effects on conduct problems using 13 polygenic scores (PGS) spanning psychiatric conditions, substance use, education-related factors, and other risk factors. Maternal or self-reports of conduct problems at ages 8 and 14 years were available for up to 15,477 children. We found significant genetic transmission effects on conduct problems for 12 out of 13 PGS at age 8 years (strongest association: PGS for smoking, β = 0.07, 95% confidence interval = [0.05, 0.08]) and for 4 out of 13 PGS at age 14 years (strongest association: PGS for externalising problems, β = 0.08, 95% confidence interval = [0.05, 0.11]). Conversely, we did not find genetic nurture effects for conduct problems using our selection of PGS. Our findings provide evidence for genetic transmission in the association between parental characteristics and child conduct problems. Our results may also indicate that genetic nurture via traits indexed by our polygenic scores is of limited aetiological importance for conduct problems-though effects of small magnitude or effects via parental traits not captured by the included PGS remain a possibility.

Beyond the factor indeterminacy problem using genome-wide association data

Latent factors, such as general intelligence, depression and risk tolerance, are invoked in nearly all social science research where a construct is measured via aggregation of symptoms, question responses or other measurements. Because latent factors cannot be directly observed, they are inferred by fitting a specific model to empirical patterns of correlations among measured variables. A long-standing critique of latent factor theories is that the correlations used to infer latent factors can be produced by alternative data-generating mechanisms that do not include latent factors. This is referred to as the factor indeterminacy problem. Researchers have recently begun to overcome this problem by using information on the associations between individual genetic variants and measured variables. We review historical work on the factor indeterminacy problem and describe recent efforts in genomics to rigorously test the validity of latent factors, advancing the understanding of behavioural science constructs.

More than nature and nurture, indirect genetic effects on children's academic achievement are consequences of dynastic social processes

Families transmit genes and environments across generations. When parents' genetics affect their children's environments, these two modes of inheritance can produce an 'indirect genetic effect'. Such indirect genetic effects may account for up to half of the estimated genetic variance in educational attainment. Here we tested if indirect genetic effects reflect within-nuclear-family transmission ('genetic nurture') or instead a multi-generational process of social stratification ('dynastic effects'). We analysed indirect genetic effects on children's academic achievement in their fifth to ninth years of schooling in N = 37,117 parent-offspring trios in the Norwegian Mother, Father, and Child Cohort Study (MoBa). We used pairs of genetically related families (parents were siblings, children were cousins; N = 10,913) to distinguish within-nuclear-family genetic-nurture effects from dynastic effects shared by cousins in different nuclear families. We found that indirect genetic effects on children's academic achievement cannot be explained by processes that operate exclusively within the nuclear family.

Causal interpretations of family GWAS in the presence of heterogeneous effects

Family-based genome-wide association studies (GWAS) have emerged as a gold standard for assessing causal effects of alleles and polygenic scores. Notably, family studies are often claimed to provide an unbiased estimate of the average causal effect (or average treatment effect; ATE) of an allele, on the basis of an analogy between the random transmission of alleles from parents to children and a randomized controlled trial. Here, we show that this interpretation does not hold in general. Because Mendelian segregation only randomizes alleles among children of heterozygotes, the effects of alleles in the children of homozygotes are not observable. Consequently, if an allele has different average effects in the children of homozygotes and heterozygotes, as can arise in the presence of gene-by-environment interactions, gene-by-gene interactions, or differences in LD patterns, family studies provide a biased estimate of the average effect in the sample. At a single locus, family-based association studies can be thought of as providing an unbiased estimate of the average effect in the children of heterozygotes (i.e., a local average treatment effect; LATE). This interpretation does not extend to polygenic scores, however, because different sets of SNPs are heterozygous in each family. Therefore, other than under specific conditions, the within-family regression slope of a PGS cannot be assumed to provide an unbiased estimate for any subset or weighted average of families. Instead, family-based studies can be reinterpreted as enabling an unbiased estimate of the extent to which Mendelian segregation at loci in the PGS contributes to the population-level variance in the trait. Because this estimate does not include the between-family variance, however, this interpretation applies to only (roughly) half of the sample PGS variance. In practice, the potential biases of a family-based GWAS are likely smaller than those arising from confounding in a standard, population-based GWAS, and so family studies remain important for the dissection of genetic contributions to phenotypic variation. Nonetheless, the causal interpretation of family-based GWAS estimates is less straightforward than has been widely appreciated.

Testing for differences in polygenic scores in the presence of confounding

Polygenic scores have become an important tool in human genetics, enabling the prediction of individuals' phenotypes from their genotypes. Understanding how the pattern of differences in polygenic score predictions across individuals intersects with variation in ancestry can provide insights into the evolutionary forces acting on the trait in question, and is important for understanding health disparities. However, because most polygenic scores are computed using effect estimates from population samples, they are susceptible to confounding by both genetic and environmental effects that are correlated with ancestry. The extent to which this confounding drives patterns in the distribution of polygenic scores depends on patterns of population structure in both the original estimation panel and in the prediction/test panel. Here, we use theory from population and statistical genetics, together with simulations, to study the procedure of testing for an association between polygenic scores and axes of ancestry variation in the presence of confounding. We use a general model of genetic relatedness to describe how confounding in the estimation panel biases the distribution of polygenic scores in a way that depends on the degree of overlap in population structure between panels. We then show how this confounding can bias tests for associations between polygenic scores and important axes of ancestry variation in the test panel. Finally, we use the understanding gained from this analysis to develop a method that uses patterns of genetic similarity between the two panels to guard against these biases, and show that this method can provide better protection against confounding than the standard PCA-based approach.

Estimation of indirect genetic effects and heritability under assortative mating

Both direct genetic effects (effects of alleles in an individual on that individual) and indirect genetic effects - effects of alleles in an individual (e.g. parents) on another individual (e.g. offspring) - can contribute to phenotypic variation and genotype-phenotype associations. Here, we consider a phenotype affected by direct and parental indirect genetic effects under assortative mating at equilibrium. We generalize classical theory to derive a decomposition of the equilibrium phenotypic variance in terms of direct and indirect genetic effect components. We extend this theory to show that popular methods for estimating indirect genetic effects or 'genetic nurture' through analysis of parental and offspring polygenic predictors (called polygenic indices or scores - PGIs or PGSs) are substantially biased by assortative mating. We propose an improved method for estimating indirect genetic effects while accounting for assortative mating that can also correct heritability estimates for bias due to assortative mating. We validate our method in simulations and apply it to PGIs for height and educational attainment (EA), estimating that the equilibrium heritability of height is 0.699 (S.E. = 0.075 ) and finding no evidence for indirect genetic effects on height. We estimate a very high correlation between parents' underlying genetic components for EA, 0.755 (S.E. = 0.035), which is inconsistent with twin based estimates of the heritability of EA, possibly due to confounding in the EA PGI and/or in twin studies. We implement our method in the software package snipar, enabling researchers to apply the method to data including observed and/or imputed parental genotypes. We provide a theoretical framework for understanding the results of PGI analyses and a practical methodology for estimating heritability and indirect genetic effects while accounting for assortative mating.

Do polygenic indices capture "direct" effects on child externalizing behavior? Within-family analyses in two longitudinal birth cohorts

Behaviors and disorders characterized by difficulties with self-regulation, such as problematic substance use, antisocial behavior, and symptoms of attention-deficit/hyperactivity disorder (ADHD), incur high costs for individuals, families, and communities. These externalizing behaviors often appear early in the life course and can have far-reaching consequences. Researchers have long been interested in direct measurements of genetic risk for externalizing behaviors, which can be incorporated alongside other known risk factors to improve efforts at early identification and intervention. In a preregistered analysis drawing on data from the Environmental Risk (E-Risk) Longitudinal Twin Study (N = 862 twins) and the Millennium Cohort Study (MCS; N = 2,824 parent-child trios), two longitudinal cohorts from the UK, we leveraged molecular genetic data and within-family designs to test for genetic effects on externalizing behavior that are unbiased by the common sources of environmental confounding. Results are consistent with the conclusion that an externalizing polygenic index (PGI) captures causal effects of genetic variants on externalizing problems in children and adolescents, with an effect size that is comparable to those observed for other established risk factors in the research literature on externalizing behavior. Additionally, we find that polygenic associations vary across development (peaking from age 5-10 years), that parental genetics (assortment and parent-specific effects) and family-level covariates affect prediction little, and that sex differences in polygenic prediction are present but only detectable using within-family comparisons. Based on these findings, we believe that the PGI for externalizing behavior is a promising means for studying the development of disruptive behaviors across child development.

Tree-based QTL mapping with expected local genetic relatedness matrices

Understanding the genetic basis of complex phenotypes is a central pursuit of genetics. Genome-wide Association Studies (GWAS) are a powerful way to find genetic loci associated with phenotypes. GWAS are widely and successfully used, but they face challenges related to the fact that variants are tested for association with a phenotype independently, whereas in reality variants at different sites are correlated because of their shared evolutionary history. One way to model this shared history is through the ancestral recombination graph (ARG), which encodes a series of local coalescent trees. Recent computational and methodological breakthroughs have made it feasible to estimate approximate ARGs from large-scale samples. Here, we explore the potential of an ARG-based approach to quantitative-trait locus (QTL) mapping, echoing existing variance-components approaches. We propose a framework that relies on the conditional expectation of a local genetic relatedness matrix given the ARG (local eGRM). Simulations show that our method is especially beneficial for finding QTLs in the presence of allelic heterogeneity. By framing QTL mapping in terms of the estimated ARG, we can also facilitate the detection of QTLs in understudied populations. We use local eGRM to identify a large-effect BMI locus, the CREBRF gene, in a sample of Native Hawaiians in which it was not previously detectable by GWAS because of a lack of population-specific imputation resources. Our investigations can provide intuition about the benefits of using estimated ARGs in population- and statistical-genetic methods in general.