Causal interpretations of family GWAS in the presence of heterogeneous effects

Family-based genome-wide association studies (GWASs) are often claimed to provide an unbiased estimate of the average causal effects (or average treatment effects; ATEs) of alleles, on the basis of an analogy between the random transmission of alleles from parents to children and a randomized controlled trial. We show that this claim 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. This feature will matter 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 linkage disequilibrium patterns. At a single locus, family-based GWAS 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 (PGSs), 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 of the LATE for any subset or weighted average of families. In practice, the potential biases of a family-based GWAS are likely smaller than those that can arise from confounding in a standard, population-based GWAS, and so family studies remain important for the dissection of genetic contributions to phenotypic variation. Nonetheless, their causal interpretation is less straightforward than has been widely appreciated.