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.