Intermediate confounding in trio relationships: The importance of complete data in effect size estimation

We present an important characteristic of trio models which may lead to bias and loss of power when one parent is unmodeled in trio analyses. Motivated by recent interest in estimating parental effects on postnatal and later-life phenotypes, we consider a causal model where each parent has both an effect on their child's phenotype which is mediated through the genotype transmitted to the child and a direct effect on the phenotype through the parentally provided environment. We derive the power and bias of models in which one parent's genotype is not modeled, showing that while the effect of the child's genotype is biased in the direction of the unmodeled parent's effect as expected, the estimated effect of the observed parent's genotype is also biased in the opposite direction. While this phenomenon may not be intuitive under the assumption of random mating, it can be explained by intermediate confounding of the child's genotype-phenotype effect. These observations have implications for the accurate estimation of maternal and paternal effects in trio data sets with missing genotype data.