Conditioning on parental mating types can reduce necessary assumptions for Mendelian randomization

Mendelian randomization (MR) has become a common tool used in epidemiological studies. However, when confounding variables are correlated with the instrumental variable (in this case, a genetic/variant/marker), the estimation can remain biased even with MR. We propose conditioning on parental mating types (a function of parental genotypes) in MR to eliminate the need for one set of assumptions, thereby plausibly reducing such bias. We illustrate a situation in which the instrumental variable and confounding variables are correlated using two unlinked diallelic genetic loci: one, an instrumental variable and the other, a confounding variable. Assortative mating or population admixture can create an association between the two unlinked loci, which can violate one of the necessary assumptions for MR. We simulated datasets involving assortative mating and population admixture and analyzed them using three different methods: 1) conventional MR, 2) MR conditioning on parental genotypes, and 3) MR conditioning on parental mating types. We demonstrated that conventional MR leads to type I error rate inflation and biased estimates for cases with assortative mating or population admixtures. In the presence of non-additive effects, MR with an adjustment for parental genotypes only partially reduced the type I error rate inflation and bias. In contrast, conditioning on parental mating types in MR eliminated the type I error inflation and bias under these circumstances. Conditioning on parental mating types is a useful strategy to reduce the burden of assumptions and the potential bias in MR when the correlation between the instrument variable and confounders is due to assortative mating or population stratification but not linkage.