Measurement Error and Power in Family-Based Extensions to Mendelian Randomization

Mendelian Randomization (MR) has become an important tool for causal inference in the health sciences. It takes advantage of the random segregation and independent assortment of alleles to control for background confounding factors. In brief, the method works by using genetic variants as instrumental variables, but it depends on the assumption of exclusion restriction, i.e., that the variants affect the outcome exclusively via the exposure variable. Equivalently, the assumption states that there is no horizontal pleiotropy from the variant to the outcome, i.e., no association with the outcome except via the exposure. This assumption is unlikely to hold in nature, so several MR extensions have been developed to increase its robustness against horizontal pleiotropy, though not eliminating the problem entirely (Sanderson et al., in Nat Rev Methods Primer 2:6, 2022). The Direction of Causation (DoC) twin model, which includes information from cross-twin cross-trait correlations to estimate causal paths, was extended with polygenic scores to explicitly model horizontal pleiotropy and a causal path (MR-DoC, Minică et al., in: Behav Genet 48:337–349, 2018). MR-DoC was further extended to accommodate bidirectional causation (MR-DoC2; Castro-de-Araujo et al., in: Behav Genet 53:63–73, 2023). In the present paper, we compared the performance of the DoC, MR-DoC, and MR-DoC2 models to evaluate the effects of phenotypic measurement error, potential unshared (individual-specific) environmental confounding, and statistical power across the three models. It was found that MR-DoC2 is less vulnerable to measurement error than is standard DoC or MR-DoC. The latter two models have biased estimates of causal paths when unshared environmental covariance between exposure and outcome is assumed to be absent.