Interpretation of two-sample Mendelian randomization for binary exposures and outcome

Mendelian randomization (MR) employs genetic variations to infer causal effects of modifiable exposures on various outcomes, with two-sample MR using GWAS summary statistics from separate studies for exposure and outcome traits. However, challenges arise when either the exposure or outcome trait, or both, are binary. Conventional two sample MR methods assume a linear and homogeneous causal effect of the exposure on the outcome, which is unrealistic for binary traits. To address this, we propose a model that treats binary traits as dichotomized continuous traits. We show that summary statistics for a binary trait, derived from either logistic or linear regressions, maintain nearly proportional relationships to those from linear regressions on the underlying continuous trait, provided the associations between the continuous trait and a single SNP are limited. The ratio is also easily calculable given the prevalence of the binary trait. Consequently, MR frameworks on the underlying continuous traits can be resolved using summary statistics from binary traits. Our analytical approximations and simulations indicate that no modifications to two-sample MR methods are needed for binary traits, only an adjustment in the interpretation of results. This novel interpretation also extends to complex MR frameworks, enhancing the applicability of MR to binary and ordered categorical traits.