Use of the instrumental inequalities in simulated mendelian randomization analyses with coarsened exposures

Mendelian randomization (MR) requires strong unverifiable assumptions to estimate causal effects. However, for categorical exposures, the MR assumptions can be falsified using a method known as the instrumental inequalities. To apply the instrumental inequalities to a continuous exposure, investigators must coarsen the exposure, a process which can itself violate the MR conditions. Violations of the instrumental inequalities for an MR model with a coarsened exposure might therefore reflect the effect of coarsening rather than other sources of bias. We aim to evaluate how exposure coarsening affects the ability of the instrumental inequalities to detect bias in MR models with multiple proposed instruments under various causal structures. To do so, we simulated data mirroring existing studies of the effect of alcohol consumption on cardiovascular disease under a variety of exposure-outcome effects in which the MR assumptions were met for a continuous exposure. We categorized the exposure based on subject matter knowledge or the observed data distribution and applied the instrumental inequalities to MR models for the effects of the coarsened exposure. In simulations of multiple binary instruments, the instrumental inequalities did not detect bias under any magnitude of exposure outcome effect when the exposure was coarsened into more than 2 categories. However, in simulations of both single and multiple proposed instruments, the instrumental inequalities were violated in some scenarios when the exposure was dichotomized. The results of these simulations suggest that the instrumental inequalities are largely insensitive to bias due to exposure coarsening with greater than 2 categories, and could be used with coarsened exposures to evaluate the required assumptions in applied MR studies, even when the underlying exposure is truly continuous.