Abstract
Mendelian randomization (MR) enables the estimation of causal effects while controlling for unmeasured confounding factors. However, traditional MR's reliance on strong parametric assumptions can introduce bias if these are violated. We describe a machine learning MR estimator named quantile instrumental variable (Quantile IV) that achieves a low estimation error in a wide range of plausible MR scenarios. Quantile IV is distinctive in its ability to estimate nonlinear and heterogeneous causal effects and offers a flexible approach for subgroup analysis. Applying quantile IV, we investigate the impact of circulating sclerostin levels on heel bone mineral density, osteoporosis, and cardiovascular outcomes. Employing various MR estimators and colocalization techniques, our analysis reveals that a genetically predicted reduction in sclerostin levels significantly increases heel bone mineral density and reduces the risk of osteoporosis while showing no discernible effect on ischemic cardiovascular diseases. As a second application, we estimated the effect of increases in low-density lipoprotein cholesterol and waist-to-hip ratio on ischemic cardiovascular diseases using this well-known association as a positive control analysis. Quantile IV contributes to the advancement of MR methodology, and the selected applications demonstrate the applicability of our estimator in various MR contexts.