Robust diagnostic detection of the horizontal pleiotropy on correlated variants in summary data Mendelian randomization.

Mendelian randomization (MR) is an epidemiological tool that is used to infer the causal relationship between an exposure and an outcome through genetic variants as instrumental variables (IVs) for the exposure. The horizontal pleiotropy can cause biased inference in MR. We conduct a mixture of the pleiotropic variant detection method, called the Mixture of Horizontal Pleiotropy Detection (MPD), for considering the horizontal pleiotropy on correlated variants in two-sample summary data. The MPD uses the inverse variance weighted (IVW) regression without an intercept to identify the invalid IVs from a group of the IVs with directional pleiotropy, while using the Egger regression with an intercept to identify the invalid IVs from a group of the IVs with balanced pleiotropy. The MPD is consequently more detailed for searching for the correlated variants associated with the outcome conditionals on the exposure, in comparison with the current pleiotropic variant detection methods using the IVW- or Egger-based regression without or with an intercept in MR. We use the simulated data and analyze the real-world data with the exposure, low-density lipoprotein cholesterol, on the outcome, coronary artery disease, to investigate the finite-sample properties of the MPD on the pleiotropic variant detection.