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Title: Two-sample MR: Correction for winner's curse and weak instruments bias for unknown degree of sample overlap Authors:  Ninon Mounier - University of Lausanne (Switzerland) [presenting]
Zoltan Kutalik - University of Lausanne (Switzerland)
Abstract: Inverse-variance weighting (IVW) two-sample Mendelian Randomization (MR) is the most widely used method to estimate the causal effect of an exposure on an outcome. However, the resulting causal effect estimates may suffer from winners curse and weak instruments, and the extent of these biases is influenced by the degree of sample overlap, which is often unknown. Assuming a spike-and-slab genomic architecture, the bias of the IVW estimator can be analytically derived. This bias is driven by two forces: one acting towards the null independently of sample overlap and a second, proportional to the degree of overlap and the phenotypic correlation. We can estimate it using only summary statistics. Hence we propose a correction of the IVW-MR estimate and compare it against its uncorrected counterpart under a wide range of simulation settings. Finally, we applied our approach to 272 pairs of traits from UKBB. Using simulated data, we observed significant differences between IVW-MR and corrected effects, for all degrees of overlap. In all explored scenarios, our correction reduced the bias, sometimes even by up to 30 folds. When applied to UKBB traits, we observed significant differences $(p<0.05/272)$ between IVW-MR and corrected effects for 15\% of pairs. For example, we showed that the effect of educational attainment on BMI was 30\% larger after correction $(\alpha_IVW=-0.462, \alpha_corrected=-0.602)$.