Bias correction for inverse variance weighting Mendelian randomization

Ninon Mounier, Zoltán Kutalik

Inverse-variance weighted two-sample Mendelian randomization (IVW-MR) is the most widely used approach that utilizes genome-wide association studies (GWAS) summary statistics to infer the existence and the strength of the causal effect between an exposure and an outcome. Estimates from this approach can be subject to different biases due to the use of weak instruments and winner's curse, which can change as a function of the overlap between the exposure and outcome samples. We developed a method (MRlap) that simultaneously considers weak instrument bias and winner's curse while accounting for potential sample overlap. Assuming spike-and-slab genomic architecture and leveraging linkage disequilibrium score regression and other techniques, we could analytically derive, reliably estimate, and hence correct for the bias of IVW-MR using association summary statistics only. We tested our approach using simulated data for a wide range of realistic settings. In all the explored scenarios, our correction reduced the bias, in some situations by as much as 30-fold. In addition, our results are consistent with the fact that the strength of the biases will decrease as the sample size increases and we also showed that the overall bias is also dependent on the genetic architecture of the exposure, and traits with low heritability and/or high polygenicity are more strongly affected. Applying MRlap to obesity-related exposures revealed statistically significant differences between IVW-based and corrected effects, both for nonoverlapping and fully overlapping samples. Our method not only reduces bias in causal effect estimation but also enables the use of much larger GWAS sample sizes, by allowing for potentially overlapping samples.