Simulated sample splitting approach to address biases due to instrument selection and participant overlap in two-sample Mendelian Randomization studies.

Mendelian randomization (MR) is a popular statistical technique that uses genetic variants to explore causal relationships in observational epidemiology. Summary-level MR, the most common form, relies on published GWAS summary statistics to estimate causal effects between exposures and outcomes. However, empirical analyses tend to ignore issues relating to Winner's Curse of instrument effects, weak instrument bias and sample overlap. Our simulations and empirical analyses using the UK Biobank indicate that such mechanisms can induce substantial bias in routine MR approaches. We propose MR Simulated Sample Splitting (MR-SimSS), a novel method that corrects this bias requiring no additional data beyond GWAS summary statistics for the exposure and outcome of interest. It operates by simulating statistically independent sets of summary statistics, analogous to what would be produced by splitting the individual-level data into independent subsets, which can then be plugged into existing two-sample MR methods. With sufficient instrument variants, MR-SimSS is robust to a range of sample overlap scenarios, providing a practical and modular solution to Winner's Curse and weak instrument bias.