MR-SPLIT: A novel method to address selection and weak instrument bias in one-sample Mendelian randomization studies.

Mendelian Randomization (MR) is a widely embraced approach to assess causality in epidemiological studies. Two-stage least squares (2SLS) method is a predominant technique in MR analysis. However, it can lead to biased estimates when instrumental variables (IVs) are weak. Moreover, the issue of the winner's curse could emerge when utilizing the same dataset for both IV selection and causal effect estimation, leading to biased estimates of causal effects and high false positives. Focusing on one-sample MR analysis, this paper introduces a novel method termed Mendelian Randomization with adaptive Sample-sPLitting with cross-fitting InstrumenTs (MR-SPLIT), designed to address bias issues due to IV selection and weak IVs, under the 2SLS IV regression framework. We show that the MR-SPLIT estimator is more efficient than its counterpart cross-fitting MR (CFMR) estimator. Additionally, we introduce a multiple sample-splitting technique to enhance the robustness of the method. We conduct extensive simulation studies to compare the performance of our method with its counterparts. The results underscored its superiority in bias reduction, effective type I error control, and increased power. We further demonstrate its utility through the application of a real-world dataset. Our study underscores the importance of addressing bias issues due to IV selection and weak IVs in one-sample MR analyses and provides a robust solution to the challenge.