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. Mendelian randomization (MR) is a method used in genetic epidemiology to determine whether a specific exposure has a causal effect on a health outcome. Ensuring the accuracy of this method is crucial for its reliability and for making informed decisions that can enhance public health and medical practices. Typically, researchers employ the two-stage least squares (2SLS) method which involves selecting a set of valid instrumental variables (IVs) to estimate and infer the causal effect. However, 2SLS can produce biased results when the effects of the IVs are weak, known as weak instrument bias. Additionally, the "winner's curse" problem may occur when using the same dataset for both IV selection and causal effect estimation, introducing additional bias. Here we introduce a novel approach called MR-SPLIT, which addresses these two bias issues by randomly splitting the data into two parts: one for IV selection and the other for IV construction and causal effect estimation. Through effective integration, this strategy enhances the power, reduces bias, and provides more precise estimates. Our approach is validated through extensive simulation studies, and its effectiveness is demonstrated by an application to a real-world dataset.
