Breaking the winner's curse in Mendelian randomization
Developments in genome-wide association studies and the increasing availability of summary genetic association data have made the application of two-sample Mendelian Randomization (MR) with summary data increasingly popular. Conventional two-sample MR methods often employ the same sample for selecting relevant genetic variants and for constructing final causal estimates. Such a practice often leads to biased causal effect estimates due to the well known "winner's curse" phenomenon. To address this fundamental challenge, we first examine the impact of the winner's curse on causal effect estimation obtained from MR analyses both theoretically and empirically. We then propose a novel framework that not only systematically breaks the winner's curse but also provides an unbiased estimate of the genetic association effect after selection. Built upon the proposed framework, we introduce a novel rerandomized inverse variance weighted (RIVW) estimator that is provably consistent when selection and parameter estimation are conducted on the same sample. Under appropriate conditions, we show that the proposed RIVW estimator for the causal treatment effect converges to a normal distribution asymptotically and its variance can be well estimated. We illustrate the finite-sample performance of our approach through Monte Carlo experiments and two empirical examples.