  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 its consequence on causal effect estimation both theoretically and
empirically. We then propose a novel framework that systematically breaks the
winner's curse, leading to unbiased association effect estimates for the
selected genetic variants. Building upon the proposed framework, we introduce a
novel rerandomized inverse variance weighted estimator that is 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
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.
