  In the past decade, the increased availability of genome-wide association
studies summary data has popularized Mendelian Randomization (MR) for
conducting causal inference. MR analyses, incorporating genetic variants as
instrumental variables, are known for their robustness against reverse
causation bias and unmeasured confounders. Nevertheless, classical MR analyses
utilizing summary data may still produce biased causal effect estimates due to
the winner's curse and pleiotropic issues. To address these two issues and
establish valid causal conclusions, we propose a unified robust Mendelian
Randomization framework with summary data, which systematically removes the
winner's curse and screens out invalid genetic instruments with pleiotropic
effects. Different from existing robust MR literature, our framework delivers
valid statistical inference on the causal effect neither requiring the genetic
pleiotropy effects to follow any parametric distribution nor relying on perfect
instrument screening property. Under appropriate conditions, we show that our
proposed estimator converges to a normal distribution and its variance can be
well estimated. We demonstrate the performance of our proposed estimator
through Monte Carlo simulations and two case studies. The codes implementing
the procedures are available at https://github.com/ChongWuLab/CARE/.
