Correction for Weak IV Bias and Winner's Curse in Mendelian Randomization Egger Regression: Rerandomized Egger estimator

TL;DR

This paper introduces the rerandomized Egger (REgger) estimator for Mendelian randomization that corrects weak instrument bias and winner's curse, improving accuracy and power in complex studies with many instruments.

Contribution

The paper develops a debiased Egger (dEgger) estimator and a rerandomized version (REgger) that address weak instrument bias and winner's curse in MR, with proven asymptotic properties.

Findings

REgger removes weak instrument bias and winner's curse effectively.

REgger outperforms existing methods in simulations and real data.

REgger provides more precise estimates under directional pleiotropy.

Abstract

In two-sample Mendelian randomization (MR), Egger regression is widely used as a sensitivity analysis when directional pleiotropy is detected. However, the increasing complexity of modern MR studies, characterized by many weak instruments, renders the original Egger method less efficient. We first identify the source of weak instrument bias in Egger regression and introduce a debiased Egger (dEgger) estimator that restores consistency and asymptotic normality under substantially weaker conditions. To boost statistical power and ensure the validity of results, we then embed a random instrument selection procedure and present the rerandomized Egger (REgger) estimator along with an associated directional pleiotropy test. Recognizing the challenge of obtaining closed-form variances, we derive simple regression-residual-based variance estimators by truncating higher-order terms. The REgger estimator simultaneously removes the weak instrument bias and winner's curse while retaining robustness to directional pleiotropy, and is asymptotically normal when the effective sample size and post-selection instrument count are sufficiently large. Under balanced pleiotropy, REgger matches the rerandomized inverse-variance-weighted estimator, differing only in having marginally wider confidence intervals; under directional pleiotropy, it achieves substantially greater precision. Extensive simulations and real-data analyses confirm REgger's superior statistical properties, making it a valuable addition to two-sample MR sensitivity analyses.