Debiased Inverse-Variance Weighted Estimator in Two-Sample Summary-Data Mendelian Randomization
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Mendelian randomization (MR) has become a popular approach to study the effect of a modifiable exposure on an outcome by using genetic variants as instrumental variables. A challenge in MR is that each genetic variant explains a relatively small proportion of variance in the exposure and there are many such variants, a setting known as many weak instruments. To this end, we provide a full theoretical characterization of the statistical properties of the two popular estimators in MR, the inverse-variance weighted (IVW) estimator and the pre-screened IVW estimator with instruments selected from an independent selection dataset, under many weak instruments. We then propose a debiased IVW estimator, a simple modification of the IVW estimator, that is robust to many weak instruments and doesn't require pre-screening. Additionally, we present two instrument selection methods to improve efficiency of the new estimator when a selection dataset is available. An extension of the debiased IVW estimator to handle balanced horizontal pleiotropy is also discussed. We conclude by demonstrating our results in simulated and real datasets.
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