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Abstract:
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Mendelian randomization (MR) is commonly understood as a study design that uses genetic variants as instrumental variables for modifiable exposures. However, it is typically only implicit in MR methodologies that the inferential basis of MR is the random transmission of alleles from parents to offspring via meiosis. Meiosis has been thoroughly studied and modelled in genetics dating back to Haldane (1919). We propose a statistical framework that enables meiosis models to be used to perform exact randomization inference for MR. Conceptually, this makes explicit the common analogy between MR and a randomization controlled trial. Furthermore, we develop a rigorous graphical framework which is used to identify sufficient confounder adjustment sets. Our randomization-based approach also has several practical advantages: 1) It sidesteps the need for correctly specifying phenotype models, although a better model will often lead to more powerful tests. We demonstrate via simulation that propensity scores obtained from the meiosis model can form powerful test statistics. 2) It is robust to arbitrarily weak instruments. 3) It is robust to biases from population and family structure.
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