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Standard Mendelian randomization analysis can produce biased results if thegenetic variant defining the instrumental variable (IV) is confounded and/orhas a horizontal pleiotropic effect on the outcome of interest not mediated bythe treatment. We provide novel identification conditions for the causal effectof a treatment in presence of unmeasured confounding, by leveraging an invalidIV for which both the IV independence and exclusion restriction assumptions maybe violated. The proposed Mendelian Randomization Mixed-Scale Treatment EffectRobust Identification (MR MiSTERI) approach relies on (i) an assumption thatthe treatment effect does not vary with the invalid IV on the additive scale;and (ii) that the selection bias due to confounding does not vary with theinvalid IV on the odds ratio scale; and (iii) that the residual variance forthe outcome is heteroscedastic and thus varies with the invalid IV. We formallyestablish that their conjunction can identify a causal effect even with aninvalid IV subject to pleiotropy. MiSTERI is shown to be particularlyadvantageous in presence of pervasive heterogeneity of pleiotropic effects onadditive scale, a setting in which two recently proposed robust estimationmethods MR GxE and MR GENIUS can be severely biased. In order to incorporatemultiple, possibly correlated and weak IVs, a common challenge in MR studies,we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach forstrengthened identification and improved accuracy MaWII MiSTERI is shown to berobust to horizontal pleiotropy, violation of IV independence assumption andweak IV bias. Both simulation studies and real data analysis resultsdemonstrate the robustness of the proposed MR MiSTERI methods.

On Mendelian Randomization Mixed-Scale Treatment Effect Robust Identification (MR MiSTERI) and Estimation for Causal Inference