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Abstract:
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Mendelian randomization (MR) is a popular method in epidemiology to estimate causal effects using genetic variants as instrumental variables (IV). Often, two-sample summary data is used in MR where in one sample, summary statistics about the marginal correlations between the IVs and the exposure are available and in another sample, summary statistics about the marginal correlations between the IVs and the outcome are available. Unfortunately, many methods in MR are biased under weak instruments, where the correlation between the IVs and exposure is small. In this work, we leverage recent works in econometrics and propose a set point estimators and test statistics that (i) are robust to weak instruments and (ii) work with two-sample summary-level data. For point estimation, we extend a popular method called limited information maximum likelihood (LIML) and an unbiased estimator with known signs. For tests, we extend the Anderson-Rubin and conditional likelihood ratio tests and derive their asymptotic properties when the instruments are weak. We show that our methods outperform current methods when IVs are weak. This is joint work with Sheng Wang (UW-Madison)
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