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Two-sample summary-data Mendelian randomization (MR) has become a popularresearch design to estimate the causal effect of risk exposures. With thesample size of GWAS continuing to increase, it is now possible to utilizegenetic instruments that are only weakly associated with the exposure. Tomaximize the statistical power of MR, we propose a genome-wide design wheremore than a thousand genetic instruments are used. For the statisticalanalysis, we use an empirical partially Bayes approach where instruments areweighted according to their strength, thus weak instruments bring lessvariation to the estimator. The estimator is highly efficient with many weakgenetic instruments and is robust to balanced and/or sparse pleiotropy. Weapply our method to estimate the causal effect of body mass index (BMI) andmajor blood lipids on cardiovascular disease outcomes and obtain substantiallyshorter confidence intervals. Some new and statistically significant findingsare: the estimated causal odds ratio of BMI on ischemic stroke is 1.19 (95% CI:1.07--1.32, p-value < 0.001); the estimated causal odds ratio of high-densitylipoprotein cholesterol (HDL-C) on coronary artery disease (CAD) is 0.78 (95%CI 0.73--0.84, p-value < 0.001). However, the estimated effect of HDL-C becomessubstantially smaller and statistically non-significant when we only use thestrong instruments. By employing a genome-wide design and robust statisticalmethods, the statistical power of MR studies can be greatly improved. Ourempirical results suggest that, even though the relationship between HDL-C andCAD appears to be highly heterogeneous, it may be too soon to completelydismiss the HDL hypothesis.

Powerful genome-wide design and robust statistical inference in two-sample summary-data Mendelian randomization