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

Two-sample summary-data Mendelian randomization (MR) has become a popular research design to estimate the causal effect of risk exposures. With the sample size of GWAS continuing to increase, it is now possible to utilize genetic instruments that are only weakly associated with the exposure. To maximize the statistical power of MR, we propose a genome-wide design where more than a thousand genetic instruments are used. For the statistical analysis, we use an empirical partially Bayes approach where instruments are weighted according to their strength, thus weak instruments bring less variation to the estimator. The estimator is highly efficient with many weak genetic instruments and is robust to balanced and/or sparse pleiotropy. We apply our method to estimate the causal effect of body mass index (BMI) and major blood lipids on cardiovascular disease outcomes and obtain substantially shorter confidence intervals. Some new and statistically significant findings are: 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-density lipoprotein 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 becomes substantially smaller and statistically non-significant when we only use the strong instruments. By employing a genome-wide design and robust statistical methods, the statistical power of MR studies can be greatly improved. Our empirical results suggest that, even though the relationship between HDL-C and CAD appears to be highly heterogeneous, it may be too soon to completely dismiss the HDL hypothesis.