  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.
