Effect of selection bias on two sample summary data based Mendelian randomization

Mendelian randomization (MR) is becoming more and more popular for inferring causal relationship between an exposure and a trait. Typically, instrument SNPs are selected from an exposure GWAS based on their summary statistics and the same summary statistics on the selected SNPs are used for subsequent analyses. However, this practice suffers from selection bias and can invalidate MR methods, as showcased via two popular methods: the summary data-based MR (SMR) method and the two-sample MR Steiger method. The SMR method is conservative while the MR Steiger method can be either conservative or liberal. A simple and yet more powerful alternative to SMR is proposed.