Abstract
Mendelian randomization using GWAS summary statistics has become a popular method to infer causal relationships across complex diseases. However, the widespread pleiotropy observed in GWAS has made the selection of valid instrumental variables problematic, leading to possible violations of Mendelian randomization assumptions and thus potentially invalid inferences concerning causation. Furthermore, current MR methods can examine causation in only one direction, so that two separate analyses are required for bi-directional analysis. In this study, we propose a ststistical framework, MRCI (Mixture model Reciprocal Causation Inference), to estimate reciprocal causation between two phenotypes simultaneously using the genome-scale summary statistics of the two phenotypes and reference linkage disequilibrium information. Simulation studies, including strong correlated pleiotropy, showed that MRCI obtained nearly unbiased estimates of causation in both directions, and correct Type I error rates under the null hypothesis. In applications to real GWAS data, MRCI detected significant bi-directional and uni-directional causal influences between common diseases and putative risk factors.