Invariance-based Mendelian Randomization Method Integrating Multiple Heterogeneous GWAS Summary Datasets

Abstract Various geographical landscapes, diverse lifestyles and genetic structures may lead the heterogeneity among the GWAS summary datasets from distinct populations, especially different ethnic groups. This increases the difficulty in inferring global causal relationships from exposures on the outcome when integrating multiple GWAS summary datasets. We proposed a mendelian randomization (MR) method called MR-EILLS, which leverages the Environment Invariant Linear Least Squares (EILLS) to deduce the global causal relationship that invariant in all heterogeneous populations. The MR-EILLS model works in both univariate and multivariate scenarios, and allows the invalid instrumental variables (IVs) violating exchangeability and exclusion restriction assumptions. In addition, MR-EILLS shows the unbiased causal effect estimations of one or multiple exposures on the outcome, whether there are valid or invalid IVs. Comparing with traditional MR and meta methods, MR-EILLS demonstrates the highest estimation accuracy, the most stable type I error rates, and the highest statistical power. Finally, MR-EILLS is applied to explore the independent causal relationships between 11 blood cells and lung function, using GWAS summary statistics from five ancestries (African, East Asian, South Asian, Hispanics Latinos and European). The results cover most of the expected causal links which have biological interpretations and several new links supported by previous observational literatures.