using only a single genetic variant. These three models include causality (Z → X → Y), pleiotropy (Z → X and Z → Y) and linkage (Z1 → X, Z2 → Y, and Z1 and Z2 are two variants in linkage disequilibrium (LD) in the cis-eQTL region). The purpose of this study was to identify genes whose expression levels had causal effect (Z → X → Y) on BMD. In Mendelian randomization studies, multiple uncorrelated instrumental variables (IVs) [22] (for example, the uncorrelated trans-eQTLs and/or cis-eQTLs) or multiple correlated IVs [27] were needed to identify the causality. Due to multiple uncorrelated IVs were not available in the Westra eQTL study [24], we applied weighted generalized linear regression method using correlated IVs to distinguish causality from pleiotropy.
