A multivariable <i>cis</i>-Mendelian randomization method robust to weak instrument bias and horizontal pleiotropy bias

Multivariable cis-Mendelian randomization (cis-MVMR) has become an effective approach for identifying therapeutic targets that influence disease susceptibility. However, biases from invalid instruments, such as weak instruments and horizontal pleiotropy, remain unsolved. In this paper, we propose a new method called the cis-Mendelian randomization bias correction estimating equation (cis-MRBEE), which mitigates weak instrument bias by leveraging a local sparse genetic architecture: most variants within a genomic region are associated with a trait through linkage disequilibrium with a few causal variants. Cis-MRBEE identifies causal variants or proxies of exposures via fine-mapping, re-estimates genetic associations using the identified variants, and applies a double-penalized minimization to estimate causal exposures and account for horizontal pleiotropic effects. Simulations showed that in the presence of weak instruments and horizontal pleiotropy, directly adapting standard MVMR methods to cis-MVMR was infeasible, and existing cis-MVMR methods failed to control type I errors. In contrast, cis-MRBEE exhibited robustness to these sources of bias. We applied cis-MRBEE to the ANGPTL3 locus and identified a credible set comprising APOA1, APOC1, and PCSK9 as likely causal proteins for LDL-C, HDL-C, and TG. The subsequent analysis revealed a complex protein regulation network that influenced lipid traits. Furthermore, we used cis-MRBEE to discover that the expressions of CR1 in the basal ganglia, hippocampus, and oligodendrocytes were potentially causal for Alzheimer's disease and its biomarkers, A$\beta $42 and pTau, in cerebrospinal fluid.