A Two-stage Linear Mixed Model (TS-LMM) for Summary-data-based Multivariable Mendelian Randomization

Summary-data-based multivariable Mendelian randomization (MVMR) methods, such as MVMR-Egger, MVMR-IVW, MVMR median-based, and MVMR-PRESSO, assess the causal effects of multiple risk factors on disease. However, accounting for variances in summary statistics related to risk factors remains a challenge. We propose a linear mixed model with measurement error correction (LMM-MEC) that accounts for the variance of summary statistics for both disease outcomes and risk factors. In step I, a linear mixed model is applied to account for the variance in disease summary statistics. Specifically, if heterogeneity is present in disease summary statistics, we treat it as a random effect and adopt an iteratively re-weighted least squares algorithm to estimate causal effects. In step II, we treat the variance in the summary statistics of risk factors as multiple measurement errors and apply a regression calibration method for simultaneous multiple measurement error correction. In a simulation study, when using independent genetic variants as instrumental variables (IV), our method showed comparable performance to existing MVMR methods under conditions of no pleiotropy or balanced pleiotropy with the outcome, and it exhibited higher coverage rates and power under directional pleiotropy. Similar findings were observed when using genetic variants with low to moderate linkage disequilibrium (LD) (0 <{rho} 2 [&le;] 0.3) as IVs, although coverage rates reduced for all methods compared to using independent genetic variants as IVs. In the application study, we examined causal associations between correlated cholesterol biomarkers and longevity. By including 739 genetic variants selected based on P values <5x10-5 from GWAS and allowing for low LD ({rho}2 [&le;] 0.1), our method identified that large LDL-c were causally associated with lower likelihood of achieving longevity.