A Linear Mixed Model With Measurement Error Correction (LMM‐MEC): A Method 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, are used to assess the causal effects of multiple risk factors on disease. However, accounting for variances in the summary statistics of risk factors remains a challenge. We propose a linear mixed model with measurement error correction (LMM-MEC) that accounts for the variance in summary statistics for both disease outcomes and risk factors. First, under the NOME assumption, we apply a linear mixed model to account for variance in disease summary statistics by treating it as fixed- or random-effects, depending on whether there is heterogeneity in the effect sizes of the genetic variants on the disease outcome. Next, we relax the NOME assumption and further take the estimation error (or variance) in the summary statistics of risk factors into consideration by measurement models through a regression calibration approach. In a simulation study, using independent genetic variants as instrumental variables (IV), our method showed comparable performance to existing MVMR methods under conditions of no pleiotropy or with balanced pleiotropy on the disease outcome, and it achieved slightly improved coverage rates and power under directional pleiotropy. When genetic variants are in low to moderate linkage disequilibrium (LD) (0 < <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow> </mml:mrow> <mml:annotation>$\rho $</mml:annotation></mml:semantics> </mml:math> ² ≤ 0.3), our method showed comparable performance to MVMR-Egger, although both methods showed reduced coverage rates and power compared to situations where genetic variants as IVs are in LD. In the application study, we examined causal associations between correlated cholesterol biomarkers and longevity. By including 739 genetic variants selected based on p values < 5 × 10^-5 from GWAS and allowing for low LD ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow> </mml:mrow> <mml:annotation>$\rho $</mml:annotation></mml:semantics> </mml:math> ² ≤ 0.1), our method identified that large LDL-c levels were causally associated with a lower likelihood of achieving longevity.