MAGIC

Mediation analysis is a powerful tool for studying causal pathways between exposure, mediator, and outcome variables of interest. While classical mediation analysis using observational data often requires strong and sometimes unrealistic assumptions, such as unconfoundedness, Mendelian Randomization (MR) avoids unmeasured confounding bias by employing genetic variants as instrumental variables. We develop a novel MR framework for mediation analysis (called MAGIC) with genome-wide associate study (GWAS) summary data, and provide solid statistical guarantees. Our framework efficiently integrates information stored in three independent GWAS summary data and mitigates the commonly encountered winner’s curse and measurement error bias (a.k.a. instrument selection and weak instrument bias) in MR. As a result, our framework provides valid statistical inference for both direct and mediation effects with enhanced statistical efficiency. As part of this endeavor, we also demonstrate that the concept of winner’s curse bias in mediation analysis with MR and summary data is more complex than previously documented in the classical two-sample MR literature, requiring special treatments to address such a bias issue. We illustrate the finite-sample performance of our approach through simulation experiments and a case study.

Please cite the following manuscript when using MAGIC or any codes listed in this repo:

Lyu, R. Q., Wu, C., Ma, X., and Wang, J. (2023+). Mediation Analysis with Mendelian Randomization and Efficient Multiple GWAS Integration. Submitted.

In this repo, we provide the following sources.

• Simulation folder: the codes for replicating simulation results in the above manuscript
• Real Data Analysis folder: the codes for replicating real data results in the above manuscript

We provide an R package MR.Rerand to implement (i) RIVW for estimating the causal effect $\beta$ from the exposure variable $X$ to the outcome variable $Y$, (ii)MAGIC for estimating the direct effects $\theta$ and $\tau_Y$, the mediation effect $\tau=\tau_X\tau_Y$, the causal effect $\tau_X$ from $X$ to $M$, and the total effect $\theta+\tau$ as parameters shown in the below figure.. The users may need to specify the working directory and install relevant packages to run it smoothly.

Causal Diagram for Mediation Analysis.

• Function Value Contour.ipynb: Provide the function contour in Supplementary Material

Simulation

• Summary_result_plot_optimal.R: Produce Figure in Figure 2-4 in the manuscript
• new_plotV2.R: Produce Figure without Plugin estimator (figures in Supplementary Material)
• mvmrefficiency_diff.R: Produce results in Table3 in the manuscript
• code4plugin.R: Produce simulation results in Figures 2-4 in the manuscript with plugin estimator
• codeforrbdiagonal.R Produce simulation results in Figures 2-4 in the manuscript without plugin estimator

Real Data Analysis

• Mediation_analysis_real_data_markdown.md: The Rmarkdown to conduct all real data analysis, for interested causal pathways, please modify the data source and the interested traits to run smoothly. In Mediation_analysis function, input indep.method = "prunning.org" to conduct LD pruning, input indep.method = "clumping" to conduct LD clumping, input input indep.method = "revised_pruning" to conduct sigmabased_pruning.

Folder: ldclumping

Real data results using LD clumping to select independent SNPs, which may also induce selection bias

• bmimedaisstroke.html: Mediation pathway is Body Mass Index -> Mediator-> Any ischemic (AIS) stroke
• BMIMEDStroke.html: Mediation pathway is Body Mass Index -> Mediator -> Stroke
• Mediation_analysis_real_data_markdown.html: Mediation pathway is Body Mass Index -> Mediator -> Cadiovascular Disease (CAD)
• obesitymedaisstroke.html: Mediation pathway is Obesity -> Mediator -> AIS stroke
• ObesityMedCAD.html: Mediation pathway is Obesity -> Mediator -> Cadiovascular Disease (CAD)
• ObesityMEDStroke.html: Mediation pathway is Obesity -> Mediator -> Stroke
• WHPmediationCAD.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> Cadiovascular Disease (CAD)
• WHRMEDaisstroke.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> AIS stroke
• WHRMEDStroke.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> Stroke

Folder: ldcpruning

Real data results using LD pruning to select independent SNPs, which is totally random

• ldpruning_bmi.html: Mediation pathway is Obesity -> Mediator -> Cadiovascular Disease (CAD)
• ldpruning_obesity.html: Mediation pathway is Body Mass Index -> Mediator -> Cadiovascular Disease (CAD)
• ldpruning_WHR.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> Cadiovascular Disease (CAD)

Folder: sigmabased_pruning

Real data results using sigma-based pruning to select independent SNPs, which uses the information in standard error

• bmimedaisstroke.html: Mediation pathway is Body Mass Index -> Mediato r-> Any ischemic (AIS) stroke
• BMIMEDStroke.html: Mediation pathway is Body Mass Index -> Mediator -> Stroke
• Mediation_analysis_real_data_markdown.html: Mediation pathway is Body Mass Index -> Mediator -> Cadiovascular Disease (CAD)
• obesitymedaisstroke.html: Mediation pathway is Obesity -> Mediator -> AIS stroke
• ObesityMedCAD.html: Mediation pathway is Obesity -> Mediator -> Cadiovascular Disease (CAD)
• ObesityMEDStroke.html: Mediation pathway is Obesity -> Mediator -> Stroke
• WHPmediationCAD.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> Cadiovascular Disease (CAD)
• WHRMEDaisstroke.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> AIS stroke
• WHRMEDStroke.html: Mediation pathway is Waist-Hip ratio (WHP) -> Mediator -> Stroke

Our real data are extracted from IEU Open GWAS project and MEGASTROKE database. The Exposure / Mediator / Outcome GWAS ID we use are summarized as follows.

Data source in real data analysis.

References

• Ma, X., Wang, J., and Wu, C. (2023a). “Breaking the winner’s curse in Mendelian randomization: rerandomized inverse variance weighted estimator,” Annals of Statistics, 51 (1), 211–232.

• Lyu, R. Q., Wu, C., Ma, X., and Wang, J. (2023). Mediation Analysis with Mendelian Randomization and Efficient Multiple GWAS Integration. arXiv preprint arXiv:2312.10563.