Unraveling time-varying causal effects of multiple exposures: integrating Functional Data Analysis with Multivariable Mendelian Randomization

TL;DR

This work addresses the challenge of estimating life-course, time-varying causal effects from genetic data when multiple exposures may act jointly or mediate each other. It introduces Multivariable Functional Mendelian Randomization (MV-FMR), combining FPCA representations of longitudinal exposures with a GMM-based multivariable IV framework to recover direct, time-varying causal functions $\beta_j(t)$ for each exposure $X_j(t)$, for both continuous and binary outcomes. Key contributions include a data-driven FPCA component selection, joint estimation that accounts for overlapping instruments and mediation, reconstruction of coefficient functions, and bootstrap-based uncertainty quantification, with extensive simulations showing improved accuracy over univariable approaches. The method is demonstrated in UK Biobank data by jointly modeling SBP and BMI trajectories to assess their time-varying effects on CAD, revealing life-course windows where effects are strongest and illustrating mediation patterns, thereby enabling more precise, temporally-targeted interventions in cardiovascular prevention.

Abstract

Mendelian Randomization is a widely used instrumental variable method for assessing causal effects of lifelong exposures on health outcomes. Many exposures, however, have causal effects that vary across the life course and often influence outcomes jointly with other exposures or indirectly through mediating pathways. Existing approaches to multivariable Mendelian Randomization assume constant effects over time and therefore fail to capture these dynamic relationships. We introduce Multivariable Functional Mendelian Randomization (MV-FMR), a new framework that extends functional Mendelian Randomization to simultaneously model multiple time-varying exposures. The method combines functional principal component analysis with a data-driven cross-validation strategy for basis selection and accounts for overlapping instruments and mediation effects. Through extensive simulations, we assessed MV-FMR's ability to recover time-varying causal effects under a range of data-generating scenarios and compared the performance of joint versus separate exposure effect estimation strategies. Across scenarios involving nonlinear effects, horizontal pleiotropy, mediation, and sparse data, MV-FMR consistently recovered the true causal functions and outperformed univariable approaches. To demonstrate its practical value, we applied MV-FMR to UK Biobank data to investigate the time-varying causal effects of systolic blood pressure and body mass index on coronary artery disease. MV-FMR provides a flexible and interpretable framework for disentangling complex time-dependent causal processes and offers new opportunities for identifying life-course critical periods and actionable drivers relevant to disease prevention.

Figures (4)

• Figure 1: Comparison of (a) Univariable functional MR (independent effects of $X_1$ and $X_2$) with (b) Multivariable functional MR (joint effects of $X_1$ and $X_2$). Dashed arrows represent confounding pathways.
• Figure 2: Illustration of the three simulation scenarios used to evaluate MV-FMR. Scenario 1: Pleiotropy model (left). Scenario 2: Null effect control (center). Scenario 3: Mediation model (right).
• Figure 3: Mean time-varying causal effect estimates at six time points for comparing MV-FMR and U-FMR with a continuous outcome. Columns represent different exposure-outcome model combinations, rows show the estimated values for $\beta_1(t)$ and $\beta_2(t)$. Black crosses indicate the true causal effects, green stars show MV-FMR estimates, and orange triangles show U-FMR estimates. Top panel: Scenario 1. Bottom panel: Scenario 3.
• Figure 4: Estimated time-varying causal effects of SBP and BMI on CAD risk from MV-FMR (top) and U-FMR (bottom). Blue curves show SBP effects with 95% bootstrap CI; red curves show BMI effects with 95% bootstrap CI.