Unraveling time-varying causal effects of multiple exposures: integrating Functional Data Analysis with Multivariable Mendelian Randomization
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.
Summary
The paper introduces Multivariable Functional Mendelian Randomization (MV-FMR), a novel statistical framework that extends functional Mendelian Randomization (FMR) to simultaneously model multiple time-varying exposures and their causal effects on health outcomes. Existing multivariable Mendelian Randomization (MV-MR) methods assume constant effects over time, which is unrealistic for many exposures. MV-FMR addresses this limitation by integrating functional principal component analysis (FPCA) with a data-driven cross-validation strategy for basis selection. This allows for modeling exposures as continuous functions of time and disentangling the direct effects of multiple exposures, accounting for overlapping instruments and mediation pathways. The authors evaluated MV-FMR's performance through extensive simulations under various scenarios, including nonlinear effects, horizontal pleiotropy, mediation, and sparse data. MV-FMR consistently outperformed univariable FMR approaches in recovering true causal functions. To demonstrate its practical utility, the authors applied MV-FMR to UK Biobank data to investigate the time-varying causal effects of systolic blood pressure (SBP) and body mass index (BMI) on coronary artery disease (CAD). The results suggest that critical exposure windows for SBP and BMI in relation to CAD risk are concentrated in the sixth decade of life. This work provides a flexible and interpretable framework for disentangling complex time-dependent causal processes, offering new opportunities for identifying life-course critical periods and actionable drivers relevant to disease prevention.
Key Insights
- •MV-FMR extends traditional MV-MR by modeling exposures as continuous functions of time using Functional Principal Component Analysis (FPCA), addressing the limitation of assuming constant effects.
- •A data-driven k-fold cross-validation procedure is used to select the optimal number of FPCA components for each exposure, balancing model complexity and generalizability and outperforming variance-based criteria.
- •Simulation results demonstrate that MV-FMR consistently outperforms univariable FMR in recovering true causal functions across a range of scenarios, including nonlinear effects, horizontal pleiotropy, and mediation. For instance, in simulations with linear effects, MV-FMR demonstrated a lower mean Integrated Squared Error (ISE) compared to the univariable approach.
- •MV-FMR addresses the challenge of horizontal pleiotropy through overlapping genetic instruments by explicitly accounting for these overlaps during the joint modeling of exposures.
- •The method includes an extension for binary outcomes using a two-stage residual inclusion (2SRI) control function approach, addressing endogeneity concerns in nonlinear models.
- •The UK Biobank application revealed that SBP and BMI exerted the strongest estimated effects on CAD risk between ages 50 and 60, with attenuated effects at older ages.
- •A limitation is the requirement for longitudinal measurements for each exposure within the same age range, which may not always be available. Furthermore, increasing the complexity of time-varying effects can reduce instrument strength.
Practical Implications
- •MV-FMR can be applied in epidemiological research to identify critical periods in the life course when exposures have the greatest impact on health outcomes, informing the design and timing of preventive interventions.
- •Researchers can use MV-FMR to disentangle the direct and indirect effects of multiple related exposures on health outcomes, providing a more comprehensive understanding of complex causal pathways.
- •Practitioners and engineers can use the results to develop targeted interventions that address specific risk factors during critical periods, potentially leading to more effective disease prevention strategies.
- •Future research directions include extending the framework to accommodate higher-dimensional exposures and investigating computational strategies for large-scale biobank applications.
- •The method can be used to assess the potential impact of interventions on modifiable risk factors, providing valuable insights for public health policy and clinical decision-making.