Causal effect heterogeneity estimation using summary statistics.

Mendelian randomization (MR) has swiftly gained popularity as a tool for causal inference in genetic epidemiology. However, existing MR methods focus exclusively on estimating the average causal effect and cannot quantify its heterogeneity, posing a major methodological limitation and impeding context-dependent causal findings. Here, we introduce MEndelian Randomization for Linear INteraction (MERLIN), a unified Bayesian framework that jointly estimates the average and context-dependent causal effects using summary data from genome-wide association and interaction studies. Through extensive simulation analyses, we demonstrate the improved power, robustness, and broad utility of MERLIN versus existing methods. We show MERLIN was able to identify sex-specific causal effects of schizophrenia on brain imaging traits, a male-specific causal effect of testosterone on bipolar disorder, and age-dependent causal effects of metabolic biomarkers on coronary artery disease risk. These results illustrate the transformative potential of summary-data-based inference for causal heterogeneity. Together, MERLIN provides a powerful and practical framework for investigating causal effect heterogeneity using summary-level observational data and greatly enhances our capability to elucidate complex disease etiology.