Beyond single-slope Mendelian randomization: structural representation of genetic heterogeneity in joint effect space

Causal effects in complex traits are typically represented by a single linear slope. While conventional Mendelian randomization (MR) provides efficient scalar estimates, projection-based summaries do not explicitly capture structural organisation in joint effect space under genetic heterogeneity. We introduce MR-UBRA (Mendelian randomization-Unified Bayesian Risk Architecture), a probabilistic framework that decomposes instrumental variants into genetic risk fragments (GRFs) and quantifies extreme deviations using tail-risk metrics defined on the standardised residual magnitude |e|. MR-UBRA preserves the classical MR estimand while offering a structurally resolved representation of genetic heterogeneity. Across stroke subtypes, AF[->]CES, smoking[->]lung cancer, and BMI[->]T2D, effect-space distributions exhibit reproducible asymmetry, amplitude stratification, and multi-modal structure. MR-UBRA resolves component-level organisation, separating tail-dominant contributions from the causal core while maintaining consistency with the classical MR estimand. Simulations and boundary regimes demonstrate adaptive model complexity: MR-UBRA selects K>1 when multi-component structure is present and collapses to K=1 under homogeneous conditions, avoiding spurious stratification. These results support viewing causal effects in complex traits as structured distributions in joint effect space, enhancing causal representation without altering the MR estimand. Graphical AbstractMendelian randomization (MR) typically represents causal effects with a single linear slope. Under genetic heterogeneity, instrumental effects in joint ({beta}X, {beta}Y) space may exhibit multi-component structure and amplitude stratification that cannot be captured by a scalar summary. MR-UBRA fits a standard error-weighted mixture model to decompose instruments into genetic risk fragments (GRFs), estimates GRF-specific effects using posterior-weighted soft-IVW, and quantifies extreme deviations through tail-risk metrics (VaR/CVaR). Across empirical analyses and boundary regimes, MR-UBRA adapts model complexity (K) to structural signal, collapsing to K=1 under homogeneous conditions. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=144 SRC="FIGDIR/small/26348288v1_ufig1.gif" ALT="Figure 1"> View larger version (31K): org.highwire.dtl.DTLVardef@1627086org.highwire.dtl.DTLVardef@1c9982eorg.highwire.dtl.DTLVardef@262730org.highwire.dtl.DTLVardef@d6e551_HPS_FORMAT_FIGEXP M_FIG C_FIG