Genetics-driven risk predictions leveraging the Mendelian randomization framework

Mathematical and computational details of the PRiMeR framework. (A) Diagram illustrating the core MR assumptions, where genetic variants (g₁, …, g_S) influence exposure (e), which in turn affects outcome (o) with directional effect α. Additions unique to PRiMeR are highlighted in purple: a risk predictor is computed as a differentiable function (parametrized by ϕ) of risk factors X. (B) Illustration of IVW regression, where genetic variant effects on outcome (β_o) are regressed on the aggregate risk predictor (β_e), accounting for their standard errors (s_o). (C) Main computations in PRiMeR, including computation of the risk predictor e(ϕ), the estimation of genetic effects on the risk predictor β_e(ϕ), and the computation of the IVW regression loss. The function h(e(ϕ), G, F) returns marginal regression weights of each variant G_:s on e(ϕ) accounting for covariates F. As all these steps are differentiable, can be learned through gradient-based optimization of the IVW regression loss.