Statistics Seminar - Hera Shi (UCL)

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Title: Empirical Bayes Transfer Learning for Cross-Ancestry Mendelian Randomization Abstract: Limited genome-wide association study (GWAS) sample sizes in underrepresented populations can reduce the precision of Mendelian randomization (MR) through uncertainty in instrument strengths. Associations from other ancestries may improve precision, but borrowing must accommodate population-specific causal effects and pleiotropy. Motivated by this problem, we develop \emph{MR-NPEB}, a nonparametric empirical Bayes method for heteroscedastic multivariate errors-in-variables models with general loading matrices. MR-NPEB estimates the joint distribution of instrument strengths and incorporates their posterior predictions into a one-step score estimator of causal effects and pleiotropy variances. In cross-ancestry MR, this enables borrowing through the dependence of genetic effects without imposing common causal parameters. Under a many-weak-instrument regime, we establish identification, asymptotic normality, and consistent covariance estimation, with no first-order variance cost from posterior estimation under suitable conditions. Our efficiency analysis distinguishes two gains: learning the effect distribution yields no larger asymptotic covariance than MR using robust adjusted profile scores (MR-RAPS), while auxiliary associations further improve precision through posterior prediction of target instrument strengths. We characterize the borrowing gain in terms of cross-population dependence and sampling precision, and establish semiparametric efficiency under homoscedasticity and completeness. Simulations and an analysis of Mexican Biobank GWAS data using UK Biobank associations illustrate the improvements in causal-effect precision.