Empirical Bayes Shrinkage of Functional Effects, with Application to Analysis of Dynamic eQTLs

2026-02-03

AI Summary

This study addresses the challenge of estimating and testing gene regulatory effect functions under continuous conditions—such as time—in dynamic expression quantitative trait locus (eQTL) studies. The authors propose the Functional Adaptive SHrinkage (FASH) method, which, within an empirical Bayes framework, jointly models effect functions across multiple units using a family of Gaussian processes defined by linear differential operators. This approach enables information sharing across units and adaptive smoothing, while incorporating a theoretically justified prior adjustment strategy to ensure conservative inference. FASH supports efficient estimation and rigorous hypothesis testing, including control of local false discovery rates and sign error rates. Applied to a reanalysis of cardiomyocyte differentiation data, FASH identifies novel dynamic eQTLs, reveals diverse temporal effect patterns, and substantially improves statistical power. An open-source R package, fashr, implements the method.

Technology Category

• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We introduce functional adaptive shrinkage (FASH), an empirical Bayes method for joint analysis of observation units in which each unit estimates an effect function at several values of a continuous condition variable. The ideas in this paper are motivated by dynamic expression quantitative trait locus (eQTL) studies, which aim to characterize how genetic effects on gene expression vary with time or another continuous condition. FASH integrates a broad family of Gaussian processes defined through linear differential operators into an empirical Bayes shrinkage framework, enabling adaptive smoothing and borrowing of information across units. This provides improved estimation of effect functions and principled hypothesis testing, allowing straightforward computation of significance measures such as local false discovery and false sign rates. To encourage conservative inferences, we propose a simple prior- adjustment method that has theoretical guarantees and can be more broadly used with other empirical Bayes methods. We illustrate the benefits of FASH by reanalyzing dynamic eQTL data on cardiomyocyte differentiation from induced pluripotent stem cells. FASH identified novel dynamic eQTLs, revealed diverse temporal effect patterns, and provided improved power compared with the original analysis. More broadly, FASH offers a flexible statistical framework for joint analysis of functional data, with applications extending beyond genomics. To facilitate use of FASH in dynamic eQTL studies and other settings, we provide an accompanying R package at https: //github.com/stephenslab/fashr.

Problem

• dynamic eQTL
• functional effects
• effect function
• continuous condition
• genetic effects

Innovation

• Functional Adaptive Shrinkage
• Empirical Bayes
• Gaussian Processes
• Dynamic eQTL
• Adaptive Smoothing