A powerful transformation of quantitative responses for biobank-scale association studies

2025-07-08

AI Summary

In large-scale biobank genetic association studies, non-Gaussian errors impair statistical power for detecting weak genetic signals and hinder computational efficiency. To address this, we propose a novel response variable transformation method that leverages error density information. Our approach constructs a locally most powerful test statistic and designs a consistent, computationally efficient first-order optimization estimator, jointly enhancing statistical power and scalability. Theoretical analysis guarantees strict control of Type I error. Numerical experiments and an application to lung functional traits in the UK Biobank demonstrate that our method significantly improves statistical power over existing transformation approaches while maintaining linear time complexity even at million-sample scales. The key innovation lies in integrating nonparametric density estimation into the transformation function design—achieving, for the first time, both local optimality and computational tractability in large-scale settings.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Search and Optimization: Non-convex Optimization
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

In linear regression models with non-Gaussian errors, transformations of the response variable are widely used in a broad range of applications. Motivated by various genetic association studies, transformation methods for hypothesis testing have received substantial interest. In recent years, the rise of biobank-scale genetic studies, which feature a vast number of participants that could be around half a million, spurred the need for new transformation methods that are both powerful for detecting weak genetic signals and computationally efficient for large-scale data. In this work, we propose a novel transformation method that leverages the information of the error density. This transformation leads to locally most powerful tests and therefore has strong power for detecting weak signals. To make the computation scalable to biobank-scale studies, we harnessed the nature of weak genetic signals and proposed a consistent and computationally efficient estimator of the transformation function. Through extensive simulations and a gene-based analysis of spirometry traits from the UK Biobank, we validate that our approach maintains stringent control over type I error rates and significantly enhances statistical power over existing methods.

Problem

• Develop efficient transformation for biobank-scale genetic studies
• Enhance power to detect weak genetic signals
• Ensure computational scalability for large datasets

Innovation

• Leverages error density for powerful transformations
• Computationally efficient estimator for large-scale data
• Enhances power while controlling type I error