Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical...

Area of Science:

• Genetical genomics
• Statistical genetics
• Bioinformatics

Background:

• Joint analysis of gene expression and genetic variants is crucial for understanding complex traits.
• High dimensionality in gene expression and genetic data often exceeds sample size.
• Classical methods struggle with high-dimensional sparse instrumental variable models.

Purpose of the Study:

• To develop a robust methodology for variable selection and estimation in high-dimensional sparse instrumental variable models.
• To identify and estimate important covariate effects while simultaneously selecting and estimating optimal instruments.
• To address challenges posed by high dimensionality and unknown optimal instruments in genetical genomics.

Main Methods:

• A two-stage regularization framework is proposed, extending two-stage least squares.
• Sparsity-inducing penalty functions are utilized in both stages to handle high dimensionality.
• Coordinate descent optimization is employed for efficient implementation.
• The methodology incorporates L1 regularization and concave regularization methods.

Main Results:

• The proposed method achieves accurate estimation, prediction, and model selection in high-dimensional settings.
• Theoretical properties are established for estimators where dimensionality grows exponentially with sample size.
• Simulation studies demonstrate the practical performance and effectiveness of the approach.

Conclusions:

• The two-stage regularization framework provides an efficient and effective solution for high-dimensional genetical genomics.
• The method successfully identifies relevant genetic variants and estimates their association with gene expression and complex traits.
• The approach is validated through simulations and a real-world application to mouse obesity data.