A novel generalized ridge regression method for quantitative genetics

Area of Science:

• Genomics
• Statistical Genetics
• Bioinformatics

Background:

• Increasing molecular marker density necessitates advanced statistical models for genome-wide association studies (GWAS) and genomic selection (GS).
• Traditional models struggle with datasets where the number of parameters (SNPs) vastly exceeds the number of observations (individuals).

Purpose of the Study:

• To develop and present a computationally efficient generalized ridge regression (RR) algorithm for high-dimensional genomic data.
• To implement and evaluate a heteroscedastic effects model (HEM) for improved QTL mapping and genomic prediction.

Main Methods:

• Developed a generalized ridge regression (RR) algorithm where computational cost depends on observations, not parameters.
• Implemented the algorithm in the R package `bigRR`, utilizing the `hglm` package.
• Developed and tested a heteroscedastic effects model (HEM) for enhanced robustness and accuracy.

Main Results:

• The RR algorithm demonstrated high computational efficiency, processing 216,130 SNPs for 84 individuals in under 10 seconds.
• Permutation tests became feasible, allowing for reliable genome-wide significance thresholds.
• HEM outperformed ordinary RR in quantitative trait loci (QTL) mapping due to SNP-specific shrinkage, and provided better genomic evaluation predictions.

Conclusions:

• The proposed computationally efficient RR algorithm and HEM are valuable tools for analyzing large-scale genomic data.
• These methods enhance the feasibility and accuracy of GWAS, QTL mapping, and genomic selection, particularly with high-density marker data.