Stochastic Lanczos estimation of genomic variance components for linear mixed-effects models

Area of Science:

• Genomics
• Statistical Genetics
• Computational Biology

Background:

• Linear mixed-effects models (LMM) are crucial for genome-wide association studies (GWAS).
• Estimating variance components using residual maximum likelihood (REML) is computationally intensive.
• Existing methods use iterative and stochastic approaches with relaxed tolerances to manage computational load.

Purpose of the Study:

• Introduce novel algorithms to accelerate REML estimation for LMM.
• Improve computational efficiency beyond current methods for GWAS.
• Provide faster and more flexible alternatives for variance component estimation.

Main Methods:

• Developed stochastic Lanczos derivative-free REML (SLDF_REML) and Lanczos first-order Monte Carlo REML (L_FOMC_REML) algorithms.
• Algorithms exploit Krylov subspace shift-invariance for computational speed-up.
• Both algorithms require a single round of iterative matrix operations, followed by efficient vector operations; SLDF_REML can leverage precomputed genomic relatedness matrices (GRMs).

Main Results:

• Numerical experiments confirm theoretical predictions.
• Interpreted-language implementations of SLDF_REML and L_FOMC_REML match or surpass compiled-language software in speed, accuracy, and flexibility.
• The novel algorithms demonstrate superior performance in REML estimation.

Conclusions:

• SLDF_REML and L_FOMC_REML algorithms outperform existing methods for REML variance component estimation in LMM.
• These algorithms are well-suited for integration into existing GWAS LMM software.
• The findings offer significant computational advantages for genetic association studies.