Asymptotically exact fit for linear mixed model in genetic association studies

Area of Science:

• Genetics
• Biostatistics
• Computational Biology

Background:

• Linear mixed models (LMMs) are crucial in genetic association studies to control for population structure and sample relatedness, minimizing false positives.
• Current LMM research often focuses on approximate computations, as exact methods are computationally intensive and lack theoretical guarantees.
• Multiomics studies, involving millions of genetic markers and thousands of phenotypes, present significant computational challenges for LMM fitting.

Purpose of the Study:

• To introduce novel iterative methods, IDUL and IDUL†, for efficient and accurate fitting of linear mixed models (LMMs).
• To address the computational demands of LMMs in large-scale genetic association studies, particularly for multiomics data.
• To provide a theoretically sound and practically efficient alternative to existing LMM fitting algorithms.

Main Methods:

• Development of IDUL, an iterative dispersion update algorithm for LMM fitting.
• Introduction of IDUL†, a modified version of IDUL ensuring monotonic likelihood increases during updates.
• Comparison of IDUL and IDUL† performance against the Newton-Raphson method in terms of computational efficiency and accuracy.

Main Results:

• IDUL and IDUL† demonstrate markedly superior efficiency compared to the state-of-the-art Newton-Raphson method.
• Both IDUL and IDUL† achieve identical results in practice.
• The methods show exceptional efficiency when analyzing additional phenotypes, making them suitable for multiomics research.

Conclusions:

• IDUL and IDUL† offer a computationally efficient and accurate approach to fitting LMMs in genetic association studies.
• The theoretical properties of IDUL† ensure asymptotic exactness due to the unimodal nature of the LMM likelihood.
• The developed software package provides a valuable tool for researchers studying the genetic underpinnings of complex multiomics traits.