Correcting for population structure and kinship using the linear mixed model: theory and extensions

Area of Science:

• Genetics
• Statistical Genetics
• Bioinformatics

Background:

• Population structure and kinship are significant confounding factors in genome-wide association studies (GWAS).
• Principal components (PCs) are commonly used to correct for population structure in regression models.
• Linear mixed models (LMMs) offer a powerful approach to simultaneously account for population structure and kinship.

Purpose of the Study:

• To formalize the statistical relationship between PC-based and LMM-based methods for GWAS.
• To introduce a novel statistic, effective degrees of freedom, for assessing model complexity.
• To develop and evaluate a low rank linear mixed model (LRLMM) for improved correction of population structure and kinship.

Main Methods:

• Theoretical analysis of the statistical properties of PC and LMM approaches.
• Introduction of 'effective degrees of freedom' as a complexity metric.
• Development and simulation-based assessment of the LRLMM.

Main Results:

• The study elucidates the statistical underpinnings of PC and LMM methods in GWAS.
• The LRLMM demonstrates effective learning of dimensionality for population structure and kinship correction.
• Application to Multi-Ethnic Study of Atherosclerosis (MESA) data shows empirical translation of theoretical findings.

Conclusions:

• The LRLMM offers a statistically rigorous and computationally efficient approach to handling population structure and kinship in GWAS.
• The LRLMM significantly enhanced the detection of associations, as exemplified by a stronger association for HDL cholesterol in Europeans.
• This method provides a valuable tool for increasing the power of genetic association studies.