A kernel of truth: statistical advances in polygenic variance component models for complex human pedigrees.

Area of Science:

• Statistical Genetics
• Computational Biology
• Genomics

Background:

• Analyzing quantitative traits in large pedigrees presents computational challenges due to relatedness.
• Rare sequence variants are increasingly recognized for their role in human quantitative variation, necessitating efficient family-based study designs.
• Current methods for optimal marker/phenotype association, like the likelihood ratio statistic, are computationally prohibitive for whole genome sequence association studies.

Purpose of the Study:

• To develop a computationally efficient method for statistical genetic analysis in large pedigrees.
• To enable accurate heritability and association analyses of sequence variants in family data.
• To facilitate fast and accurate analytical power analyses, reducing reliance on computer simulations.

Main Methods:

• Developed a rapid and efficient eigen simplification of the likelihood function based on a spectral representation.
• Derived simple exact expressions for the expected likelihood ratio test statistic (ELRT) for heritability and association analyses in pedigrees.
• Investigated the exact distribution of the ELRT under the null hypothesis and potential issues with empirical genetic relationship kernels (GRKs).

Main Results:

• The eigen simplification makes family data analysis computationally feasible, comparable to analyzing unrelated individuals.
• Exact expressions for the ELRT were derived for heritability (involving heritability and eigenvalues of GRK) and sequence variant association (involving different heritability components).
• Fast analytical power analyses are now possible, and the exact distribution of the ELRT under the null hypothesis was determined, differing from asymptotic theory.

Conclusions:

• The eigen simplification of the likelihood provides a computationally efficient and accurate approach for statistical genetic analysis in large pedigrees.
• This method enhances the analysis of heritability and genetic associations with sequence variants in family studies.
• The developed procedures offer advantages for power analysis and understanding the ELRT distribution, with applications in the SOLAR package.