Estimating linkage disequilibrium from genotypes under Hardy-Weinberg equilibrium

Area of Science:

• Population Genetics
• Statistical Genetics

Background:

• Linkage Disequilibrium (LD) measures are crucial for genetic studies like disease association and demographic history.
• Estimating true population LD from genetic samples is challenging due to inherent measurement error.
• Prior studies on LD measure r-squared (r²) bias and variance focused only on zero LD, not applicable to real-world non-zero LD data.

Purpose of the Study:

• To generalize the estimation of r-squared (r²) to all levels of linkage disequilibrium (LD).
• To develop accurate methods for estimating LD from both phased and unphased genetic data.
• To introduce improved statistical tools for genetic analysis.

Main Methods:

• Derived new formulas for the impact of finite sample size on observed r² values.
• Developed an empirical formula for the variance of observed r²: 2E[r²](1-E[r²])/n.
• Proposed Constrained ML, a novel likelihood-based method for estimating haplotype frequencies and r² from diploid genotypes under Hardy-Weinberg Equilibrium.
• Introduced a new likelihood-ratio test for haplotype absence.

Main Results:

• Provided generalized formulae for r² estimation applicable to all LD levels.
• Established a new formula for r² variance, accounting for sample size.
• Demonstrated that Constrained ML offers improved convergence and ease of use compared to the Expectation-Maximisation algorithm.
• Validated findings through extensive simulations.

Conclusions:

• The developed methods enhance the accuracy of genetic analyses relying on LD measures.
• Findings are broadly applicable to various LD-based inferences, including estimation and hypothesis testing.
• Improved LD estimation will lead to more reliable genetic association studies and demographic analyses.