Variance Formulae for Correlation Measures of Linkage Disequilibrium

Abstract

Background: Linkage disequilibrium (LD) is the non-random association between alleles at different loci and remains important for disease mapping studies in humans. A common measure of LD is the sample correlation between indicator variables for alleles at the 2 loci. Knowledge of LD estimate precision may help inform biomedical decisions based on those estimates. Objectives and Methods: Variance formulae are obtained for correlation measures of LD in 4 scenarios. These scenarios include data in the form of gametic and genotypic counts, with different assumptions used to simplify the analysis. Results: The formulae are expressed as polynomials (or ratios of polynomials) in higher-order disequilibrium coefficients with constants which are functions of the allele frequencies and Hardy-Weinberg disequilibrium coefficients. With genotypic data, the variance is the same as with gametic data when the phase is known and there is random mating. When the phase is unknown, the correlation LD has variance which is twice as large. Conclusions: Symbolic computation proved to be effective in facilitating algebraic derivations which would otherwise have been intractable.