Supplementary Material for: Variance Formulae for Correlation Measures of Linkage Disequilibrium

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.