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.