A novel unbiased Linkage Disequilibrium estimator through Random Probing

Abstract

The linkage disequilibrium (LD) or correlation of alleles at different loci is a fundamental statistic in population genetics. This work presents a new estimator for the standardised LD measure r^2 between a pair of loci. The Random Probe (RP) estimator involves generating a set of random dummy loci, before calculating the r^2 between each synthetic locus and the two focal loci using one of the existing estimators (even it is known to be biased). The correlation between the two vectors of r^2 is the LD estimate. Computer simulations show promising results, with the RP estimator at least as unbiased as the current Ragsdale and Gravel estimator in most common scenarios. In the more challenging scenarios with skewed allele frequencies and small sample size, RP is preferred by having notably reduced bias, and that the bias is less sensitive to sample size and underlying LD, while maintaining mean squared error comparable to existing methods. The new estimator will most benefit applications relying on accurate measures of LD. Beyond LD, this study stimulates further discussions on whether RP estimator can be generalised to other genetic summary statistics or measures of relatedness.