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Chunk #21 — ONLINE METHODS — Estimation of LD Score

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LD Score regression distinguishes confounding from polygenicity in genome-wide association studies.
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We used a window of radius 1cM around the index variant for the sum of r2’s (using the genetic map and phased genotypes from the IMPUTE2 website, see URLs), no r2 cutoff, and excluded singletons (MAF < 0.13%). The standard estimator of the Pearson correlation coefficient has upward bias of approximately 1 / N, where N is sample size, so we employed an approximately unbiased estimator of LD Score given by radj2^≔r2^−1−r2^N−2 where r̂2 denotes the standard, biased estimator of the squared Pearson correlation. Note that it is possible to have radj2^<1, which is a mathematically necessary feature of any unbiased estimator of r2. Thus, some estimated LD Scores will be less than 1. In practice, almost all variants with estimated LD Score less than 1 were rare: only 0.01% of variants with MAF > 5% had estimated LD Scores below 1.