Calculating non-gametic (or trans) linkage disequilibrium in PLINK

[Gabriele Sgarlata]

Hi Chris,

I was wondering whether PLINK is able to calculate non-gametic (sometimes called also trans-) linkage disequilibrium. That is, linkage disequilibrium between pairs of variants that are in different homologous chromosomes (for instance both SNPs in a pairs are on chromosome 1, but each on one of the two homologous chromosomes 1).

If we consider that linkage disequilibrium is defined as Cov(x,g), where "x" is the diploid genotype at locus "x" and "g" is the diploid genotype at locus "g", then:

Cov(x,g) = Cov(x' + x", g' + g") = Cov(x',g') + Cov(x',g'') + Cov(x'',g') + Cov(x'',g'') = 2D' + 2D"

here, the indexes ' or "  defines loci on different chromosomes and D' indicates gametic (or cis-) LD and D" indicates non-gametic (or trans) LD. 

Since, I am interested in the "r2" and "r" statistics, I figure out that based on this calculation, and considering what plink2 can do, one way of calculating 'non-gametic LD' would be to subtract the "r" statistics computed with "--r-unphased" with the "r" statistics computed with "--r-phased". This should be correct if we consider that the "--r-unphased" option calculate r = (2r' + 2r")(1/2).

What are your thoughts on that?

Thank you,

Best,

Gabriele