Hello Milos. Hope you found all the answers useful. I guess one thing I should emphasise, to add on my previous comment is that the allele frequencies are the key. R2 will drop with low allele frequencies, whilst D' is robust as I pointed out earlier (due to scaling by theoretical maximum of the statistic). However, D' can still give more false positives in that regard. This is because rare variants may indicate a high level of disequilibrium/non-random association between loci simply due to chance.  At the same time R2 may give false negatives in this regard. However, D' can still be reliable if one of the variants being measured for LD is a common variant, and the other is rare. It can also compensate for rare variants (to some extent) of the population size being measured for LD is very large (if alleles at both loci are rare). However, when dealing with pairwise LD exclusively between rare variants, in populations that are not so large, one must take care in using the D' output. Identifying LD among rare variants is always more difficult. R2 will successfully identify LD for common variants, but unlikely to do so when dealing with rare alleles (due to its frequency dependency). D' theoretically can have a better chance of identifying LD among rare variants compared to R2, but one may accumulate more false positives as I said earlier. The bottom line is, both have their positives and drawbacks, but allele frequency is the key, when deciding which to use. Hope that helps.  

Hi Milos

You usually want to work with di-nucleotide SNPs (i.e., only two states possible; for example either A or G, C or T, etc). Thus, please check the MAFs in your example.

Perhaps you are a little confused by the fact that ranges of D depend on allele frequencies. However, D' = D/Dmin is a standardization to avoid such problems. Therefore, you should be equally safe selecting SNPs based on r2 or D'.

Hope this helps

Pablo

That was an example how r2 drops with a shift of allele frequencies. It equally applies to di-nucleotide SNPs.

If fact, my question is related to the relationship of r2 and D', as I have a feeling that when selecting a proxy SNP or SNPs in LD, with a threshold of r2>0.8 (today being a standard threshold), we are being too stringent. In addition, by choosing r2 over D' and trying to avoid rare variants, we might be missing variants that are in perfect disequilibrium simply due to the allele frequencies.

 Hello Milos

Yes, you are correct. I'm sure you are aware of the differences in the formal definitions of r^2 and D'. Therefore, you will know that D' accounts for the difference between the observed and expected allele frequencies (D = Pab - PaPb), and is scaled by the theoretical maximum value of D. On the other hand r^2 is only scaled by the individual allele frequencies of the 2 loci only (and is more frequency dependent than D') as in the following equation:

r^2 = D^2/(PaPb(1-Pa)(1-Pb). Therefore, looking at these equations D' has a more accurate scaling adjustment overall, the normalisation is accounting for the observed frequency of correlation between the alleles at the 2 separate loci, whereas r^2 is too frequency dependent as you rightly pointed out. Therefore, as you were saying, it is better to use D', thereby minimising risk of excluding variants in LD, purely due to allele frequencies. This is just the way I see it. Please correct me if I'm wrong, but I hope that helps.  

Hi again

I see... The reason why  r2 is so popular in population geneticis is that a high value of D' does not imply you can predict perfectly one locus composition when you know the other, whereas a high r2 value implies perfect predictability.

Regarding your worries about missing rare variants (false negatives), I would be more worried by false positives. Anyhow, you are right in that both measures have some advantages and some disadvantages...Nobody's perfect :-)

Hello Milos. Hope you found all the answers useful. I guess one thing I should emphasise, to add on my previous comment is that the allele frequencies are the key. R2 will drop with low allele frequencies, whilst D' is robust as I pointed out earlier (due to scaling by theoretical maximum of the statistic). However, D' can still give more false positives in that regard. This is because rare variants may indicate a high level of disequilibrium/non-random association between loci simply due to chance.  At the same time R2 may give false negatives in this regard. However, D' can still be reliable if one of the variants being measured for LD is a common variant, and the other is rare. It can also compensate for rare variants (to some extent) of the population size being measured for LD is very large (if alleles at both loci are rare). However, when dealing with pairwise LD exclusively between rare variants, in populations that are not so large, one must take care in using the D' output. Identifying LD among rare variants is always more difficult. R2 will successfully identify LD for common variants, but unlikely to do so when dealing with rare alleles (due to its frequency dependency). D' theoretically can have a better chance of identifying LD among rare variants compared to R2, but one may accumulate more false positives as I said earlier. The bottom line is, both have their positives and drawbacks, but allele frequency is the key, when deciding which to use. Hope that helps.