Definition of relatedness as implemented in somalier

This might be more of a request for clarification than an actual issue or problem with the code.

I noticed that the definition of relatedness seem to have changed with the release of version 0.2.12 of somalier.

The change was, as far as I can tell, prompted by the following issue reported by Filipe Garrett Vieira (fgvieira): https://github.com/brentp/somalier/issues/55

In the Somalier-paper [ https://doi.org/10.1186/s13073-020-00761-2 ], relatedness was defined as

(shared-hets(i,j) - 2 * ibs0(i, j)) / min(hets(i), hets(j))

In #55, Filipe suggested that the definition of relatedness to be :

(shared-hets(i,j) - 2 * ibs0(i, j)) / min(hets_in_common_pos(i), hets_in_common_pos(j))

where hets_in_common_pos(i) stands for the number of hets in sample "i" among the positions shared ("n")

Judging from your reply to Filipe, I was expecting that you had implemented his suggestion, but when I looked at your commit https://github.com/brentp/somalier/commit/3e0b8401ac71e79de9afc13a2b1fd5df8d1dabdb

I got the impression that you didn’t implement Filipe’s suggestion but instead implemented relatedness as

r_{brent} = 2(shared-hets(i,j) - 2 * ibs0(i, j)) / hets_{ij}

where hets_{ij} is hets_in_common_pos(i) + hets_in_common_pos(j). As pointed out to me by Filipe, your definition could also be stated as

r_{brent} = (shared-hets(i,j) - 2 * ibs0(i, j)) / mean(hets_in_common_pos(i), hets_in_common_pos(j))

r_{brent} is, of course, always less than or equal to the relatedness suggested by Filipe.

It seems to me that your implementation corresponds to the following definition from Manichaikul [PMID: 20926424] equation (9) - except perhaps for a factor 2? The definition from Manichaikul et al.:

Can you confirm that there is this factor 2 difference between your definition and the one given my Manichaikul et al.?

In any case, if the definition of relatedness in the Somalier-paper doesn't correspond to the one used in the current version of somalier, perhaps this should be stated in the README-file?

brentp / somalier

Definition of relatedness as implemented in somalier #74