Check calculation of allele frequency for X chromosome

[gregorgorjanc]

Goal

Check that allele frequency is estimated correctly for autosomal and X chromosome.

Proposed approach

Allele frequency for diploids is estimated as sum(g) / (2 * nInd) where g are genotypes coded as [0, 1, 2] and 2 * nInd is the total number of alleles. With X chromosome, we have in males only g = [0, 1] so the total number of alleles is smaller, hence the correct formula for allele freq in that case is sum(g) / (2 * nFemales + nMales). We should of course work with underlying genotype probabilities, but these are added up into allele dosages (g) anyway.

I think the actions are:

• Take a small example and calculate allele frequencies for the founder by hand
• Compare the above calculation with what AlphaPeel - if they match, we have no issue, but might still want to add a unit test; if they don't match, we should fix the calculation

Scope

What files/modules are affected? Would have to check;)

#270 reported that in the code, we have the following warning (edited 2026-05-25):

if peelingInfo.isXChr:
        warnings.warn(
            "Updating error rates and alternative allele frequencies for X chromosomes are not well test and will break in interesting ways. Recommend running without that option."
        )

Done when

The above proposed check, tests, and changes are sorted, and lastly the warning is removed. (edited 2026-05-25).

[XingerTang]

Just add here as to why this discussion starts, the MAF estimation for the female individuals with x_chr option in the imputation against the true MAF from the female individuals of simulation data for x_chr is:

This is much noisier than the similar plot for the regular multi imputation:

---

Edited: Sorry, the graph for the female X chromosome is wrong. It is deleted now.

[XingerTang]

Correction: for female individuals, the MAF estimation is good. While it might be inflated for the male individuals.

For female individuals:

For male individuals:

Note that I didn't change the MAF calculation formulae for male individuals (so that the formulae still think the values should range from 0, 1, 2). But since the same "wrong" formulae are applied to the true simulation data as well, we should expect to see a similar skew if the MAF estimation given by AlphaPeel is true.

[gregorgorjanc]

These results make sense given the autosomal and X chromosome allele frequency formula differs. @AprilYUZhang will you be able to implement this?

[XingerTang]

Further looking into the patterns, it seems that the true-X_chr_geno_prob_male is a condensed version of multi_x_chr_male. Recalled that the sex chromosome output for the X chromosome of males has encoding that aa means 0 and AA means 1.

For the genotype probability interpretation, it does not match how ImputationQuality expect it.

By switching the column for representing 2 and 1 for the male individuals, the MAF estimation now looks much similar.

[XingerTang]

Further looking into the patterns, it seems that the true-X_chr_geno_prob_male is a condensed version of multi_x_chr_male. Recalled that the sex chromosome output for the Y chromosome has encoding that aa means 0 and AA means 1.

For the genotype probability interpretation, it does not match how ImputationQuality expect it.

By switching the column for representing 2 and 1 for the male individuals, the MAF estimation now looks much similar.

The blue points at a value of 1 are not explainable, given that we are assessing Y chromosomes. It is caused by the code that assigns the data with MAF equal to 0 to a value very close to 1, and MAF equal to 1 to a value very close to 0. I have replaced the code with machine epsilon and 1- machine epsilon. Now, the range is between 0 and 0.5.

[gregorgorjanc]

Now, the range is between 0 and 0.5.

And this is exactly the issue. Since we use one allele frequency for both males and females we have to count how many alleles there is - 2 alleles on X chr in females and just 1 allele on X chr in males. So when we calculate allele frequency we should take into account the number of alleles - the above plot with a max of 0.5 shows that the division was by 2*nInd = nAutosomalAlleles and not with nXAlleles. This is what we have to check and possibly fix in this issue.

[XingerTang]

Now, the range is between 0 and 0.5.

And this is exactly the issue. Since we use one allele frequency for both males and females we have to count how many alleles there is - 2 alleles on X chr in females and just 1 allele on X chr in males. So when we calculate allele frequency we should take into account the number of alleles - the above plot with a max of 0.5 shows that the division was by 2*nInd = nAutosomalAlleles and not with nXAlleles. This is what we have to check and possibly fix in this issue.

You are right. The MAF is generated by the ImputationQuality software based on genotype probability output, not AlphaPeel MAF output. And according to its German comment, it is given by
Hier f_A=Allel-count / Anz. Haplotypen (2xPersonen)
Google translate: Here f_A = Allele count / Number of haplotypes (2 x people)
and it probably suggests that we shouldn't directly evaluate against the male individuals with the metrics provided by the software. As they are all assuming two haplotypes.

[gregorgorjanc]

@AprilYUZhang hve you had a chance to look into this issue?