Does Hail's linear regression method account for additivity or dominance?

Hail Query & hailctl
1

Hi folks,

I’m pretty new to statistical genetics, and I’m wondering whether Hail’s linear regression outputs separate beta values for additivity/dominance.

When I learned about GWAS, I was taught to define random variables (X_a, X_d) = (-1, -1), (0, 1), and (1, -1) corresponding to genotypes homozygous ref, heterozygous, and homozygous alt, respectively. This would then give you two betas, beta_a and beta_d, whose values tell you whether the trait is additive, dominant, neither, or some mixture.

My guess from the documentation is that it only outputs a single beta corresponding to the genotype (I’m running it the same way as in the documentation—feeding in GT.num_alt_alleles()).

If this is the case, could Hail’s method miss some associations because a trait isn’t strictly linear?

Best,
Jeremy

2

That’s right, Hail only runs one test per phenotype per variant. If you’re using mt.GT.n_alt_alleles you’re testing the additive model. Regarding the -1,0,1 model vs the 0,1,2 model, I think you should be able to convert between the betas from these two representations but I don’t know the math off the top of my head.

You can run a dominance model by manually producing a dominance encoding which is orthogonal to the 0,1,2 model.

Alternatively, you could just write write the dominance and additive models using your representation:

mt = mt.annotate_entries(
    mt_add = mt.GT.n_alt_alleles() - 1, # assuming biallelic
    mt_dom = 1 - 2 * mt.GT.is_het()
)

NB: When is_het you get 1 when !is_het you get -1.