Interpretation of GWAS-by-Subtraction Effect Estimates

[Michael Levin]

My understanding is that the "sumstats" function transforms coefficients and SEs "such that they are scaled relative to unit-variance scaled phenotypes" (https://github.com/GenomicSEM/GenomicSEM/wiki/4.-Common-Factor-GWAS). When performing a GWAS-by-Subtraction, my understanding is that SNP effects are similarly reported based on unit-variance identification. Can we therefore directly compare the effect estimates for a given SNP on the parent trait and the adjusted trait (either as a difference or ratio)?

For example, given two traits T1 and T2, we could perform GWAS-by-Subtraction to estimate the effect of a SNP on T2adjT1 (T2 independent of T1). For any given SNP we have 1) effect the SNP on T2 scaled to unit variance (from the "sumstats" function), and 2) the effect of the SNP on T2adjT1 scaled to unit variance (from the GWAS-by-Subtraction). Calculating a difference or ratio of these effect estimates seems like it would provide some quantitative assessment of whether the effect of a SNP on T2 is "mediated" by T1. Is this interpretation/intuition correct?

[Elliot Tucker-Drob]

Hi Michael,

For GWAS-by-subtraction with unit-scaled factors and free loadings, the SNP effects actually get rescaled by the loadings. This is because this parameterization scales the genetic variance, rather than the phenotypic variance, of the factor to 1.0, whereas the sumstats function scales the SNP effects relative to unit-scaled phenotypes (this is exactly what we typically want because that's the scale that heritability is on). You could parameterize the GWAS-by-subtraction model such that the variances of the factors are free and the loadings are fixed to 1.0 (keep the cross loading of EA on Cog free), which would be an equivalent model but put the SNP effects on the same scale as those from the sumstats function. The rGs, top hits, mean chi sq, etc.. will all be the same as the original parameterization but the scale will just be changed for the SNP betas.

You'll be able to confirm whether or not the betas are indeed on the same scale as those from sumstats by comparing the SNP betas for the Cog factor from the GWAS-by-subtraction model to those for Cognitive Performance from the sumstats function. Cog and cognitive performance are the same in this model, since nothing is being subtracted from Cognitive Performance when forming the Cog factor, so the Z statistics should match regardless, but the betas will be rescaled depending on your parameterization.

Hope that helps,

Elliot

On Wed, Aug 17, 2022 at 3:52 PM Michael Levin <mgl...@gmail.com> wrote:

My understanding is that the "sumstats" function transforms coefficients and SEs "such that they are scaled relative to unit-variance scaled phenotypes" (https://github.com/GenomicSEM/GenomicSEM/wiki/4.-Common-Factor-GWAS). When performing a GWAS-by-Subtraction, my understanding is that SNP effects are similarly reported based on unit-variance identification. Can we therefore directly compare the effect estimates for a given SNP on the parent trait and the adjusted trait (either as a difference or ratio)?

For example, given two traits T1 and T2, we could perform GWAS-by-Subtraction to estimate the effect of a SNP on T2adjT1 (T2 independent of T1). For any given SNP we have 1) effect the SNP on T2 scaled to unit variance (from the "sumstats" function), and 2) the effect of the SNP on T2adjT1 scaled to unit variance (from the GWAS-by-Subtraction). Calculating a difference or ratio of these effect estimates seems like it would provide some quantitative assessment of whether the effect of a SNP on T2 is "mediated" by T1. Is this interpretation/intuition correct?

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[Michael Levin]

Great - thanks for the quick reply! Using the example from the tutorial (https://rpubs.com/MichelNivard/565885) the model would look something like this? 

model<-

'C=~NA*EA + 1*CP 

 NC=~1*EA

 C~SNP 

 NC~SNP 

 NC~~NA*NC 

 C~~NA*C 

 C~~0*NC 

 CP~~0*EA 

 CP~~0*CP 

 EA~~0*EA 

 SNP~~SNP'

And similar modification would be made in the multivariate ldsc model passed to the "covstruc" argument of the "userGWAS" function?

[Elliot Tucker-Drob]

That looks right but always best to run a test sample of SNPs and check the output. 

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