Adjusting binary phenotype (case/ctrl) for Polygenic Risk Score (PRS)

Question

[landscape95]

Hi everyone,

I am a little confusing of how to adjust binary phenotype for polygenic risk score given values of covariates.

For instance, in a continuous trait, we use the residual of a linear model as an adjusted phenotype. Is it ok to also use the residual of a logistic model as an adjusted phenotype, then I would use this adjusted phenotype (by LOGISTIC model) to build a LINEAR model for all the SNP to train the PRS in the discovery set? E.g:

Adjusted phenotype_i from a logistic model = beta_i x SNP_i

Your help is really appreciated!

Answer 1

[Sam]

The covariate should only affects the parameter optimization part of PRS calculation, but not for the actual PRS calculation. If you look at your equation carefully, you will note that the PRS is only determined by the beta obtained from the summary statistics and the genotype of the individual within the target data.

Generally, you can then express the optimization equation of a typical PRS analysis as

Phenotype ~ PRS + Covariates

This function is implemented in PRSice as --cov, lassosum (see here) and to some extend LDpred (see here, but also see here). It should be the same for both quantitative and binary traits

[landscape95]

Thank you very much, Sam! so technically when we say "adjust for phenotype" it is implicitly understand as a linear regression for the original phenotypes with all covariates, isn't it? As I have read some papers mentioned they used logistic regression for binary traits so I'm a bit confusing though I know that beta coefficients from linear regression or OR from logistic regression can be transformed to each other.

[Sam]

I am not sure what you meant by "adjust for phenotype". Maybe you want to elaborate a bit more? We almost always use logistic regression for binary traits and we can adjust for covariates using the logistic regression model.