palogist & covariates

[Daniel E. Weeks]

We are analyzing some binary traits where we need to adjust for relatedness, but each trait also needs to be adjusted for some relevant covariates. When using a quantitative trait, one runs polygenic to generate the required inverse of the variance/covariance matrix and then uses palinear to analyze the residuals, but with a binary trait, I found this advice on the forum regarding the usage of palogist:

in fact you should not use the residuals but the phenofile shoud contain the original phenotype and the covariates also.

However, it is still not clear if the invmat correlation matrix should be generated from a run of polygenic_hglm where the covariates were included or when they were excluded.

So is this the proper approach?:

1) Use polygenic_hgm with trait.type = "binomial" to compute the required correlation matrix, while adjusting for the covariates:

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polygene <- polygenic_hglm(obesity  ~ age + as.factor(sex) + I(age^2) + age:as.factor(sex), ibs2, data, trait.type = "binomial",verbose=TRUE)
invmat <- polygene$InvSigma * polygene$h2an$estimate[length(polygene$h2an$estimate)]


2) Then use palogist --mmscore to regress the binary trait against exactly the same set of covariates plus the SNP of interest.


The InvSigma matrix is computed by the polygenic_hglm program as follows:

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Sigma <- tVar * out$esth2 * relmat + diag(tVar * (1 - out$esth2), ncol = length(y), nrow = length(y))
out$InvSigma <- ginv(Sigma)
 

where

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  tVar <- res_hglm$varRan + res_hglm$varFix
  out$esth2 <- res_hglm$varRan/tVar


so it is scaled by the esth2 estimate of heritability, but if we are estimating h2 while adjusting for exactly the same set of covariates,
then I think this might be O.K.

Thank you,
Dan Weeks