Plink logistic regression algorithm: How can it compute the standard error for each coefficient with extremly large SNPs array( >500k)?

Question

[adrien.f.badre-1]

Hello Biostars community,

I'm a little bit interested in plink under the hood. I'm very surprised that plink handles so well the logistic regression for association analysis.

For a Dataset with 500k SNPs, if I'm correct, in order to get the standard error, we would need to compute the Hessian matrix for the parameters. It would lead to a matrix of size 500k500k so something extremely large for the ram of any cluster( assuming that each element of a matrix is a float16-> 0.000004 megabytes by number and, if I am correct, it would represent 500k0.5*4 MB for the matrix which is approximatly1000GB of ram to handle the matrix).

Does anyone know what sort of algorithm/process is used to achieve the computation of the hessian and/or the standard error without killing the ram of a cluster/Personal computer ( if applicable)?

Regards

Answer 1

[chrchang523]

You seem to be misunderstanding the computation that plink is performing. The logistic regressions for each variant are completely independent of each other; there isn't a single giant regression performed with 500k predictors.

[adrien.f.badre-1]

Oh, it makes sense then!

So basically, it takes 1 SNP at a time, perform a regression on it and then return the standard error?

Thank you for your previous answer. it helps a lot!