I have a data-set with a continuous outcome variable and some confounding variables (like age, gender, ...) and many gene expressions (more than samples). The goal is to find relevant genes in association with the outcome.
Now the first idea was to use the LASSO (Tibshirani 1996). Some questions arose regarding the whole procedure.
- Does one include the confounding variables in the variable selection stage and keep them in the model without regularization? I have seen that including such fixed variables changes the selected genes.
- In order to only select stable genes I used the stability selection procedure (Meinshausen and Bühlmann 2010). Does one need confidence intervals in this procedure or only in the basic LASSO?
- Would it also make sense to use some LASSO generalization (like group LASSO or newer ideas) to look for relevant networks/groups of genes instead of single genes? Or could one look for associated genes with the selected genes from LASSO, in order for the results to be more interpretable (e.g. clustering by correlation, nodewise regression, group LASSO with groups based on correlation...)? Can this be done on the same data-set or are new measurements needed?
- Can the residuals of the LASSO model be analysed? Or does one construct an ordinary regression with the selected variables and look at that model? Or what is the procedure here?
- Which other approach would you suggest?