This post is sort of a follow-up questions from this previous thread: Exploring association between genes by their expression.
Briefly, say I have a list of candidate genes whose expressions showed (1) to be associated with overall survival (OS) (Cox regression), and (2) also associated among themselves (multivariate linear modeling). For example, high levels of gene A AND low levels of gene B AND low levels of gene C are associated with poor prognosis. So, if I am using only these 3 variables and a decent number of patients (e.g. n=200), it is not hard to find those patients with that combination of genes outcome.
However, if for instance I have a list comprising 8 of such candidates, the chances of finding a patient that fits this criterion (now for these 8 hits) is nearly none.
So my question is: is there a way to do some sort of permutation/combinatorial analysis coupled with Cox regression to find the combination of those 8 targets that best associates with OS? Considering that a satisfactory combination of factors is represented say in at least 30% of the patient population.
Would there be any package in R in which one could accomplish that?
Any light shed on this is very much appreciated.