How to calculate module-trait relationship when trait data is in binary format?
Answer from @m, converted from comment:
Personally I'd build a tree. Whats your question patients or the relationship between RNAseq 'signatures'? Its not the definitive analysis, but its good mining.
Pearson is doable but how many Pearson's? You'll end up with a 2x2 matrix. How will you resolve the matrix clustering? A maximum likelihood phylogeny solution would work here making use of the binary format. There are other approaches.
Spearman correlation would be better than Pearson's you end up with a 2x2 matrix.
Answer from @peter-langfelder, converted from comment:
You can use Pearson correlation, it is equivalent to carrying out an equal-variance t-test for the module eigengene between the two groups specified by the binary variable.