I would like to know how can we find the correlation between miRNA and gene expression data from TCGA. The data available in TCGA for miRNA and gene are in two different units like its RPKM for the gene and reads per million for miRNA.
You can use Spearman's correlation, its a non-parametric measure of rank correlation. You should be able to get around the problem of different units. Another approach would be to use linear models to test associations instead of using correlations.
Hope that helps.