I am working with RNA-seq data from the Cancer Genome Atlas TCGA and I have been reading about how people have compared gene expression levels measured by RNA-seq. Many of the papers I have read talk about "differential expression" for comparing each gene's expression levels in the Experimental and Control conditions.
In TCGA data, I typically have a patient cohort who have had the mRNA in their tumors sequenced just once so there is no Experimental-vs-Control dynamic. I am interested in finding which patients' tumors show gene-expression that is significantly higher than the rest of the cohort but I have not had any luck finding literature describing this kind of comparison. I'm thinking maybe I can apply existing differential expression techniques to my situation but that seems cumbersome and not-necessarily appropriate so thought I'd ask the community here if there's a better way of finding which members of a cohort are outliers for specific genes.
Also: all of my RNA-seq data has already been RPKM normalized for me. I have been advised that using RSEM instead would be better for comparing gene expression across multiple samples but, for logistic reasons, I'm probably stuck with my RPKM-normalized expression levels.
Fundamentally, I'm looking for the best way to compare gene expression across samples to determine which samples have outlying high/low gene expression. Intuitively, I figure I could just compute median z-scores for each gene's expression levels within my cohort and consider anyone with a |z-score| greater than 2 to be an "outlier" but I haven't found any literature to support this kind of approach either.
Any suggestions, papers, or advice will be greatly appreciated.