I have a gene expression data from 1065 different cell lines, let's say "BRAF" gene. BRAF gene expression levels are ordered. Most TP53 mutated cell lines are high BRAF expression (see the figure below). So what kind of statistical method should I use to test the enrichment or overrepresent for TP53 status (WT vs Mutant) on BRAF expression?
Status of TP53 mutation and BRAF expression are two independent variables. You can compare the mean of BRAF expression in the group of cell lines carrying wild-type TP53 with TP53-mutant group. The simplest approach is independent (unpaired) Student t- test (parametric) or Mann-Whitney test (non-parametric).
There are various assumptions for parametric tests, for example the continuous variable (BRAF expression in your case) should be normally distributed. You can check it for example with Shapiro-Wilk test of normality.
See: https://statistics.berkeley.edu/computing/r-t-tests and http://www.r-tutor.com/elementary-statistics/non-parametric-methods/mann-whitney-wilcoxon-test
Edit: If your expression data come from high-throughput sequencing experiment (like RNA-Seq) I would recommend to follow the well-established protocols for this kind of analysis (for example R package DESeq2 or edgeR).
How about a gene set enrichment analysis (1)? It's designed for this situation and is the conventional test. It uses a kolmogorov-smirnov-like statistic to measure how "bunched" your annotation terms are (mutated terms vs wild type terms) in the sorted list.
The test is simple so you can code your own. Otherwise online tools exist, e.g. David as well as R packages.
1 Subramanian, Aravind, et al. "Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles." Proceedings of the National Academy of Sciences 102.43 (2005): 15545-15550.
