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An active area in cancer biomarker research is the development of statistical methods to identify expression signatures reflecting the heterogeneity of cancer across affected individuals. Tomlins et al.  observed heterogeneous patterns of oncogene activation within several cancer types, and introduced a statistical method called Cancer Outlier Profile Analysis (COPA) to identify "cancer outlier genes". Several related statistical approaches have since been developed, but the operating characteristics of these procedures (e.g. power, false positive rate), have not yet been fully characterized, especially in a proteomics setting. Here, we use simulation to identify the degree to which an outlier pattern of differential expression must hold in order for outlier-based approaches to be more effective than mean-based approaches. We also propose a diagnostic procedure that characterizes the potentially unequal levels of differential expression in the tails and in the center of a distribution of expression values. We find that for sample sizes and effect sizes typical of proteomics studies, the outlier pattern must be strong in order for outlier-based analysis to provide a meaningful benefit. This is corroborated by analysis of proteomics data from a melanoma study, in which the differential expression is most often present throughout the distribution, rather than being concentrated in the tails, albeit with a few proteins showing expression patterns consistent with outlier expression.