Thousands of samples are needed to generate a robust gene list for predicting outcome in cancer

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Abstract
Predicting at the time of discovery the prognosis and metastatic potential of cancer is a major challenge in current clinical research. Numerous recent studies searched for gene expression signatures that outperform traditionally used clinical parameters in outcome prediction. Finding such a signature will free many patients of the suffering and toxicity associated with adjuvant chemotherapy given to them under current protocols, even though they do not need such treatment. A reliable set of predictive genes also will contribute to a better understanding of the biological mechanism of metastasis. Several groups have published lists of predictive genes and reported good predictive performance based on them. However, the gene lists obtained for the same clinical types of patients by different groups differed widely and had only very few genes in common. This lack of agreement raised doubts about the reliability and robustness of the reported predictive gene lists, and the main source of the problem was shown to be the small number of samples that were used to generate the gene lists. Here, we introduce a previously undescribed mathematical method, probably approximately correct (PAC) sorting, for evaluating the robustness of such lists. We calculate for several published data sets the number of samples that are needed to achieve any desired level of reproducibility. For example, to achieve a typical overlap of 50% between two predictive lists of genes, breast cancer studies would need the expression profiles of several thousand early discovery patients.