On the relation between the true and sample correlations under Bayesian modelling of gene expression datasets

The prediction of cancer prognosis and metastatic potential immediately after the initial diagnoses is a major challenge in current clinical research. The relevance of such a signature is clear, as it will free many patients from the agony and toxic side-effects associated with the adjuvant chemotherapy automatically and sometimes carelessly subscribed to them. Motivated by this issue, several previous works presented a Bayesian model which led to the following conclusion: thousands of samples are needed to generate a robust gene list for predicting outcome. This conclusion is based on existence of some statistical assumptions including asymptotic independence of sample correlations. The current work makes two main contributions: (1) It shows that while the assumptions of the Bayesian model discussed by previous papers seem to be non-restrictive, they are quite strong. To demonstrate this point, it is shown that some standard sparse and Gaussian models are not included in the set of models which are mathematically consistent with these assumptions. (2) It is shown that the empirical Bayes methodology which was applied in order to test the relevant assumptions does not detect severe violations and consequently an overestimation of the required sample size might be incurred. Finally, we suggest that under some regularity conditions it is possible that the current theoretical results can be used for development of a new method to test the asymptotic independence assumption.