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Abstract:
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Scientists routinely compare gene expression levels in cases vs. controls to determine genes associated with a disease. Similarly, detecting differences in co-expression among genes can be highly informative; however methods have been limited due to the high dimensional nature of the comparison. Our test is based on the differential matrix, defined as the difference between a pair of relationship matrices such covariance matrices or weighted adjacency matrices. Relationship matrices are used in gene clustering and networks studies. We propose a novel permutation procedure that is applicable to a high dimension setting. The procedure provides exact support recovery of the differential matrix in many situations. Theoretical and numerical results illustrate that our test maintains valid size in finite samples, and is more powerful than other existing methods under many biologically plausible settings. Applying our testing procedure to the largest gene-expression dataset comparing schizophrenia and control brains, we provide a novel list of potential risk genes. We also discuss how this reveals important biological insights into the underlying genetic architecture of Schizophrenia.
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