A step-down method for correcting multiple hypothesis testing in biomedical signal processing

Multiple hypothesis testing in biomedical signal analysis and genomic signal processing has been facing a difficult dilemma regarding the adjustment of significance values. Studies that report unadjusted values may fail to control false positives. On the other hand, classical correction methods may be too conservative while handling high-dimensional variable spaces, yielding a high type II error rate. We present a novel stepwise method for estimating the adjusted p-values in applications that require multiple hypothesis testing. The method increases the statistical power of the results by refuting the assumption of independence among variables, while keeping the probability of false positives low. It is based on the spectral decomposition of the correlation matrix, from which it is possible to obtain valuable information about the dependence levels among the variables of the problem. The method is compared to other relevant stepwise adjustment models such as Holm´s step-down extension of the Bonferroni/Sidak method, the false discovery rate method and resampling. We illustrate the effectiveness of the method in a magnetic resonance imaging study involving progressively larger sets of variables. The results show that the proposed method is able to compute adjusted p-values that are closer to the ones obtained by resampling, at a much lower computational cost.