Weighted step-down confidence procedures with applications to gene expression data

It is critical to incorporate additional information of parameters into the simultaneous estimation process. In this paper, we propose a new confidence method that utilizes the information on parameter priority and keeps the elegance and simplicity of Holm's weighted testing procedure. The new method is grounded on the method of random partitions, in conjunction with probability inequalities, to ensure the control of the simultaneous confidence level. Simulation studies show significant power improvements for appropriately assigned weights. The new confidence method casts new lights on differential gene expression among mutant genes that are associated with BRCA1 and BRCA2 proteins in the DNA repair process.