On Permutation Procedures for Strong Control in Multiple Testing with Gene Expression Data.

We consider two popular, permutation-based, step-down procedures of p-values adjustment in multiple testing problems known as min P and max T and intended for strong control of the family-wise error rate, under the so-called subset pivotality property (SPP). We examine key but subtle issues involved in ascertaining validity of these methods, and also introduce a new, slightly narrower notion of strong control which ensures proper bounds on the family-wise error rate in min P and max T without SPP.