On the Structure of Multiple Testing Procedures
The field of "multiple hypothesis testing" has traditionally focused on defining and estimating various error measures based on the p-values individually obtained from each test. In this paper we discuss common structure present in typical multiple testing procedures. We introduce "single thresholding procedures" (STPs), a large class of multiple testing procedures encompassing the majority of those used in practice. We propose new concepts of significance for STPs, eliminating the intermediate step of calculating p-values for each test individually. With these developments, it is straightforward to consider the optimality of STPs and show that many complicated procedures actually reduce to a STP. As a specific example, we show that single-stage multiple hypothesis testing procedures are optimal over their corresponding multiple-stage procedures, an open question of much interest in the genomics field.
Biostatistics | Multivariate Analysis | Statistical Methodology | Statistical Theory
Leek, Jeffrey and Storey, John D., "On the Structure of Multiple Testing Procedures" (September 2006). UW Biostatistics Working Paper Series. Working Paper 294.