Permutation-based true discovery guarantee by sum tests

• 成果类型: Article
• 署名作者: Vesely, Anna; Finos, Livio; Goeman, Jelle J.
• 署名单位: University of Bremen; Leibniz Association; Leibniz Institute for Prevention Research & Epidemiology (BIPS); University of Padua; Leiden University - Excl LUMC; Leiden University; Leiden University Medical Center (LUMC)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad019
• 发表日期: 2023
• 页码: 664-683
• 关键词: combining p-values; truncated product; multiple tests; association; combination; confidence; inference; sample; rare

摘要

Sum-based global tests are highly popular in multiple hypothesis testing. In this paper, we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDPs), simultaneously over all subsets of hypotheses. These simultaneous inferences come for free, i.e., without any adjustment of the alpha-level, whenever a global test is used. Our method allows for an exploratory approach, as simultaneity ensures control of the TDP even when the subset of interest is selected post hoc. It adapts to the unknown joint distribution of the data through permutation testing. Any sum test may be employed, depending on the desired power properties. We present an iterative shortcut for the closed testing procedure, based on the branch and bound algorithm, which converges to the full closed testing results, often after few iterations; even if it is stopped early, it controls the TDP. We compare the properties of different choices for the sum test through simulations, then we illustrate the feasibility of the method for high-dimensional data on brain imaging and genomics data.