title: A decision-theory approach to interpretable set analysis for high-dimensional data.
abstract: A key problem in high-dimensional significance analysis is to find pre-defined sets that show enrichment for a statistical signal of interest; the classic example is the enrichment of gene sets for differentially expressed genes. Here, we propose a new decision-theory approach to the analysis of gene sets which focuses on estimating the fraction of non-null variables in a set. We introduce the idea of "atoms," non-overlapping sets based on the original pre-defined set annotations. Our approach focuses on finding the union of atoms that minimizes a weighted average of the number of false discoveries and missed discoveries. We introduce a new false discovery rate for sets, called the atomic false discovery rate (afdr), and prove that the optimal estimator in our decision-theory framework is to threshold the afdr. These results provide a coherent and interpretable framework for the analysis of sets that addresses the key issues of overlapping annotations and difficulty in interpreting p values in both competitive and self-contained tests. We illustrate our method and compare it to a popular existing method using simulated examples, as well as gene-set and brain ROI data analyses.
authors.affiliation: Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, Maryland 20892, U.S.A.
authors.forename: Simina M
authors.initials: SM
authors.lastname: Boca
authors.forename: Héctor Céorrada
authors.initials: HC
authors.lastname: Bravo
authors.forename: Brian
authors.initials: B
authors.lastname: Caffo
authors.forename: Jeffrey T
authors.initials: JT
authors.lastname: Leek
authors.forename: Giovanni
authors.initials: G
authors.lastname: Parmigiani
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001699:Biometry / Q000379:methods*; D001921:Brain / Q000033:anatomy & histology / Q000502:physiology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D003662:Decision Theory; D059907:Functional Neuroimaging / Q000706:statistics & numerical data; D020869:Gene Expression Profiling / Q000706:statistics & numerical data; D023281:Genomics / Q000706:statistics & numerical data; D006801:Humans; D008279:Magnetic Resonance Imaging / Q000706:statistics & numerical data; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis / Q000706:statistics & numerical data
keywords: Atomic false discovery rate; Gene-sets; Hypothesis testing; Set-level inference
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