A Decision‐Theory Approach to Interpretable Set Analysis for High‐Dimensional Data. Issue 3 (2nd August 2013)

• Record Type: Journal Article
• Authors: Boca, Simina M.; Bravo, Héctor Céorrada; Caffo, Brian; Leek, Jeffrey T.; Parmigiani, Giovanni
• Is Part Of: Biometrics. Volume 69:Issue 3(2013)
• Page Start: 614
• Page End: 623
• Publication Date: 2013-08-02
• Subjects: Biometry -- Periodicals; 570.15195
• DOI: 10.1111/biom.12060
• Languages: English
• ISSNs: 0006-341X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Summary</title> <sec id="biom12060-sec-0001" sec-type="section"> <p>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 (<italic>afdr</italic>), and prove that the optimal estimator in our decision‐theory framework is to threshold the <italic>afdr</italic>. 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.</p> </sec> </abstract>