### 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.

Original language | English (US) |
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Pages (from-to) | 614-623 |

Number of pages | 10 |

Journal | Biometrics |

Volume | 69 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2013 |

### Keywords

- Atomic false discovery rate
- Gene-sets
- Hypothesis testing
- Set-level inference

### ASJC Scopus subject areas

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

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## Cite this

*Biometrics*,

*69*(3), 614-623. https://doi.org/10.1111/biom.12060