## The Annals of Applied Statistics

### Statistical tests for the intersection of independent lists of genes: Sensitivity, FDR, and type I error control

#### Abstract

Public data repositories have enabled researchers to compare results across multiple genomic studies in order to replicate findings. A common approach is to first rank genes according to an hypothesis of interest within each study. Then, lists of the top-ranked genes within each study are compared across studies. Genes recaptured as highly ranked (usually above some threshold) in multiple studies are considered to be significant. However, this comparison strategy often remains informal, in that type I error and false discovery rate (FDR) are usually uncontrolled. In this paper, we formalize an inferential strategy for this kind of list-intersection discovery test. We show how to compute a $p$-value associated with a “recaptured” set of genes, using a closed-form Poisson approximation to the distribution of the size of the recaptured set. We investigate operating characteristics of the test as a function of the total number of studies considered, the rank threshold within each study, and the number of studies within which a gene must be recaptured to be declared significant. We investigate the trade off between FDR control and expected sensitivity (the expected proportion of true-positive genes identified as significant). We give practical guidance on how to design a bioinformatic list-intersection study with maximal expected sensitivity and prespecified control of type I error (at the set level) and false discovery rate (at the gene level). We show how optimal choice of parameters may depend on particular alternative hypothesis which might hold. We illustrate our methods using prostate cancer gene-expression datasets from the curated Oncomine database, and discuss the effects of dependence between genes on the test.

#### Article information

Source
Ann. Appl. Stat., Volume 6, Number 2 (2012), 521-541.

Dates
First available in Project Euclid: 11 June 2012

https://projecteuclid.org/euclid.aoas/1339419606

Digital Object Identifier
doi:10.1214/11-AOAS510

Mathematical Reviews number (MathSciNet)
MR2976481

Zentralblatt MATH identifier
1243.62135

#### Citation

Natarajan, Loki; Pu, Minya; Messer, Karen. Statistical tests for the intersection of independent lists of genes: Sensitivity, FDR, and type I error control. Ann. Appl. Stat. 6 (2012), no. 2, 521--541. doi:10.1214/11-AOAS510. https://projecteuclid.org/euclid.aoas/1339419606

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#### Supplemental materials

• Supplementary material: Online supplement: Statistical tests for the intersection of independent lists of genes. Simulation studies and proofs are in the online supplement. In Section S1 we show by simulation that the Poisson approximation to the null distribution of the test statistic gives reliable $p$-values under a wide range of parameters, both for the independent case (Section S1.1) and under a range of moderate positive correlation structures (Section S1.2). We confirm that the Poisson approximation computed under assumed independence yields conservative $p$-values under examples of extreme positive correlation, as conjectured in the text (Section 6.1). In Section S2 we derive the alternative distribution of the test statistic for some useful special cases, using combinatorial results Feller (1957).