TESTING SIGNIFICANCE OF FEATURES BY LASSOED PRINCIPAL COMPONENTS

Overview

Journal Ann Appl Stat

Date 2009 Sep 17

PMID 19756232

Citations 8

Authors

Daniela M Witten

Robert Tibshirani

Affiliations

Soon will be listed here.

Abstract

We consider the problem of testing the significance of features in high-dimensional settings. In particular, we test for differentially-expressed genes in a microarray experiment. We wish to identify genes that are associated with some type of outcome, such as survival time or cancer type. We propose a new procedure, called Lassoed Principal Components (LPC), that builds upon existing methods and can provide a sizable improvement. For instance, in the case of two-class data, a standard (albeit simple) approach might be to compute a two-sample t-statistic for each gene. The LPC method involves projecting these conventional gene scores onto the eigenvectors of the gene expression data covariance matrix and then applying an L(1) penalty in order to de-noise the resulting projections. We present a theoretical framework under which LPC is the logical choice for identifying significant genes, and we show that LPC can provide a marked reduction in false discovery rates over the conventional methods on both real and simulated data. Moreover, this flexible procedure can be applied to a variety of types of data and can be used to improve many existing methods for the identification of significant features.

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References

Sjoblom T, Jones S, Wood L, Parsons D, Lin J, Barber T . The consensus coding sequences of human breast and colorectal cancers. Science. 2006; 314(5797):268-74. DOI: 10.1126/science.1133427. View

Carvalho C, Chang J, Lucas J, Nevins J, Wang Q, West M . High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics. J Am Stat Assoc. 2011; 103(484):1438-1456. PMC: 3017385. DOI: 10.1198/016214508000000869. View

Allison D, Cui X, Page G, Sabripour M . Microarray data analysis: from disarray to consolidation and consensus. Nat Rev Genet. 2005; 7(1):55-65. DOI: 10.1038/nrg1749. View

Beer D, Kardia S, Huang C, Giordano T, Levin A, Misek D . Gene-expression profiles predict survival of patients with lung adenocarcinoma. Nat Med. 2002; 8(8):816-24. DOI: 10.1038/nm733. View

Bair E, Tibshirani R . Semi-supervised methods to predict patient survival from gene expression data. PLoS Biol. 2004; 2(4):E108. PMC: 387275. DOI: 10.1371/journal.pbio.0020108. View

Smyth G . Linear models and empirical bayes methods for assessing differential expression in microarray experiments. Stat Appl Genet Mol Biol. 2006; 3:Article3. DOI: 10.2202/1544-6115.1027. View

Alon U, Barkai N, Notterman D, Gish K, Ybarra S, Mack D . Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc Natl Acad Sci U S A. 1999; 96(12):6745-50. PMC: 21986. DOI: 10.1073/pnas.96.12.6745. View

Witten D, Tibshirani R . TESTING SIGNIFICANCE OF FEATURES BY LASSOED PRINCIPAL COMPONENTS. Ann Appl Stat. 2009; 2(3):986-1012. PMC: 2743444. DOI: 10.1214/08-AOAS182SUPP. View

Rosenwald A, Wright G, Chan W, Connors J, Campo E, Fisher R . The use of molecular profiling to predict survival after chemotherapy for diffuse large-B-cell lymphoma. N Engl J Med. 2002; 346(25):1937-47. DOI: 10.1056/NEJMoa012914. View

10.

Cui X, Hwang J, Qiu J, Blades N, Churchill G . Improved statistical tests for differential gene expression by shrinking variance components estimates. Biostatistics. 2004; 6(1):59-75. DOI: 10.1093/biostatistics/kxh018. View

11.

Alter O, Brown P, Botstein D . Singular value decomposition for genome-wide expression data processing and modeling. Proc Natl Acad Sci U S A. 2000; 97(18):10101-6. PMC: 27718. DOI: 10.1073/pnas.97.18.10101. View

12.

Shen R, Ghosh D, Chinnaiyan A, Meng Z . Eigengene-based linear discriminant model for tumor classification using gene expression microarray data. Bioinformatics. 2006; 22(21):2635-42. DOI: 10.1093/bioinformatics/btl442. View

13.

Zhao H, Ljungberg B, Grankvist K, Rasmuson T, Tibshirani R, Brooks J . Gene expression profiling predicts survival in conventional renal cell carcinoma. PLoS Med. 2005; 3(1):e13. PMC: 1298943. DOI: 10.1371/journal.pmed.0030013. View

14.

Storey J, Dai J, Leek J . The optimal discovery procedure for large-scale significance testing, with applications to comparative microarray experiments. Biostatistics. 2006; 8(2):414-32. DOI: 10.1093/biostatistics/kxl019. View

15.

Tusher V, Tibshirani R, Chu G . Significance analysis of microarrays applied to the ionizing radiation response. Proc Natl Acad Sci U S A. 2001; 98(9):5116-21. PMC: 33173. DOI: 10.1073/pnas.091062498. View

16.

Cui X, Churchill G . Statistical tests for differential expression in cDNA microarray experiments. Genome Biol. 2003; 4(4):210. PMC: 154570. DOI: 10.1186/gb-2003-4-4-210. View

17.

Price A, Patterson N, Plenge R, Weinblatt M, Shadick N, Reich D . Principal components analysis corrects for stratification in genome-wide association studies. Nat Genet. 2006; 38(8):904-9. DOI: 10.1038/ng1847. View

18.

Getz G, Hofling H, Mesirov J, Golub T, Meyerson M, Tibshirani R . Comment on "The consensus coding sequences of human breast and colorectal cancers". Science. 2007; 317(5844):1500. DOI: 10.1126/science.1138764. View

19.

Leek J, Storey J . Capturing heterogeneity in gene expression studies by surrogate variable analysis. PLoS Genet. 2007; 3(9):1724-35. PMC: 1994707. DOI: 10.1371/journal.pgen.0030161. View