A Mixture-Model Approach for Parallel Testing for Unequal Variances

Statistical Applications in Genetics and Molecular Biology

Volumn 11, Issue 1, 2020, Pages

  Bar, Haim Y ^a   Booth, James G ^a   Wells, Martin T ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

EM algorithm; empirical Bayes; false discovery rate; mixture model; shrinkage estimation; simultaneous tests

Indexed keywords

ALGORITHM; ARTICLE; SAMPLE SIZE; ANALYSIS OF VARIANCE; BAYES THEOREM; DNA MICROARRAY; GENE EXPRESSION PROFILING; METHODOLOGY; STATISTICAL MODEL;

ANALYSIS OF VARIANCE; BAYES THEOREM; GENE EXPRESSION PROFILING; MODELS, STATISTICAL; OLIGONUCLEOTIDE ARRAY SEQUENCE ANALYSIS; SAMPLE SIZE;

MLCS; MLOWN;

EID: 84864881889     PISSN: None     EISSN: 15446115     Source Type: Journal    
DOI: 10.2202/1544-6115.1762     Document Type: Article

References (33)

1. Bar, H., J. Booth, E. D. Schifano, and M.T. Wells (2010): "Laplace approximated em microarray analysis: An empirical bayes approach for comparative microarray experiments, " Statistical Science, 25, 388-407.
2. Bar, H. and E. Schifano (2010): Lemma: Laplace approximated EM Microarray Analysis, URL http://CRAN.R-project.org/package=lemma, r package version 1.3-1.
3. Bartlett, M. S. (1937): "Properties of sufficiency and statistical tests, " Proceedings of The Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), 160, 268-282.
4. Benjamini, Y. and Y. Hochberg (1995): "Controlling the false discovery rate-a practical and powerful approach to multiple testing, " Journal of The Royal Statistical Society Series B, 57, 499-517.
5. Boos, D. D. and C. Brownie (1989): "Bootstrap Methods for Testing Homogeneity of Variances, " Technometrics, 31, 69-82, URL http://dx.doi.org/10.2307/1270366.
6. Boos, D. D. and C. Brownie (2004): "Comparing variances and other measures of dispersion, " Statistical Science, 19, 571-578.
7. Box, G. E. P. (1953): "Non-normality and tests on variances, " Biometrika, 40, 318-335.
8. Brown, M. and A. Forsythe (1974): "Robust tests for equalit y of variances, " Journal of the American Statistical Association, 69, 364-367.
9. Cai, L., N. Friedman, and X. S. Xie (2006): "Stochastic protein expression in individual cells at the single molecule level, " Nature, 440, 358-362, URL http://dx.doi.org/10.1038/nature04599.
10. Callow, M. J., S. Dudoit, E. L. Gong, T. P. Speed, and E. M. Rubin (2000): "Microarray expression profiling identifies genes with altered expression in HDLdeficient mice." Genome Research, 10, 2022-2029.
11. Colman-Lerner, A., A. Gordon, E. Serra, T. Chin, O. Resnekov, D. Endy, C. Gustavo Pesce, and R. Brent (2005): "Regulated cell-to-cell variation in a cell-fate decision system, " Nature, 437, 699-706, URL http://dx.doi.org/10.1038/nature03998.
12. DeBerardinis, R. J., A. Mancuso, E. Daikhin, I. Nissim, M. Yudkoff, S. Wehrli, and C. B. Thompson (2007): "Beyond aerobic glycolysis: Transformed cells can engage in glutamine metabolism that exceeds the requirement for protein and nucleotide synthesis." Proceedings of the National Academy of Sciences of the United States of America, 104, 19345-19350, URL http://dx.doi.org/10.1073/pnas.0709747104.
13. Efron, B. (2008): "Microarrays, empirical bayes and the two groups model, " Statistical Science, 23, 1-22.
14. Efron, B. and C. Morris (1975): "Data Analysis Using Stein's Estimator and its Generalizations, " Journal of the American Statistical Association, 70, 311-319.
15. Efron, B., B. B. Turnbull, and B. Narasimhan (2008): Locfdr: Computes local false discovery rates, R package version 1.1-6.
16. Eichler, E. E., J. Flint, G. Gibson, A. Kong, S. M. Leal, J. H. Moore, and J. H. Nadeau (2010): "Missing heritability and strategies for finding the underlying causes of complex disease, " Nature Reviews Genetics, 11, 446-450, URL http://dx.doi.org/10.1038/nrg2809.
17. Feinberg, A.P. and R. A. Irizarry (2010): "Stochastic epigenetic variation as a driving force of development, evolutionary adaptation, and disease, " Proceedings of the National Academy of Sciences, 107, 1757-1764, URL http://dx.doi.org/10.1073/pnas.0906183107.
18. Gastwirth, J. LY.., R. Gel, and W. Miao (2010): "The Impact of Levene'sTest of Equality ofVariances on Statistical Theory and Practice, " Statistical Science, 24, 343-360.
19. Hansen, K. D., W. Ti mp, H. C. Bravo, S. Sabunciyan, B. Langmead, O. G. McDonald, B. Wen, H. Wu, Y. Liu, D. Diep, E. Briem, K. Zhang, R. A. Irizarry, and A.P. Feinberg (2011): "Increased methylation variation in epigenetic domains across cancer types, " Nature Genetics, 43, 768-775, URL http://dx.doi.org/10.1038/ng.865.
20. Ho, J.W., M. Stefani, C. G. dos Remedios, and M. A. Charleston (2008): "Differential variability analysis of gene expression and its application to human diseases, " Bioinformatics, 24, 1390-1398, URL http://dl.acm.org/citation.cfm?id=1388083.1388131.
21. Hwang, J.T. G. and P. Liu (2010): "Optimal tests shrinking both means and variances applicable to microarray data analysis ." Statistical Applications in Genetics and Molecular Biology, 9, Article36.
22. James, W. and C. Stein (1961): "Estimation with quadratic loss, " Proceedings of theFourth Berkeley Symposium on Mathematical Statistics and Probability, 361-379.
23. Levene, H. (1960): "Robust tests for equality of variances, " In Contributions to Probability and Statistics, 278-292.
24. Levsky, J. M., S. M. Shenoy, R. C. Pezo, and R. H. Singer (2002): "Single-cell gene expression profiling." Science (NewYork, N.Y.), 297, 836-840, URL http://dx.doi.org/10.1126/science.1072241.
25. Manolio, T. A., F. S. Collins, N. J. Cox, D. B. Goldstein, L. A. Hindorff, D. J. Hunter, M. I. McCarthy, E. M. Ramos, L. R. Cardon, A. Chakravarti, J. H. Cho, A. E. Guttmacher, A. Kong, L. Kruglyak, E. Mardis, C. N. Rotimi, M. Slatkin, D.Valle, A. S. Whittemore, M. Boehnke, A. G. Clark, E. E. Eichler, G. Gibson, J. L. Haines, T. F. C. Mackay, S. A. McCarroll, andP. M. Vi sscher (2009): "Finding the missing heritability of complex diseases, " Nature, 461, 747-753, URL http://dx.doi.org/10.1038/nature08494.
26. Mar, J. C., N. A. Matigian, A. Mackay-Sim, G. D. Mellick, C. M. Sue, P. A. Silburn, J. J. McGrath, J. Quackenbush, and C. A. Wells (2011): "Variance of Gene Expression Identifies Altered Network Constraints in Neurological Disease, " PLoS Genetics, 7.
27. Mar, J. C., R. Rubio, and J. Quackenbush (2006): "Inferring steady state single-cell gene expression distributions from analysis of mesoscopic samples, " Genome Biology, 7, R119+, URL http://dx.doi.org/10.1186/gb-2006-7-12-r119.
28. Marko, N. F., J. Quackenbush, and R. J. Weil (2011): "Why is there a lack of consensus on molecular subgroups of glioblastoma? understanding the nature of biological and statistical variability in glioblastoma expression data, " PLoS ONE, 6.
29. Ozbudak, E. M., M. Thattai, I. Kurtser, A. D. Grossman, and A. van Oudenaarden (2002): "Regulation of noise in the expression of a single gene." Nature Genetics, 31, 69-73, URL http://dx.doi.org/10.1038/ng869.
30. Ravasi, T., C. Wells, A. Forest, D. Underhill, B. Wainwright, A. Aderem, S. Grimmond, and D. Hume (2002): "Generation of diversity in the innate immune system: Macrophage heterogeneity arises from gene-autonomous transcriptional probability of individual inducible genes." Journal of Immunology, 168, 44-50.
31. Smyth, G. K. (2004): "Linear Models for Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments, " Statistical Applications in Genetics and Molecular Biology, 3, article 2.
32. Smyth, G. K. (2005): Limma: Linear Models for Microarray Data, New York: Springer, 397-420.
33. Soliman, F., C. E. Glatt, K. G. Bath, L. Levita, R. M. Jones, S. S. Pattwell, D. Jing, N. Tottenham, D. Amso, L. H. Somerville, H. U. Voss, G. Glover, D. J. Ballon, C. Liston, T. Teslovich, T. V. Kempen, F. S. Lee, and B. J. Casey (2010): "A genetic variant bdnf polymorphism alters extinction learning in both mouse and human, " Science, 327, 863-866.