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Statistical challenges in functional genomics. (With comments and a rejoinder). (English) Zbl 1048.62108
Summary: On February 12, 2001, the Human Genome Project announced the completion of a draft physical map of the human genome – the genetic blueprint for a human being. Now the challenge is to annotate this map by understanding the functions of genes and their interplay with proteins and the environment to create complex, dynamic living systems. This is the goal of functional genomics. Recent technological advances enable biomedical investigators to observe the genome of entire organisms in action by simultaneously measuring the level of activation of thousands of genes under the same experimental conditions. This technology, known as microarrays, today provides unparalleled discovery opportunities and is reshaping biomedical sciences. One of the main aspects of this revolution is the introduction of computationally intensive data analysis methods in biomedical research. This article reviews the foundations of this technology and describes the statistical challenges posed by the analysis of microarray data.

62P10 Applications of statistics to biology and medical sciences; meta analysis
92C40 Biochemistry, molecular biology
92D10 Genetics and epigenetics
sma; AutoClass
Full Text: DOI
[1] Affymetrix, Inc. (2002). Statistical Algorithms Description Document. Available from http://www.affymetrix.com/ support/technical/whitepapers/sadd_whitepaper.pdf.
[2] Alizadeh, A. A., Eisen, M. B., Davis, R. E., Ma, C., Lossos, I. S., Rosenwald, A., Boldrick, J. C., Sabet, H., Tran, T., Yu, X., Powell, J. I., Yang, L., Marti, G. E., Moore, T., Hudson, Jr., J., Lu, L., Lewis, D. B., Tibshirani, R., Sherlock, G., Chan, W. C., Greiner, T. C., Weisenburger, D. D., Armitage, J. O., Warnke, R., Levy, R., Wilson, W., Grever, M. R., Byrd, J. C., Botstein, D., Brown, P. O. and Staudt, L. M. (2000). Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature 403 503–511.
[3] Alter, O., Brown, P. O. and Botstein, D. (2000). Singular value decomposition for genome-wide expression data processing and modeling. Proc. Natl. Acad. Sci. U.S.A. 97 10101–10106.
[4] Alwine, J. C., Kemp, D. J. and Stark, G. R. (1977). Method for detection of specific RNAs in agarose gels by transfer to diazobenzyloxymethyl-paper and hybridization with DNA probes. Proc. Natl. Acad. Sci. U.S.A. 74 5350–5354.
[5] Baldi, P. and Long, A. D. (2001). A Bayesian framework for the analysis of microarray expression data: Regularized \(t\)-test and statistical inferences of gene changes. Bioinformatics 17 509–519. · Zbl 0992.92024
[6] Banfield, J. D. and Raftery, A. E. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics 49 803–821. · Zbl 0794.62034
[7] Bhattacharjee, A., Richards, W. G., Staunton, J., Li, C., Monti, S., Vasa, P., Ladd, C., Beheshti, J., Bueno, R., Gillette, M., Loda, M., Weber, G., Mark, E. J., Lander, E. S., Wong, W., Johnson, B. E., Golub, T. R., Sugarbaker, D. J. and Meyerson, M. (2001). Classification of human lung carcinomas by mRNA expression profiling reveals distinct adenocarcinoma subclasses. Proc. Natl. Acad. Sci. U.S.A. 98 13790–13795.
[8] Bittner, M., Meltze, P., Chen, Y., Jiang, Y., Seftor, E., Hendrix, M., Radmacher, M., Simon, R., Yakhini, Z., Ben-Dor, A., Sampas, N., Dougherty, E., Wang, E., Marincola, F., Gooden, C., Lueders, J., Glatfelter, A., Pollock, P., Carpten, J., Gillanders, E., Leja, D., Dietrich, K., Beaudry, C., Berens, M., Alberts, D., Sondak, V., Hayward, N. and Trent, J. (2000). Molecular classification of cutaneous malignant melanoma by gene expression profiling. Nature 406 536–540.
[9] Bowtell, D. D. L. (1999). Options available—from start to finish—for obtaining expression data by microarray. Nature Genetics 21 25–32.
[10] Brown, M. P. S., Grundy, W. N., Lin, D., Cristianini, N., Sugnet, C. W., Furey, T. S., Ares, Jr., M. and Haussler, D. (2000). Knowledge-based analysis of microarray gene expression data by using support vector machines. Proc. Natl. Acad. Sci. U.S.A. 97 262–267.
[11] Brown, P. O. and Botstein, D. (1999). Exploring the new world of the genome with DNA microarrays. Nature Genetics 21 33–37.
[12] Butte, A. J., Tamayo, P., Slonim, D., Golub, T. R. and Kohane, I. S. (2000). Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks. Proc. Natl. Acad. Sci. U.S.A. 97 12182–12186.
[13] Causton, H. C., Ren, B., Koh, S. S., Harbison, C. T., Kanin, E., Jennings, E. G., Lee, T. I., True, H. L., Lander, E. S. and Young, R. A. (2001). Remodeling of yeast genome expression in response to environmental changes. Molecular Biology of the Cell 12 323–337.
[14] Cheeseman, P. and Stutz, J. (1996). Bayesian classification (AutoClass): Theory and results. In Advances in Knowledge Discovery and Data Mining (V. M. Fayyad et al., eds.) 153–180. MIT Press, Cambridge, MA. · Zbl 0925.62119
[15] Chen, Y., Dougherty, E. R. and Bittner, M. L. (1997). Ratio-based decisions and the quantitative analysis of cDNA microarray images. Journal of Biomedical Optics 2 364–374.
[16] Cheng, Y. and Church, G. M. (2000). Biclustering of expresssion data. In Proc. 8th International Conference on Intelligent Systems for Molecular Biology 93–103. AAAI Press, Menlo Park, CA.
[17] Churchill, G. A. and Oliver, B. (2001). Sex, flies and microarrays. Nature Genetics 29 355–356.
[18] Clark, E. A., Golub, T. R., Lander, E. S. and Hynes, R. O. (2000). Genomic analysis of metastasis reveals an essential role for RhoC. Nature 406 532–535.
[19] Coller, H. A., Grandori, C., Tamayo, P., Colbert, T., Lander, E. S., Eisenman, R. N. and Golub, T. R. (2000). Expression analysis with oligonucleotide microarrays reveals that MYC regulates genes involved in growth, cell cycle, signaling, and adhesion. Proc. Natl. Acad. Sci. U.S.A. 97 3260–3265.
[20] Cowell, R. G., Dawid, A. P., Lauritzen, S. L. and Spiegelhalter, D. J. (1999). Probabilistic Networks and Expert Systems . Springer, New York. · Zbl 0937.68121
[21] Cox, D. R. and Reid, N. (2000). The Theory of the Design of Experiments . CRC Press, Boca Raton, FL. · Zbl 1009.62061
[22] Crick, F. H. C. (1970). Central dogma of molecular biology. Nature 227 561–563.
[23] Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1–38. · Zbl 0364.62022
[24] DeRisi, J. L., Iyer, V. R. and Brown, P. O. (1997). Exploring the metabolic and genetic control of gene expression on a genomic scale. Science 278 680–686.
[25] Dudoit, S., Fridlyand, J. and Speed, T. P. (2002). Comparison of discrimination methods for the classification of tumors using gene expression data. J. Amer. Statist. Assoc. 97 77–87. · Zbl 1073.62576
[26] Dudoit, S., Yang, Y. H., Callow, M. J. and Speed, T. P. (2002). Statistical methods for identifying differentially expressed genes in replicated cDNA microarrays experiments. Statist. Sinica 12 111–139. · Zbl 1004.62088
[27] Duggan, D. J., Bittner, M., Chen, Y., Meltzer, P. and Trent, J. M. (1999). Expression profiling using cDNA microarrays. Nature Genetics 21 10–14.
[28] Efron, B., Storey, J. D. and Tibshirani, R. (2001). Microarrays, empirical Bayes methods, and false discovery rate. Technical report, Dept. Statistics, Stanford Univ. · Zbl 1073.62511
[29] Efron, B., Tibshirani, R., Storey, J. D. and Tusher, V. (2001). Empirical Bayes analysis of a microarray experiment. J. Amer. Statist. Assoc. 96 1151–1160. · Zbl 1073.62511
[30] Eisen, M. B., Spellman, P. T., Brown, P. O. and Botstein, D. (1998). Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. U.S.A. 95 14863–14868.
[31] Ekins, R. and Chu, F. W. (1999). Microarrays: Their origins and applications. Trends in Biotechnology 17 217–218.
[32] Fraley, C. and Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. J. Amer. Statist. Assoc. 97 611–631. · Zbl 1073.62545
[33] Friedman, N., Linial, M., Nachman, I. and Pe’er, D. (2000). Using Bayesian networks to analyze expression data. Journal of Computational Biology 7 601–620.
[34] Getz, G., Levine, E. and Domany, E. (2000). Coupled two-way clustering analysis of gene microarray data. Proc. Natl. Acad. Sci. U.S.A. 97 12079–12084.
[35] Gilovich, T., Vallone, R. and Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology 17 295–314.
[36] Glynne, R., Akkaraju, S., Healy, J. I., Rayner, J., Goodnow, C. C. and Mack, D. H. (2000). How self-tolerance and the immunosuppressive drug FK506 prevent B-cell mitogenesis. Nature 403 672–676.
[37] Golub, T. R., Slonim, D. K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J. P., Coller, H., Loh, M., Downing, J. R., Caligiuri, M. A., Bloomfield, C. D. and Lander, E. S. (1999). Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring. Science 286 531–537. · Zbl 1047.65504
[38] Griffiths, A. J. F., Miller, J. H., Suzuki, D. T., Lewontin, R. C. and Gelbart, W. M. (2000). An Introduction to Genetic Analysis , 7th ed. Freeman, New York (Available from http://www.ncbi.nlm.nih.gov/books/.)
[39] Hand, D. J. (1997). Construction and Assessment of Classification Rules . Wiley, New York. · Zbl 0997.62500
[40] Hastie, T., Tibshirani, R., Eisen, M. B., Alizadeh, A. A., Levy, R., Staudt, L., Chan, W. C., Botstein, D. and Brown, P. O. (2000). “Gene shaving” as a method for identifying distinct sets of genes with similar expression patterns. Genome Biology 1 (2) research0003.1-3.21.
[41] Holstege, F. C. P., Jennings, E. G., Wyrick, J. J., Lee, T. I., Hengartner, C. J., Green, M. R., Golub, T. R., Lander, E. S. and Young, R. A. (1998). Dissecting the regulatory circuitry of a eukaryotic genome. Cell 95 717–728.
[42] Holter, N. S., Maritan, A., Cieplak, M., Fedoroff, N. V. and Banavar, J. (2001). Dynamic modeling of gene expression data. Proc. Natl. Acad. Sci. U.S.A. 98 1693–1698.
[43] Hoyle, D. C., Rattray, M., Jupp, R. and Brass, A. (2002). Making sense of microarray data distributions. Bioinformatics 18 576–584. · Zbl 1255.68136
[44] Ibrahim, J. G., Chen, M. H. and Gray, R. J. (2002). Bayesian models for gene expression with DNA microarray data. J. Amer. Statist. Assoc. 97 88–99. · Zbl 1073.62578
[45] International Human Genome Sequencing Consortium (2001). Initial sequencing and analysis of the human genome. Nature 409 860–921.
[46] Irizarry, R. A., Parmigiani, G., Guo, M., Dracheva, T. and Jen, J. (2001). A statistical analysis of radiolabeled gene expression data. In Proc. 33rd Symposium on the Interface: Computing Science and Statistics . Interface Foundation of North America, Fairfax Station, VA.
[47] Iyer, V. R., Eisen, M. B., Ross, D. T., Schuler, G., Moore, T., Lee, J. C. F., Trent, J. M., Staudt, L. M., Hudson, Jr., J., Boguski, M. S., Lashkari, D., Shalon, D., Botstein, D. and Brown, P. O. (1999). The transcriptional program in the response of human fibroblasts to serum. Science 283 83–87.
[48] Jackson-Grusby, L., Beard, C., Possemato, R., Tudor, M., Fambrough, D., Csankovszki, G., Dausman, J., Lee, P., Wilson, C., Lander, E. S. and Jaenisch, R. (2001). Loss of genomic methylation causes p53-dependent apoptosis and epigenetic deregulation. Nature Genetics 27 31–39.
[49] Jacob, F. and Monod, J. (1961). Genetic regulatory mechanisms in the synthesis of proteins. Journal of Molecular Biology 3 318–356.
[50] Jin, W., Riley, R. M., Wolfinger, R. D., White, K. P., Passador-Gurgel, G. and Gibson, G. (2001). The contributions of sex, genotype and age to transcriptional variance in Drosophila melanogaster . Nature Genetics 29 389–395.
[51] Kane, M. D., Jatkoe, T. A., Stumpf, C. R., Lu, J., Thomas, J. D. and Madore, S. J. (2000). Assessment of the sensitivity and specificity of oligonucleotide (50 mer) microarrays. Nucleic Acids Research 28 4552–4557.
[52] Keller, A. D., Schummer, M., Hood, L. and Ruzzo, W. L. (2000). Bayesian classification of DNA array expression data. Technical Report UW-CSE-2000-08-01, Dept. Computer Science and Engineering, Univ. Washington, Seattle.
[53] Kerr, M. K. and Churchill, G. A. (2001a). Bootstrapping cluster analysis: Assessing the reliability of conclusions from microarray experiments. Proc. Natl. Acad. Sci. U.S.A. 98 8961–8965. · Zbl 1047.62110
[54] Kerr, M. K. and Churchill, G. A. (2001b). Experimental design for gene expression microarrays. Biostatistics 2 183–201. · Zbl 1097.62562
[55] Kerr, K. M. and Churchill, G. A. (2001c). Statistical design and the analysis of gene expression microarray data. Genetical Research 77 123–128.
[56] Kohane, I. S., Kho, A. T. and Butte, A. J. (2002). Microarrays for an Integrative Genomics . MIT Press, Cambridge, MA.
[57] Kohonen, T. (1997). Self Organizing Maps , 2nd ed. Springer, Berlin. · Zbl 0866.68085
[58] Lakhani, S. R. and Ashworth, A. (2001). Microarray and histopathological analysis of tumours: The future and the past? Nature Reviews Cancer 1 151–157.
[59] Lander, E. S. (1999). Array of hope. Nature Genetics 21 3–4.
[60] Lazzeroni, L. and Owen, A. B. (2002). Plaid models for gene expression data. Statist. Sinica 12 61–86. · Zbl 1004.62084
[61] Lee, C. K., Weindruch, R. and Prolla, T. A. (2000). Gene-expression profile of the ageing brain in mice. Nature Genetics 25 294–297.
[62] Lee, M. T., Kuo, F. C., Whitmore, G. A. and Sklar, J. (2000). Importance of replication in microarray gene expression studies: Statistical methods and evidence from repetitive cDNA hybridizations. Proc. Natl. Acad. Sci. U.S.A. 18 9834–9839. · Zbl 0955.92016
[63] Lennon, G. G. and Lehrach, H. (1991). Hybridization analyses of arrayed cDNA libraries. Trends in Genetics 7 314–317.
[64] Lipshutz, R. J., Fodor, S. P. A., Gingeras, T. R. and Lockhart, D. J. (1999). High density synthetic oligonucleotide arrays. Nature Genetics 21 20–24.
[65] Lockhart, D. J. and Barlow, C. (2001). Expressing what’s on your mind: DNA arrays and the brain. Nature Reviews Neuroscience 2 63–68.
[66] Lockhart, D. J., Dong, H., Byrne, M. C., Follettie, M. T., Gallo, M. V., Chee, M. S., Mittmann, M., Wang, C., Kobayashi, M., Horton, H. and Brown, E. L. (1996). Expression monitoring by hybridization to high-density oligonucleotide arrays. Nature Biotechnology 14 1675–1680.
[67] Lockhart, D. J. and Winzeler, E. A. (2000). Genomics, gene expression and DNA arrays. Nature 405 827–836.
[68] Lönnstedt, I. and Speed, T. P. (2002). Replicated microarray data. Statist. Sinica 12 31–46. · Zbl 1004.62086
[69] Ly, D. H., Lockhart, D. J., Lerner, R. A. and Schultz, P. G. (2000). Mitotic misregulation and human aging. Science 287 2486–2492.
[70] McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models , 2nd ed. Chapman and Hall, London. · Zbl 0588.62104
[71] Mitchell, T. (1997). Machine Learning . McGraw–Hill, New York. · Zbl 0913.68167
[72] Nadon, R. and Shoemaker, J. (2002). Statistical issues with microarrays: processing and analysis. Trends in Genetics 18 265–271.
[73] National Human Genome Research Institute. (2001). Talking glossary of genetic terms. Available from http://www.genome.gov/glossary.cfm.
[74] Newton, M. A., Kendziorski, C. M., Richmond, C. S., Blattner, F. R. and Tsui, K. W. (2001). On differential variability of expression ratios: Improving statistical inference about gene expression changes from microarray data. Journal of Computational Biology 8 37–52.
[75] Nguyen, D. V. and Rocke, D. M. (2002). Tumor classification by partial least squares using microarray gene expression data. Bioinformatics 18 39–50.
[76] Olshen, A. B. and Jain, A. N. (2002). Deriving quantitative conclusions from microarray expression data. Bioinformatics 18 961–970.
[77] Pan, W., Lin, J. and Le, C. T. (2001). A mixture model approach to detect differentially expressed genes with microarray data. Technical report, Division of Biostatistics, School of Public Health, Univ. Minnesota.
[78] Pan, W., Lin, J. and Le, C. T. (2002). How many replicates of arrays are required to detect gene expression changes in microarrays experiments? A mixture model approach. Genome Biology 3 (5) research 0022.1-22.10.
[79] Park, P. J., Tian, L. and Kohane, I. S. (2002). Linking gene expression data with patient survival times using partial least squares. Bioinformatics 18 S120–S127.
[80] Phimister, B. (1999). Going global. Nature Genetics 21 1.
[81] Pilpel, Y., Sudarsanam, P. and Church, G. M. (2001). Identifying regulatory networks by combinatorial analysis of promoter elements. Nature Genetics 29 153–159.
[82] Quackenbush, J. (2001). Computational analysis of microarray data. Nature Reviews Genetics 2 418–427.
[83] Ramoni, M., Sebastiani, P. and Kohane, I. S. (2002). Cluster analysis of gene expression dynamics. Proc. Natl. Acad. Sci. U.S.A. 99 9121–9126. · Zbl 1023.62110
[84] Relogio, A., Schwager, C., Richter, A., Ansorge, W. and Valcarcel, J. (2002). Optimization of oligonucleotide-based DNA microarrays. Nucleic Acids Research 30 (11) e51.
[85] Roberts, C. J., Nelson, B., Marton, M. J., Stoughton, R., Meyer, M. R., Bennett, H. A., He, Y. D., Dai, H., Walker, W. L., Hughes, T. R., Tyers, M., Boone, C. and Friend, S. H. (2000). Signaling and circuitry of multiple MAPK pathways revealed by a matrix of global gene expression profiles. Science 287 873–880.
[86] Rocke, D. M. and Durbin, B. (2001). A model for measurement error for gene expression arrays. Journal of Computational Biology 8 557–569.
[87] Sabatti, C., Karsten, S. L. and Geschwind, D. (2001). Thresholding rules for recovering a sparse signal from microarray experiments. Math. Biosci. 176 17–34. · Zbl 0996.92022
[88] Schadt, E. E., Li, C., Su, C. and Wong, W. H. (2000). Analyzing high-density oligonucleotide gene expression array data. Journal of Cellular Biochemistry 80 192–202.
[89] Schena, M., Shalon, D., Davis, R. W. and Brown, P. O. (1995). Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science 270 467–470.
[90] Schena, M., Shalon, D., Heller, R., Chai, A., Brown, P. O. and Davis, R. W. (1996). Parallel human genome analysis: Microarray-based expression monitoring of 1000 genes. Proc. Natl. Acad. Sci. U.S.A. 93 10614–10619.
[91] Sebastiani, P., Ramoni, M. and Kohane, I. (2003). Bayesian model-based clustering of gene expression dynamics. In The Analysis of Microarray Data: Methods and Software (G. Parmigiani, R. Irizarry and S. L. Zeger, eds.). Springer, New York. · Zbl 1023.62110
[92] Segal, E., Taskar, B., Gasch, A., Friedman, N. and Koller, D. (2001). Rich probabilistic models for gene expression. Bioinformatics 17 S243–252. · Zbl 1131.62098
[93] Smyth, G. K., Yang, Y. H. and Speed, T. P. (2003). Statistical issues in cDNA microarray data analysis. In Functional Genomics: Methods and Protocols (M. J. Brownstein and A. B. Khodursky, eds.). Humana, Totowa, NJ.
[94] Sorlie, T., Perou, C. M., Tibshirani, R., Aas, T., Geisler, S., Johnsen, H., Hastie, T., Eisen, M. B., van de Rijn, M., Jeffrey, S. S., Thorsen, T., Quist, H., Matese, J. C., Brown, P. O., Botstein, D., Eystein Lønning, P. and Borresen-Dale, A. L. (2001). Gene expression patterns of breast carcinomas distinguish tumor subclasses with clinical implications. Proc. Natl. Acad. Sci. U.S.A. 98 10869–10874.
[95] Southern, E., Mir, K. and Shchepinov, M. (1999). Molecular interactions on microarrays. Nature Genetics 21 5–9.
[96] Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., Brown, P. O., Botstein, D. and Futcher, B. (1998). Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell 9 3273–3297.
[97] Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Kitareewan, S., Dmitrovsky, E., Lander, E. S. and Golub, T. R. (1999). Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation. Proc. Natl. Acad. Sci. U.S.A. 96 2907–2912.
[98] Tavazoie, S., Hughes, J. D., Campbell, M. J., Cho, R. J. and Church, G. M. (1999). Systematic determination of genetic network architecture. Nature Genetics 22 281–285.
[99] Thomas, J. G., Olson, J. M., Tapscott, S. J. and Zhao, L. P. (2001). An efficient and robust statistical modeling approach to discover differentially expressed genes using genomic expression profiles. Genome Research 11 1227–1236.
[100] Tibshirani, R., Walther, G. and Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. J. Roy. Stat. Soc. Ser. B Stat. Methodol. 63 411–423. · Zbl 0979.62046
[101] Tusher, V. G., Tibshirani, R. and Chu, G. (2001). Significance analysis of microarrays applied to the ionizing radiation response. Proc. Natl. Acad. Sci. U.S.A. 98 5116–5121. · Zbl 1012.92014
[102] Tversky, A. and Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science 185 1124–1131.
[103] Vapnik, V. (1998). Statistical Learning Theory . Wiley, New York. · Zbl 0935.62007
[104] Velculescu, V. E., Zhang, L., Vogelstein, B. and Kinzler, K. W. (1995). Serial analysis of gene expression. Science 270 484–487.
[105] West, M., Blanchette, C., Dressman, H., Huang, E., Ishida, S., Spang, R., Zuzan, H., Olson, Jr., J. A., Marks, J. R. and Nevins, J. R. (2001). Predicting the clinical status of human breast cancer by using gene expression profiles. Proc. Natl. Acad. Sci. U.S.A. 98 11462–11467.
[106] White, B. (1995). Southerns, Northerns, Westerns, and Cloning: “molecular searching” techniques. MIT Biology Hypertextbook . MIT Press. Available at http://web.mit.edu/esgbio/ www/rdna/rdna.html.
[107] Wolfinger, R. D., Gibson, G., Wolfinger, E. D., Bennett, L., Hamadeh, H., Bushel, P., Afshari, C. and Paules, R. S. (2001). Assessing gene significance from cDNA microarray expression data via mixed models. Journal of Computational Biology 8 625–637.
[108] Wyrick, J. J., Holstege, F. C. P., Jennings, E. G., Causton, H. C., Shore, D., Grunstein, M., Lander, E. S. and Young, R. A. (1999). Chromosomal landscape of nucleosome-dependent gene expression and silencing in yeast. Nature 402 418–421.
[109] Yang, Y. H., Dudoit, S., Luu, P., Lin, D. M., Peng, V., Ngai, J. and Speed, T. P. (2002). Normalization for cDNA microarray data: A robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Research 30 (4) e15.
[110] Yang, Y. H., Dudoit, S., Luu, P. and Speed, T. P. (2001). Normalization for cDNA microarray data. In Microarrays: Optical Technologies and Informatics (M. L. Bittner, Y. Chen, A. N. Dorsel and E. R. Dougherty, eds.) 141–152. SPIE, Bellingham, WA.
[111] Yang, Y. H. and Speed, T. P. (2002). Design issues for cDNA microarray experiments. Nature Reviews Genetics 3 579–588.
[112] Yeung, K. Y., Fraley, C., Murua, A., Raftery, A. E. and Ruzzo, W. L. (2001). Model-based clustering and data transformations for gene expression data. Bioinformatics 17 977–987.
[113] Yoo, C., Thorsson, V. and Cooper, G. F. (2002). Discovery of causal relationships in a gene-regulation pathway from a mixture of experimental and observational DNA microarray data. In Proc. Pacific Symposium on Biocomputing 7 498–509. Available from http://psb.stanford.edu.
[114] Zuzan, H., Blanchette, C., Dressman, H., Huang, E., Ishida, S., Marks, J. R., Nevins, J. R., Spang, R., West, M. and Johnson, V. E. (2001). Estimation of probe cell locations in high-density synthetic-oligonucleotide DNA microarrays. Technical report, Institute of Statistics and Decision Sciences, Duke Univ., Durham, NC. \endthebibliography
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