Statistical two-group comparisons are widely used to identify the significant differentially expressed (DE) signatures against a therapy response for microarray data analysis. We applied a rank order statistics based on an Autoregressive Conditional Heteroskedasticity (ARCH) residual empirical process to DE analysis. This approach was considered for simulation data and publicly available datasets, and was compared with two-group comparison by original data and Auto-regressive (AR) residual. The significant DE genes by the ARCH and AR residuals were reduced by about 20% - 30% to these genes by the original data. Almost 100% of the genes by ARCH are covered by the genes by the original data unlike the genes by AR residuals. GO enrichment and Pathway analyses indicate the consistent biological characteristics between genes by ARCH residuals and original data. ARCH residuals array data might contribute to refining the number of significant DE genes to detect the biological feature as well as ordinal microarray data.
KeywordsTime Series ModelARCHWilcoxon StatisticVolatilityDeferentially Expressed Gene SignaturesTwo-Group ComparisonBreast Cancer GEOGenome-Wide Expression ProfilingGO Analysis
Zhao, X., Rodland, E.A., Sorlie, T., Naume, B., Langerod, A., Frigessi, A., Kristensen, V.N., Borresen-Dale, A.L. and Lingjaerde, O.C. (2011) Combining Gene Signatures Improves Prediction of Breast Cancer Survival. PLoS ONE, 6.
Yang, Y.H., Xiao, Y. and Segal, M.R. (2005) Identifying Differentially Expressed Genes from Microarray Experiments via Statistics Synthesis. Bioinformatics, 21, 1084-1093. https://doi.org/10.1093/bioinformatics/bti108
Tusher, V.G., Tibshirani, R. and Chu, G. (2001) Significance Analysis of Microarrays Applied to the Ionizing Radiation Response. Proceedings of the National Academy of Sciences, 98, 5116-5121. https://doi.org/10.1073/pnas.091062498
Campain, A. and Yang, Y.H. (2010) Comparison Study of Microarray Meta-Analysis Methods. BMC Bioinformatics, 11, 408. https://doi.org/10.1186/1471-2105-11-408
Benjamini, Y. and Hockberg, Y. (1995) Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society B, 57, 289-300.
Engle, R.F. (1982) Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK Inflation. Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
Chandra, S.A. and Taniguchi, M. (2003) Asymptotics of Rank Order Statistics for ARCH Residual Empirical Processes. Stochastic Processes and Their Applications, 104, 301-324. https://doi.org/10.1016/S0304-4149(02)00239-9
Ozaki, T. and Iino, M. (2001) An Innovation Approach to Non-Gaussian Time Series Analysis. Journal of Applied Probability, 38A, 78-92. https://doi.org/10.1017/S0021900200112690
Stoffer, D.S., Tyler, D.E. and Wendt, D.A. (2000) The Spectral Envelope and Its Applications. Statistical Science, 15, 224-253. https://doi.org/10.1214/ss/1009212816
Koren, A., Tirosh I. and Barki, N. (2007) Autocorrelation Analysis Reveals Widespread Spatial Biases in Microarray Experiments. BMC Genomics, 8, 164. https://doi.org/10.1186/1471-2164-8-164
Lee, S. and Taniguchi, M. (2005) Asymptotic Theory for ARCH-SM Models: LAN and Residual Empirical Processes. Statistica Sinica, 15, 215-234.
Van Vliet, M.H., Reyal, F., Horlings, H.M., van de Vijver, M.J., Reinders, M.J.T. and Wessels, L.F.A. (2010) Pooling Breast Cancer Datasets Has a Synergetic Effect on Classification Performance and Improves Signature Stability. BMC Genomics, 9, 375. https://doi.org/10.1186/1471-2164-9-375
Rezaul, K., Thumar, J.K., Lundgren, D.H., Eng, J.K., Claffey, K.P., Wilson, L. and Han, D.K. (2010) Differential Protein Expression Profiles in Estrogen Receptor-Positive and -Negative Breast Cancer Tissues Using Label-Free Quantitative Proteomics. Genes Cancer, 1, 251-271. https://doi.org/10.1177/1947601910365896
Milhoj, A. (1985) The Moment Structure of ARCH Processes. Scandinavian Journal of Statistics, 12, 281-292.
Akaike, H. (1974) A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, 19, 716-723. https://doi.org/10.1109/TAC.1974.1100705
Glass, K. and Girvan, M. (2014) Annotation Enrichment Analysis: An Alternative Method for Evaluating the Functional Properties of Gene Sets. Scientific Reports, 4, 4191. https://doi.org/10.1038/srep04191
Eden, E., Navon, R., Steinfeld, I., Lipson, D. and Yakhini, Z. (2009) GOrilla: A Tool for Discovery and Visualization of Enriched GO Terms in Ranked Gene Lists. BMC Bioinformatics, 10, 48. https://doi.org/10.1186/1471-2105-10-48
Deihn, M., Sherlock, G., Binkley, G., Jin, H., Matese, J.C., Hernandez-Boussard, T., Rees, C.A., Cherry, J.M., Botstein, D., Brown, P.O. and Alizadeh, A.A. (2003) SOURCE: A Unified Genomic Resource of Functional Annotations, Ontologies, and Gene Exrpression Data. Nucleic Acids Research, 31, 219-223. http://source-search.princeton.edu/cgi-bin/source/sourceSearch https://doi.org/10.1093/nar/gkg014
Joshi-Tope, G., Gillespie, M., Vastrik, I., D’Eustachio, P., Schmidt, E., de Bono, B., Jassal, B., Gopinah, G.R., Wu, G.R., Matthews, L., Lewis, S., Birney, E. and Stein, L. (2005) Reactome: A Knowledgebase of Biological Pathways. Nucleic Acids Research, 1, D428-D432.
Edgar, R., Domrachev, M. and Lash, A.E. (2002) Gene Expression Omnibus: NCBI Gene Expression and Hybridization Array Data Repository. Nucleic Acids Research, 30, 207-210. https://doi.org/10.1093/nar/30.1.207
Loi, S., Haibe-Kains, B., Desmedt, C., Lallemand, F., Tutt, A.M., Gillet, C., Ellis, P., Harris, A., Bergh, J., Foekens, J.A., Klijn, J.G., Larsimont, D., Buyse, M., Botempi, G., Delorenzi, M., Piccart, M.J. and Sotiriou, C. (2007) Definition of Clinically Distinct Molecular Subtypes in Estrogen Receptor-Positive Breast Carcinomas through Genomic Grade. Journal of Clinical Oncology, 25, 1239-1246. https://doi.org/10.1200/JCO.2006.07.1522
MillerL, D., Smeds, J., George, J., Vega, V.B., Vergara, L., Ploner, A., Pawitan, Y., Hall, P., Klaar, S., Liu, E.T. and Bergh, J. (2005) An Expression Signature for p53 Status in Human Breast Cancer Predicts Mutation Status, Transcriptional Effects, and Patient Survival. Proceedings of the National Academy of Sciences of the United States of America, 102, 13550-13555. https://doi.org/10.1073/pnas.0506230102
Desmedt, C., Piette, F., Loi, S., Wang, Y., Lallemand, F., Haibe-Kains, B., Delorenzi, M., d’Assignies, M.S., Bergh, J., Lidereau, R., Ellis, P., Harris, A.L., Klijn, J.G., Foekens, J.A., Cardoso, F., Piccart, M.J., Buyse, M. and Sotiriou, C. (2007) Strong Time Dependence of the 76-Gene Prognostic Signature for Node-Negative Breast Cancer Patients in the TRANSBIG Multicenter Independent Validation Series. Clinical Cancer Research, 13, 3207-3214. https://doi.org/10.1158/1078-0432.CCR-06-2765
Minn, A.J., Gupta, G.P., Siegel, P.M., Bos, P.D., Shu, W., Giri, D.D., Viale, A., Olshen, A.B., Gerald, W.L. and Massaqué, J. (2005) Genes That Mediate Breast Cancer Metastasis to Lung. Nature, 436, 518-524. https://doi.org/10.1038/nature03799
Chin, K., DeVries, S., Fridlyand, J., Spellman, P.T., Roydasgupta, R., Kuo, W.L., Lapuk, A., Neve, R.M., Qian, Z., Ryder, T., Chen, F., Feiler, H., Tokuyasu, T., Kingsley, C., Dairkee, S., Meng, Z., Chew, K., Pinkel, D., Jain, A., Ljung, B.M., Esseman, L., Albertson, D.G., Waldman, F.M. and Gray, J.W. (2006) Genomic and Transcriptional Aberrations Linked to Breast Cancer Pathophysiologies. Cancer Cell, 10, 529-541. https://doi.org/10.1016/j.ccr.2006.10.009
Zhao, X., Rodland, E.A., Sorlie, T., Vollan, H.K.M., Russnes, H.G., Kristensen, V.N., Lingjorde, O.C. and Borresen-Dale, A.L. (2014) Systematic Assessment of Prognstic Gene Signatures for Breast Cancer Shows Distinct Influence of Time and ER Status. BMC Cancer, 14, 211. https://doi.org/10.1186/1471-2407-14-211
Bolstad, B.M., Collin, F., Brettschneider, J., Simpson, K., Cope, L., Irizarry, R.A. and Speed, T.P. (2005) Quality Assessment of Affymetrix Gene Chip Data. In: Gentleman, R., Carey, V., Huber, W., Irizarry, R. and Dudoit, S., Eds., Bioinformatics and Computational Biology Solutions Using R and Bioconductor Statistics for Biology and Health, Springer, Berlin, 33-47. https://doi.org/10.1007/0-387-29362-0_3
Irizarry, R.A., Bolstad, B.M., Collin, F., Cope, L.M., Hobbs, B. and Speed, T.P. (2003) Summaries of Affymetrix Gene Chip Probe Level Data. Nucleic Acids Research, 31, e15. https://doi.org/10.1093/nar/gng015
Sims, A.H., Smethurst, G.J., Hey, Y., Okoniewski, M.J., Pepper, S.D., Howell, A., Miller, C.J. and Clarke, R.B. (2008) The Removal of Multiplicative, Systematic Bias Allows Integration of Breast Cancer Gene Expression Datasets—Improving Meta-Analysis and Prediction of Prognosis. BMC Medical Genomics, 1, 42. https://doi.org/10.1186/1755-8794-1-42
Perou, C.M., Sorlie, T., Eisen, M.B., van de Rijn, M., Jeffrey, S.S., Rees, C.A., Pollack, J.R., Ross, D.T., Johnsen, H., Akslen, L.A., Fluge, O., Pergamenschikov, A., Williams, C., Zhu, S.X., Lonning, P.E., Borresen-Dale, A.L., Brown, P.O. and Botstein, D. (2000) Molecular Portraits of Human Breast Tumours. Nature, 406, 747-752. https://doi.org/10.1038/35021093
Teschendorff, A.E., Journée, M., Absil, P.A., Sepulchre, R. and Caldas, C. (2007) Elucidating the Altered Transcriptional Programs in Breast Cancer Using Independent Component Analysis. PLoS Computational Biology, 3, e161. https://doi.org/10.1371/journal.pcbi.0030161