zbMATH — the first resource for mathematics

Sparse graphical models for exploring gene expression data. (English) Zbl 1047.62104
Summary: We discuss the theoretical structure and constructive methodology for large-scale graphical models, motivated by their potential in evaluating and aiding the exploration of patterns of association in gene expression data. The theoretical discussion covers basic ideas and connections between Gaussian graphical models, dependency networks and specific classes of directed acyclic graphs we refer to as compositional networks. We describe a constructive approach to generating interesting graphical models for very high-dimensional distributions that builds on the relationships between these various stylized graphical representations.
Issues of consistency of models and priors across dimension are key. The resulting methods are of value in evaluating patterns of association in large-scale gene expression data with a view to generating biological insights about genes related to a known molecular pathway or set of specified genes. Some initial examples relate to the estrogen receptor pathway in breast cancer, and the Rb-E2F cell proliferation control pathway.

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J99 Linear inference, regression
05C90 Applications of graph theory
62F15 Bayesian inference
HdBCS; Graphviz
PDF BibTeX Cite
Full Text: DOI
[1] Al-azzeh, E.; Fegert, P.; Blin, N.; Gott, P., Transcription factor GATA-6 activates expression of gastroprotective trefoil genes TFF1 and TFF2, Biochem. biophys. acta, 1490, 324-332, (2000)
[2] Anderson, S.A.; Madigan, D.; Perlman, M.D., A characterization of Markov equivalence classes for acyclic digraphs, Ann. statist., 25, 505-541, (1997) · Zbl 0876.60095
[3] Barkhem, T.; Haldosen, L.A.; Gustafsson, J.A.; Nilsson, S., Gene expression in hepg2 cells: complex regulation through crosstalk between the estrogen receptor alpha, an estrogen-response element, and the activator protein 1 response element, Molecular pharmacol., 61, 1273-1283, (2002)
[4] Beck, S.; Sommer, P.; Do Santos Silva, E.; Blin, N.; Gott, P., Hepatocyte nuclear factor 3 (winged helix domain) activates trefoil factor gene TFF1 through a binding motif adjacent to the TATA box, DNA cell biol., 18, 157-164, (1999)
[5] Dawid, A.P., Some matrix-variate distribution theory: notational considerations and a Bayesian application, Biometrika, 68, 265-274, (1981) · Zbl 0464.62039
[6] Dawid, A.P.; Lauritzen, S.L., Hyper Markov laws in the statistical analysis of decomposable graphical models, Ann. statist., 3, 1272-1317, (1993) · Zbl 0815.62038
[7] Dyson, N., The regulation of E2F by prb family proteins, Gene. dev., 12, 2245-2262, (1998)
[8] Geiger, D.; Heckerman, D., Parameter priors for directed acyclic graphical models and the characterization of several probability distributions, Ann. statist., 5, 1412-1440, (2002) · Zbl 1016.62064
[9] P. Giudici, Learning in graphical Gaussian models, in: J.M. Bernardo, J. Berger, A. Dawid, A. Smith (Eds.), Bayesian Statistics, Vol. 5, Oxford University Press, Oxford, 1994, pp. 621-628.
[10] GraphViz, Open source graph drawing software, AT&T Research Labs., http://www.research.att.com/sw/tools/graphviz/.
[11] Heckerman, D.; Chickering, D.M.; Meek, C.; Rounthwaite, R.; Kadie, C., Dependency networks for inference, collaborative filtering, and data visualization, J. Mach. learning res., 1, 49-75, (2000) · Zbl 1008.68132
[12] Hegde, S.P.; Kumar, A.; Kurschner, C.; Shapiro, L.H., C-maf interacts with c-myb to regulate transcription of an early myeloid gene during differentiation, Molecular cell. biol., 18, 2729-2737, (1998)
[13] Henry, J.A.; Nicholson, S.; Fandon, J.R.; Westley, B.R.; May, F.E., Measurement of oestrogen receptor mrna levels in human breast tumours, J. breast cancer, 58, 600-605, (1988)
[14] R. Hofmann, V. Tresp, Nonlinear Markov networks for continuous variables, in: M.I. Jordan, M.J. Kearns, S.A. Solla (Eds.), Advances in Neural Information Processing Systems, Vol. 10, Proceedings of the 1997 Conference, MIT Press, Cambridge, MA, 1998, pp. 521-527.
[15] Huang, E.; Cheng, S.; Dressman, H.; Pittman, J.; Tsou, M.-H.; Horng, C.-F.; Bild, A.; Iversen, E.; Liao, M.; Chen, C.-M.; West, M.; Nevins, J.; Huang, A., Gene expression predictors of breast cancer outcomes, Lancet, 361, 1590-1596, (2003)
[16] E. Huang, M. West, J.R. Nevins, Gene expression profiles and predicting clinical characteristics of breast cancer, Recent Progr. Hormone Res. (2003) 55-73.
[17] Knight, W.A.; Livingston, R.B.; Gregory, E.J.; McGuire, W.L., Estrogen receptor as an independent prognostic factor for early recurrence in breast cancer, Cancer res., 37, 4669-4671, (1977)
[18] Lauritzen, S.L., Graphical models, (1996), Clarendon Press Oxford · Zbl 0907.62001
[19] May, F.E.; Westley, B.R., Identification and characterization of estrogen-regulated RNAs in human breast cancer cells, J. biol. chem., 263, 12901-12908, (1988)
[20] Nevins, J.R., Towards an understanding of the functional complexity of the E2F and retinoblastoma families, Cell growth differ., 9, 585-593, (1998)
[21] Pichon, M.F.; Broet, P.; Magdelenat, H.; Delarue, J.C.; Spyratos, F.; Basuyau, J.P.; Saez, S.; Rallet, A.; Courriere, P.; Millon, R.; Asselain, B., Prognostic value of steroid receptors after long term follow up of 2257 operable breast cancers, British J. cancer, 73, 1545-1551, (1996)
[22] Reiss, K.; Ferber, A.; Travali, S.; Porcu, P.; Phillips, P.D.; Baserga, R., The protooncogene c-myb increases the expression of insulin-like growth factor 1 and insulin-like growth factor 1 receptor messenger RNAs by a transcriptional mechanism, Cancer res., 51, 5997-6000, (1991)
[23] A. Roverato, G. Consonni, Compatible prior distributions for DAG models, DIMACS Technical Report 2002-17, 2002. · Zbl 1062.62050
[24] Sahlin, L.; Norstedt, G.; Eriksson, H., Androgen regulation of the insulin-like growth factori and the estrogen receptor in rat uterus and liver, J. steroid biochem. molecular biol., 51, 57-66, (1994)
[25] Schuur, E.R.; Loktev, A.V.; Sharma, M.; Sun, Z.; Roth, A.A.; Weigel, R.J., Ligand-dependent interaction of estrogen receptor alpha with members of the forkhead transcription factor family, J. biol. chem., 276, 33554-33560, (2001)
[26] Spiegelhalter, D.J.; Lauritzen, S.L., Sequential updating of conditional probabilities on directed graphical structures, Networks, 20, 579-605, (1990) · Zbl 0697.90045
[27] M. West, Bayesian factor regression models in the “large p, small n” paradigm, in: J.M. Bernardo, M. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith, M. West (Eds.), Bayesian Statistics, Vol. 7, Oxford University Press, Oxford, 2003, pp. 723-732.
[28] M. West, C. Blanchette, H. Dressman, E. Huang, S. Ishida, R. Spang, H. Zuzan, M.J.R., J.R. Nevins, Predicting the clinical status of human breast cancer using gene expression profiles, Proc. Nat. Acad. Sci. 98 (2001) 11462-11467.
[29] Zellner, A., An introduction to Bayesian inference in econometrics, (1971), Wiley New York · Zbl 0246.62098
[30] Zhou, X.; Kao, M.J.; Wong, W.H., Transitive functional annotation by shortest path analysis of gene expression data, Proc. nat. acad. sci., 99, 12783-12788, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.