Abstract
Nowadays, microarray technology is available to generate a huge amount of information on gene expression. This information must be statistically processed and analyzed, in particular, to identify those genes which are useful for the diagnosis and prognosis of specific diseases. We discuss the possibility of applying game-theoretical tools, like the Shapley value, to the analysis of gene expression data.
Via a “truncation” technique, we build a coalitional game whose aim is to stress the relevance (“sufficiency”) of groups of genes for the specific disease we are interested in. The Shapley value of this game is used to select those genes which deserve further investigation. To justify the use of the Shapley value in this context, we axiomatically characterize it using properties with a genetic interpretation.
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Alon U, Barkai N, Notterman DA, Gish K, Ybarra S, Mack D, Levine AJ (1999) Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissue probed by oligonucleotide arrays. Proc Natl Acad Sci USA 96:6745–6750
Banzhaf JF III (1965) Weighted voting doesn’t work: a game theoretic approach. Rutgers Law Rev 19:317–343
Becquet C, Blachon S, Jeudy B, Boulicaut JG, Gandrillon O (2002) Strong-association-rule mining for large-scale gene-expression data analysis: a case study on human SAGE data. Genome Biol 3(12)
Bower JM, Bolouri H (eds) (2001) Computational modelling of genetic and biochemical networks computational molecular biology series. MIT Press, Cambridge
Branzei R, Moretti S, Norde H, Tijs S (2004) The P-value for cost sharing in minimum cost spanning tree situations. Theory Decis 56:47–61
Dudoit S, Fridlyand J (2003) Classification in microarray experiments. In: Speed TP (ed) Statistical analysis of gene expression microarray data. Chapman & Hall/CRC, London/Boca Raton, pp 93–158
Dudoit S, Yang YH, Luu P, Speed TP (2001) Normalization for cDNA microarray data. In: Bittner ML, Chen Y, Dorsel AN, Dougherty ER (eds) Microarrays: optical technologies and informatics. Proceedings of SPIE, vol 4266, pp 141–152
Fragnelli V, Moretti S (2007) A game theoretical approach to the classification problem in gene expression data analysis. Comput Math Appl, doi:10/1016/j.camwa.2006.12.088
Fujarewicz K, Wiench M (2003) Selecting differentially expressed genes for colon tumor classification. Int J Appl Math Comput Sci 13(3):327–335
Gentleman RC, Carey VJ, Bates DM, Bolstad B, Dettling M, Dudoit S, Ellis B, Gautier L, Ge Y, Gentry J, Hornik K, Hothorn T, Huber W, Iacus S, Irizarry R, Leisch F, Li C, Maechler M, Rossini AJ, Sawitzki G, Smith C, Smyth G, Tierney L, Yang JYH, Zhang J (2004) Bioconductor: open software development for computational biology and bioinformatics. Genome Biol 5:80, http://genomebiology.com/2004/5/10/R80
Golub T, Slonim D, Tamayo P, Huard C, Gaasenbeek M, Mesirov J, Coller H, Loh M, Downing J, Caligiuri M, Bloomfield C, Lander E (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286:531–537
Grabisch M, Roubens M (1999) An axiomatic approach to the concept of interaction among players in cooperative games. Int J Game Theory 28:547–565
Jager J (2006) Deriving small diagnostic biomarker panels from genome wide. PhD Dissertation, Max Planck Institute for Molecular Genetics
Kalai E, Samet D (1988) Weighted Shapley values. In: Roth A (ed) The Shapley value, essays in honor of Lloyd S. Shapley. Cambridge University Press, Cambridge, pp 83–100
Kasahara M, Takahashi Y, Nagata T, Asai S, Eguchi T, Ishii Y, Fujii M, Ishikawa K (2000) Thymidylate synthase expression correlates closely with E2F1 expression in colon cancer. Clin Cancer Res 6:2707–2711
Kaufman A, Kupiec M, Ruppin E (2004) Multi-knockout genetic network analysis: the Rad6 example. In: Proceedings of the 2004 IEEE computational systems bioinformatics conference (CSB’04), August 16–19, 2004, Standford, California
Keinan A, Sandbank B, Hilgetag CC, Meilijson I, Ruppin E (2004) Fair attribution of functional contribution in artificial and biological networks. Neural Comput 16(9):1887–1915
Moler EJ, Chow, ML, Mian IS (2000) Analysis of molecular profile data using generative and discriminative methods. Physiol Genomics 4:109–126
Moretti S (2006a) Game Theory applied to gene expression analysis. PhD Dissertation, University of Genoa, Italy
Moretti S (2006b) Minimum cost spanning tree games and gene expression data analysis. In: ACM international conference proceeding series, p 199
Owen G (1995) Game theory, 3rd edn. Academic, San Diego
Parmigiani G, Garret ES, Irizarry RA, Scott SL (2003) The analysis of gene expression data: an overview of methods and software. In: Parmigiani G, Garret ES, Irizarry RA, Zeger SL (eds) The analysis of gene expression data: methods and software. Springer, New York
R Development Core Team (2004) R: a language and environment for statistical. R foundation for statistical computing, Vienna, Austria, 2004, ISBN 3-900051-00-3, http://www.R-project.org
Ramamurthy KG (1990) Coherent structures and simple games. Kluwer Academic, Dordrecht
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Annals of mathematics studies, vol 28. Princeton University Press, Princeton, pp 307–317
Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. Am Political Sci Rev 48:787–792
Smith K, Speed T (2003) Normalization of cDNA microarray data. Methods 31:265–273
Storey JD, Tibshirani R (2003) SAM thresholding and false discovery rates for detecting differential gene expression in DNA microarrays. In: Parmigiani G, Garret ES, Irizarry RA, Zeger SL (eds) The analysis of gene expression data: methods and software. Springer, New York
Su Y, Murali TM, Pavlovic V, Schaffer M, Kasif S (2003) RankGene: identification of diagnostic genes based on expression data. Bioinformatics 19(12):1578–1579
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The authors are grateful to two anonymous referees for their extremely helpful comments.
An earlier version of this paper was presented at the VI Spanish Meeting on Game Theory and Practice, July 12–14, 2004, Elche, Spain.
S. Moretti gratefully acknowledges the financial support of the EU project NewGeneris, European Union 6th FP (FOOD-CT-2005-016320).
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Moretti, S., Patrone, F. & Bonassi, S. The class of microarray games and the relevance index for genes. TOP 15, 256–280 (2007). https://doi.org/10.1007/s11750-007-0021-4
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DOI: https://doi.org/10.1007/s11750-007-0021-4