Application of the Shapley value to microarray data analysis
Transcript of Application of the Shapley value to microarray data analysis
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Application of the Shapley valueto microarray data analysis.
Stefano Moretti
DIMA: Mathematics Department, University of Genova and
IST: National Cancer Research Institute
Fioravante Patrone
DIMA: Mathematics Department, University of Genova
VI Spanish Meeting on Game Theory and PracticeElche, 12-14 July 2004
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N.B.
• E’ una versione “ridotta” dellapresentazione fatta ad Elche
• E’ stata omessa la parte tecnica in cui siindividua una nuova caratterizzazione del valore Shapley, singificativa per lo specifico contesto applicativo
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Plan:
• What is a “microarray” and why is itinteresting?
• A game to play• The Shapley value is of any help?• Related developments and comments
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Fundamental principle: hybridization
ATATCGGCATCAGTCGATCGATCATCGATCGAT
UAUAGCCGUAGUCAGCUAGCUAGUAGCUAGCUA
ATATCGGCATCAGTCGATCGATCATCGATCGAT
DNA
mRNA
cDNA
DNA RNA Protein
Transcription
Reverse transcription
TranslationReplication
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(Slide source: http://www.bsi.vt.edu/)
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Experiments with cDNA microarray
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Matrix:
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Intensity rate
• M<0, the gene is more “expressed” in the control sample (marked in green)
• M=0, the gene is equally expressed• M>0, the gene is more “expressed” in the
tumor (or treated...) sample (marked in green)
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6.12.47g3
1.69.81.1g2
12204.2g1
s3s2s1
Microarray expression data from desease samples
0.53.55g3
2.17.84.2g2
2.76.34.1g1
s3s2s1
Microarray expression data from normal samples
50.57.82.16.32.7><
cutoffs
101g3111g2110g1s3s2s1
Discretized matrix
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EXAM PLE:
Microarray TU game:• Players are genes;• games with [0-1] characteristic function;• on each sample:
-If a coalition has value 1 then that coalitions activates the disease;-If a coalition has value 0 then that coalition does not activate the disease.
101g3
111g2
110g1
s3s2s1The corresponding [0,1]-game <{g1,g2,g3},v>:v({g1,g2})=v({g3,g2})=1/3v({g1,g2,g3})=1 andv(S)=0 for each other different coalition S.
The Shapley value is: (5/18,8/18,5/18).
Microarray discr. data
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Application 1: tumor versus normal
• Alon et al. (1999)wereinterested in identifying coregulated fam iliesof genesin tum orand norm alcolon tissues.
• Theystudied 6500 hum an genes.
• G eneswerecollected on 62 sam ples, –40 tum or colon tissues–22 norm al colon tissues
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Espression values of one gene in 22 normal samples
Gene labels
Expr
essi
onva
lues
Valuesconsideredunderexpressed
Valuesconsideredoverexpressed
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Shapley value of 2000 genes
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Shapley value of 100 genes
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MYOSIN REGULATORY LIGHT CHAIN 2, SMOOTH MUSCLE ISOFORM
H.sapiens mRNA for GCAP-II/uroguanylin precursor
Human desmin gene, complete cds.
Human vasoactive intestinal peptide (VIP) mRNA, complete cds.
It has been suggested topromote the growth and proliferation of tumor cells (Fujarewicz & Wiench, 2003).
Group of four genes with the highest Shapley values (in decreasing order from top to down).
It might provide an indication propensityfor metastasis of cells (Moler et al., 2000).
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Application 2: ALL versus AML
• G olub etal.(1999) wereinterested in identifyinggenesthatare differentially expressed in patientswith two typeof leukem ias, Acute Lym phoblasticLeukem ia (ALL) and Acute M yeloid Leukem ia(AM L).
• Theystudied 6817 hum an genes.
• G eneswerecollected on 38 sam ples, – 27 ALL cases– 11 AM L cases
• We discretized the expression values of genes in ALLsamples on the basis of expression values in AMLsamples
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Espression values of one gene in 11 AML samples
Gene labels
Expr
essi
onva
lues
Valuesconsideredoverexpressed
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Shapley value of 3051 genes
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Shapley value of 50 genes
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TOP2B Topoisomerase (DNA) II beta (180kD)
SPTAN1 Spectrin, alpha, non-erythrocytic 1 (alpha-fodrin)
Oncoprotein 18 (Op18) gene
Macmarcks
KIAA0181 gene, partial cds
Encode a critical protein for the cell cycle progression related to leukemia (Glub et al., 1999)
Group of five genes with the same highest Shapley value.
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Related references
• Kaufman, Kupiec and Ruppin: Multi-Knockout Genetic Network Analysis: The Rad6 Example, preprint
• Keinan, Kaufman, Sachs, Hilgetag and Ruppin: Fair localization of function via multi-lesion analysis, to appear on Neuroinformatics, 2004.
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three comments
• Be humble: many approaches, a lot of knowledge around
• Be determined: if you have an idea, follow it to see really what it can give
• Be critical: a characteristic which is not as widespread as it should be
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The END
Thanks for your attention