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==Introduction==
Microarray data analysis is the final step in reading and processing data produced by a microarray chip. Samples undergo various processes including purification and scanning using the microchip, which then produces a large amount of data that requires processing via computer software. It involves several distinct steps, as outlined in the image below. Changing any one of the steps will change the outcome of the analysis, so the MAQC Project<ref>{{cite web | url = https://www.fda.gov/nctr/science/centers/toxicoinformatics/maqc/ | archive-url = https://web.archive.org/web/20051208055601/http://www.fda.gov/nctr/science/centers/toxicoinformatics/maqc/ | url-status = dead | archive-date = December 8, 2005 | title = MicroArray Quality Control (MAQC) Project | access-date = 2007-12-26 | author = Dr. Leming Shi, National Center for Toxicological Research | publisher = U.S. Food and Drug Administration }}</ref> was created to identify a set of standard strategies. Companies exist that use the MAQC protocols to perform a complete analysis.<ref>{{cite web |url=http://www.genusbiosystems.com/services-data.shtml |title=GenUs BioSystems - Services - Data Analysis |access-date=2008-01-02 }}</ref>
[[File:Microarray exp horizontal.svg|thumb|800px|none|The steps required in a microarray experiment]]
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===Aggregation and normalization===
Comparing two different arrays or two different samples hybridized to the same array generally involves making adjustments for systematic errors introduced by differences in procedures and dye intensity effects. Dye normalization for two color arrays is often achieved by [[local regression]]. LIMMA provides a set of tools for background correction and scaling, as well as an option to average on-slide duplicate spots.<ref>{{cite web |url=http://bioinf.wehi.edu.au/limma/ |title=LIMMA Library: Linear Models for Microarray Data |access-date=2008-01-01 }}</ref> A common method for evaluating how well normalized an array is, is to plot an [[MA plot]] of the data. MA plots can be produced using programs and languages such as R and MATLAB.<ref>{{Cite journal |
Raw Affy data contains about twenty probes for the same RNA target. Half of these are "mismatch spots", which do not precisely match the target sequence. These can theoretically measure the amount of nonspecific binding for a given target. Robust Multi-array Average (RMA)<ref>{{cite journal|last1=Irizarry|first1=RA|author-link1=Rafael Irizarry (scientist) |author2=Hobbs, B |author3=Collin, F |author4=Beazer-Barclay, YD |author5=Antonellis, KJ |author6=Scherf, U |author7= Speed, TP |title=Exploration, normalization, and summaries of high density oligonucleotide array probe level data.|journal=Biostatistics|volume=4|issue=2|pages=249–64|year=2003|pmid=12925520 |doi=10.1093/biostatistics/4.2.249|doi-access=free}}</ref> is a normalization approach that does not take advantage of these mismatch spots but still must summarize the perfect matches through [[median polish]].<ref>{{cite journal |vauthors=Bolstad BM, Irizarry RA, Astrand M, Speed TP |title=A comparison of normalization methods for high density oligonucleotide array data based on variance and bias |journal=Bioinformatics |volume=19 |issue=2 |pages=185–93 |year=2003 |pmid=12538238 |doi=10.1093/bioinformatics/19.2.185|doi-access=free }}</ref> The median polish algorithm, although robust, behaves differently depending on the number of samples analyzed.<ref>{{cite journal |vauthors=Giorgi FM, Bolger AM, Lohse M, Usadel B |title=Algorithm-driven Artifacts in median polish summarization of Microarray data |journal=BMC Bioinformatics |volume=11 |pages=553 |year=2010 |pmid=21070630 |doi=10.1186/1471-2105-11-553 |pmc=2998528 |doi-access=free }}</ref> [[Quantile normalization]], also part of RMA, is one sensible approach to normalize a batch of arrays in order to make further comparisons meaningful.
The current Affymetrix MAS5 algorithm, which uses both perfect match and mismatch probes, continues to enjoy popularity and do well in head to head tests.<ref>{{cite journal |vauthors=Lim WK, Wang K, Lefebvre C, Califano A |title=Comparative analysis of microarray normalization procedures: effects on reverse engineering gene networks |journal=Bioinformatics |volume=23 |issue=13 |pages=i282–8 |year=2007 |pmid=17646307 |doi=10.1093/bioinformatics/btm201|doi-access=free }}</ref>
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===Identification of significant differential expression===
Many strategies exist to identify array probes that show an unusual level of over-expression or under-expression. The simplest one is to call "significant" any probe that differs by an average of at least twofold between treatment groups. More sophisticated approaches are often related to [[t-test]]s or other mechanisms that take both [[effect size]] and variability into account. Curiously, the p-values associated with particular genes do not reproduce well between replicate experiments, and lists generated by straight fold change perform much better.<ref name=":1">{{cite journal |vauthors=Shi L, Reid LH, Jones WD, etal |title=The MicroArray Quality Control (MAQC) project shows inter- and intraplatform reproducibility of gene expression measurements |journal=Nat. Biotechnol. |volume=24 |issue=9 |pages=1151–61 |year=2006 |pmid=16964229 |doi=10.1038/nbt1239 |pmc=3272078}}</ref><ref>{{cite journal |vauthors=Guo L, Lobenhofer EK, Wang C, etal |title=Rat toxicogenomic study reveals analytical consistency across microarray platforms |journal=Nat. Biotechnol. |volume=24 |issue=9 |pages=1162–9 |year=2006 |pmid=17061323 |doi=10.1038/nbt1238|s2cid=8192240 }}</ref> This represents an extremely important observation, since the point of performing experiments has to do with predicting general behavior. The MAQC group recommends using a fold change assessment plus a non-stringent [[p-value]] cutoff, further pointing out that changes in the background correction and scaling process have only a minimal impact on the rank order of fold change differences, but a substantial impact on p-values.<ref name=":1" />
=== Clustering ===
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==== Hierarchical clustering ====
{{main|Hierarchical clustering}}
Hierarchical clustering is a statistical method for finding relatively [[Homogeneity and heterogeneity#Homogeneity|homogeneous]] clusters. Hierarchical clustering consists of two separate phases. Initially, a [[distance matrix]] containing all the pairwise distances between the genes is calculated. [[Pearson product-moment correlation coefficient|Pearson's correlation]] and [[Spearman's rank correlation coefficient|Spearman's correlation]] are often used as dissimilarity estimates, but other methods, like [[Taxicab geometry|Manhattan distance]] or [[Euclidean distance]], can also be applied. Given the number of distance measures available and their influence in the clustering algorithm results, several studies have compared and evaluated different distance measures for the clustering of microarray data, considering their intrinsic properties and robustness to noise.<ref name=Gentleman>{{cite book|last1=Gentleman|first1=Robert|title=Bioinformatics and computational biology solutions using R and Bioconductor|date=2005|publisher=Springer Science+Business Media|___location=New York|isbn=978-0-387-29362-2|display-authors=etal}}</ref><ref name=Jaskowiak2013>{{cite journal|last1=Jaskowiak|first1=Pablo A.|last2=Campello|first2=Ricardo J.G.B.|last3=Costa|first3=Ivan G.|title=Proximity Measures for Clustering Gene Expression Microarray Data: A Validation Methodology and a Comparative Analysis|journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics|volume=10|issue=4|pages=845–857|doi=10.1109/TCBB.2013.9|pmid=24334380|year=2013|s2cid=760277}}</ref><ref name=Jaskowiak2014>{{cite journal|last1=Jaskowiak|first1=Pablo A|last2=Campello|first2=Ricardo JGB|last3=Costa|first3=Ivan G|title=On the selection of appropriate distances for gene expression data clustering|journal=BMC Bioinformatics|volume=15|issue=Suppl 2|pages=S2|doi=10.1186/1471-2105-15-S2-S2|pmid=24564555|pmc=4072854|year=2014 |doi-access=free }}</ref> After calculation of the initial distance matrix, the hierarchical clustering algorithm either (A) joins iteratively the two closest clusters starting from single data points (agglomerative, bottom-up approach, which is fairly more commonly used), or (B) partitions clusters iteratively starting from the complete set (divisive, top-down approach). After each step, a new distance matrix between the newly formed clusters and the other clusters is recalculated. Hierarchical [[cluster analysis]] methods include:
* Single linkage (minimum method, nearest neighbor)
* Average linkage ([[UPGMA]])
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[[File:Funrich.jpg|thumb|500px|none|Example of FunRich tool output. Image shows the result of comparing 4 different genes.]]
Specialized software tools for statistical analysis to determine the extent of over- or under-expression of a gene in a microarray experiment relative to a reference state have also been developed to aid in identifying genes or gene sets associated with particular [[phenotype]]s. One such method of analysis, known as [[Gene Set Enrichment]] Analysis (GSEA), uses a [[Kolmogorov-Smirnov]]-style statistic to identify groups of genes that are regulated together.<ref name=":0">{{cite journal |vauthors=Subramanian A, Tamayo P, Mootha VK, etal |title=Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=102 |issue=43 |pages=15545–50 |year=2005 |pmid=16199517 |doi=10.1073/pnas.0506580102 |pmc=1239896|doi-access=free }}</ref> This third-party statistics package offers the user information on the genes or gene sets of interest, including links to entries in databases such as NCBI's [[GenBank]] and curated databases such as Biocarta<ref>{{cite web |url=http://www.biocarta.com/ |title=BioCarta - Charting Pathways of Life |access-date=2007-12-31 }}</ref> and [[Gene Ontology]]. Protein complex enrichment analysis tool (COMPLEAT) provides similar enrichment analysis at the level of protein complexes.<ref>{{cite journal |vauthors=Vinayagam A, Hu Y, Kulkarni M, Roesel C, etal |title= Protein Complex-Based Analysis Framework for High-Throughput Data Sets. 6, rs5 (2013). |journal= Sci. Signal. |volume=6 |issue=r5 |year=2013 |pmid= 23443684 |doi= 10.1126/scisignal.2003629 |url= http://www.flyrnai.org/compleat/ |pages=rs5 |pmc=3756668}}</ref> The tool can identify the dynamic protein complex regulation under different condition or time points. Related system, PAINT<ref>{{cite web |url=http://www.dbi.tju.edu/dbi/staticpages.php?page=tools&menu=37 |title=DBI Web |access-date=2007-12-31 |url-status=dead |archive-url=https://web.archive.org/web/20070705061522/http://www.dbi.tju.edu/dbi/staticpages.php?page=tools |archive-date=2007-07-05 }}</ref> and SCOPE<ref>{{cite web |url=http://genie.dartmouth.edu/scope/ |title=SCOPE |access-date=2007-12-31 |archive-date=2011-08-17 |archive-url=https://web.archive.org/web/20110817031914/http://genie.dartmouth.edu/scope/ |url-status=dead }}</ref> performs a statistical analysis on gene promoter regions, identifying over and under representation of previously identified [[transcription factor]] response elements. Another statistical analysis tool is Rank Sum Statistics for Gene Set Collections (RssGsc), which uses rank sum probability distribution functions to find gene sets that explain experimental data.<ref>{{cite web |url=
==Significance analysis of microarrays (SAM)==
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