Editing DNA microarray (section)

=== Data analysis ===
{{main|Microarray analysis techniques}}
{{See also|Gene chip analysis}}
[[File:Toxicology Research at FDA (NCTR 1470) (6009042166).jpg|thumb|[[National Center for Toxicological Research]] scientist reviews microarray data.]]

Microarray data sets are commonly very large, and analytical precision is influenced by a number of variables. [[Statistics|Statistical]] challenges include taking into account effects of background noise and appropriate [[Normalization (statistics)|normalization]] of the data. Normalization methods may be suited to specific platforms and, in the case of commercial platforms, the analysis may be proprietary.<ref>{{cite web|title=Prosigna {{!}} Prosigna algorithm|url=http://prosigna.com/x-us/overview/prosigna-algorithm/|website=prosigna.com|access-date=22 June 2017}}</ref> Algorithms that affect statistical analysis include:

* Image analysis: gridding, spot recognition of the scanned image (segmentation algorithm), removal or marking of poor-quality and low-intensity features (called ''flagging'').
* Data processing: background subtraction (based on global or local background), determination of spot intensities and intensity ratios, visualisation of data (e.g. see [[MA plot]]), and log-transformation of ratios, global or [[Local regression|local]] normalization of intensity ratios, and segmentation into different copy number regions using [[step detection]] algorithms.<ref>{{cite journal|last=Little|first= M.A.|author2=Jones, N.S.|title=Generalized Methods and Solvers for Piecewise Constant Signals: Part I| journal=[[Proceedings of the Royal Society A]]|url=http://www.maxlittle.net/publications/pwc_filtering_arxiv.pdf|date = 2011 |doi=10.1098/rspa.2010.0671|pmid= 22003312|pmc= 3191861|volume=467|issue= 2135|pages=3088–3114}}</ref>
* Class discovery analysis: This analytic approach, sometimes called unsupervised classification or knowledge discovery, tries to identify whether microarrays (objects, patients, mice, etc.) or genes cluster together in groups. Identifying naturally existing groups of objects (microarrays or genes) which cluster together can enable the discovery of new groups that otherwise were not previously known to exist. During knowledge discovery analysis, various unsupervised classification techniques can be employed with DNA microarray data to identify novel clusters (classes) of arrays.<ref name="Peterson">{{cite book|author=Peterson, Leif E.
|date= 2013|title=Classification Analysis of DNA Microarrays|publisher=John Wiley and Sons|isbn=978-0-470-17081-6|url=http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470170816.html}}</ref> This type of approach is not hypothesis-driven, but rather is based on iterative pattern recognition or statistical learning methods to find an "optimal" number of clusters in the data. Examples of unsupervised analyses methods include self-organizing maps, neural gas, k-means cluster analyses,<ref>De Souto M et al. (2008) Clustering cancer gene expression data: a comparative study, BMC Bioinformatics, 9(497).</ref> hierarchical cluster analysis, Genomic Signal Processing based clustering and model-based cluster analysis. For some of these methods the user also has to define a distance measure between pairs of objects. Although the Pearson correlation coefficient is usually employed, several other measures have been proposed and evaluated in the literature.<ref>{{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> The input data used in class discovery analyses are commonly based on lists of genes having high informativeness (low noise) based on low values of the coefficient of variation or high values of Shannon entropy, etc. The determination of the most likely or optimal number of clusters obtained from an unsupervised analysis is called cluster validity. Some commonly used metrics for cluster validity are the silhouette index, Davies-Bouldin index,<ref>Bolshakova N, Azuaje F (2003) Cluster validation techniques for genome expression data, Signal Processing, Vol. 83, pp. 825–833.</ref> Dunn's index, or Hubert's <math>\Gamma</math> statistic. 
* Class prediction analysis: This approach, called supervised classification, establishes the basis for developing a predictive model into which future unknown test objects can be input in order to predict the most likely class membership of the test objects. Supervised analysis<ref name="Peterson"/> for class prediction involves use of techniques such as linear regression, k-nearest neighbor, learning vector quantization, decision tree analysis, random forests, naive Bayes, logistic regression, kernel regression, artificial neural networks, support vector machines, [[mixture of experts]], and supervised neural gas. In addition, various metaheuristic methods are employed, such as [[genetic algorithm]]s, covariance matrix self-adaptation, [[particle swarm optimization]], and [[ant colony optimization]]. Input data for class prediction are usually based on filtered lists of genes which are predictive of class, determined using classical hypothesis tests (next section), Gini diversity index, or information gain (entropy).
* Hypothesis-driven statistical analysis: Identification of statistically significant changes in gene expression are commonly identified using the [[t-test]], [[ANOVA]], [[Bayesian method]]<ref name="Ben-GalShani2005">{{cite journal|last1=Ben Gal|first1=I.|last2=Shani|first2=A.|last3=Gohr|first3=A.|last4=Grau|first4=J.|last5=Arviv|first5=S.|last6=Shmilovici|first6=A.|last7=Posch|first7=S.|last8=Grosse|first8=I.|title=Identification of transcription factor binding sites with variable-order Bayesian networks|journal=Bioinformatics|volume=21|issue=11|year=2005|pages=2657–2666|issn=1367-4803|doi=10.1093/bioinformatics/bti410|pmid=15797905|doi-access=}}</ref> [[Mann–Whitney test]] methods tailored to microarray data sets, which take into account [[multiple comparisons]]<ref>Yuk Fai Leung and Duccio Cavalieri, Fundamentals of cDNA microarray data analysis. Trends in Genetics Vol.19 No.11 November 2003.</ref> or [[cluster analysis]].<ref name="Priness2007">{{cite journal|author=Priness I.|author2=Maimon O.|author3=Ben-Gal I.|date=2007|title=Evaluation of gene-expression clustering via mutual information distance measure|journal=BMC Bioinformatics|volume=8|issue=1|page=111|doi=10.1186/1471-2105-8-111|pmid=17397530|pmc=1858704 |doi-access=free }}</ref> These methods assess statistical power based on the variation present in the data and the number of experimental replicates, and can help minimize [[type I and type II errors]] in the analyses.<ref name="Wei">{{cite journal|author=Wei C |author2=Li J |author3=Bumgarner RE|date= 2004|title=Sample size for detecting differentially expressed genes in microarray experiments|journal=BMC Genomics|volume=5|pages=87|pmid=15533245|doi=10.1186/1471-2164-5-87|pmc=533874 |doi-access=free }}</ref>
<!-- {{Citation needed|date=July 2008}}as in many other cases where authorities disagree, a sound conservative approach is to directly compare different normalization methods to determine the effects of these different methods on the results obtained. This can be done, for example, by investigating the performance of various methods on data from "spike-in" experiments. {{Citation needed|date=July 2008}} -->
* Dimensional reduction: Analysts often reduce the number of dimensions (genes) prior to data analysis.<ref name="Peterson"/> This may involve linear approaches such as principal components analysis (PCA), or non-linear manifold learning (distance metric learning) using kernel PCA, diffusion maps, Laplacian eigenmaps, local linear embedding, locally preserving projections, and Sammon's mapping.
* Network-based methods: Statistical methods that take the underlying structure of gene networks into account, representing either associative or causative interactions or dependencies among gene products.<ref name="Emmert">{{cite book |author=Emmert-Streib, F.|author2=Dehmer, M.|name-list-style=amp |date=2008 |title=Analysis of Microarray Data A Network-Based Approach |publisher=Wiley-VCH |isbn=978-3-527-31822-3}}</ref> [[Weighted correlation network analysis|Weighted gene co-expression network analysis]] is widely used for identifying co-expression modules and intramodular hub genes. Modules may corresponds to cell types or pathways. Highly connected intramodular hubs best represent their respective modules.

Microarray data may require further processing aimed at reducing the dimensionality of the data to aid comprehension and more focused analysis.<ref>{{cite journal
 | author = Wouters L| author2 = Gõhlmann HW| author3 = Bijnens L| author4 = Kass SU| author5 = Molenberghs G| author6 = Lewi PJ | date = 2003
 | title = Graphical exploration of gene expression data: a comparative study of three multivariate methods
 | journal = Biometrics
 | volume = 59 | pages = 1131–1139
 | doi = 10.1111/j.0006-341X.2003.00130.x
 | pmid = 14969494
 | issue = 4
| citeseerx = 10.1.1.730.3670| s2cid = 16248921}}</ref> Other methods permit analysis of data consisting of a low number of biological or technical [[Replication (statistics)|replicate]]s; for example, the Local Pooled Error (LPE) test pools [[standard deviation]]s of genes with similar expression levels in an effort to compensate for insufficient replication.<ref>{{cite journal
 | author = Jain N| author2 = Thatte J| author3 = Braciale T| author4 =  Ley K| author5 = O'Connell M| author6 = Lee JK | date = 2003
 | title = Local-pooled-error test for identifying differentially expressed genes with a small number of replicated microarrays
 | journal = Bioinformatics
 | volume = 19 | pages = 1945–1951
 | doi = 10.1093/bioinformatics/btg264
 | pmid = 14555628
 | issue = 15
| doi-access = free}}</ref>