Microarray Data Preprocessing and Clustering Analysis
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1 Microarray Data Preprocessing and Clustering Analysis Spotted Microarray WorkshopMicroarray Data Preprocessing and Clustering AnalysisLiangjiang (LJ) WangKSU Bioinformatics Center, Biology DivisionJune, 2005
2 Outline Overview of microarray data analysis. Microarray data preprocessing.Statistical inference of significant genes.Clustering analysis and visualization.Microarray databases and standards.
4 Overview of Microarray Data Analysis Microarray experimentImage analysis and data normalizationSample classificationStatistical inference of significant genesClustering analysis of co-expressed genesList of significant or co-expressed genesPromoter analysis, gene function prediction, and pathway analysis
5 Microarray Image Analysis Spot finding: place a grid to identify spot locations.Segmentation: separate each spot (foreground) from the background.Spot intensity extraction: often use mean or median intensity of all the pixels within a spot.Background subtraction: may subtract local background or globally estimated background.
6 Microarray Data Normalization To remove the systemic bias in the data so that meaningful biological comparisons can be made:Unequal quantities of starting RNA.Differences in labeling (e.g., Cy3 versus Cy5).Different detection efficiencies between the dyes.Differences in hybridization and washing.Other experimental variations.Normalization is based on some assumptions:A subset of genes (housekeeping genes) is assumed to be constant.The total intensity or overall intensity distributions between the two channels are comparable.
7 Global Normalization Total intensity normalization: A normalization factor is calculated by summing the measured intensities in both channels and then taking the ratio:All the intensities in one channel are multiplied by the normalization factor:A subset of genes (housekeeping genes) may be also used for the global normalization.
8 Scatter Plot of Cy3 vs Cy5 Intensities Intensities from “self-self” hybridizationAfter normalizationBefore normalization(Quackenbush, 2001)
9 Lowess NormalizationProbably the most widely used approach for spotted microarray normalization.A locally weighted linear repression is used to estimate the systematic bias in the data.Ratio-Intensity (R-I) plot (also called MA plot)Raw datalog ratio, log2(R / G)(Quackenbush, 2001)After lowesslog ratio, log2(R / G)(Quackenbush, 2001)
10 Why Log Transformation? Log 2 (R / G) treats up-regulated and down-regulated genes in a similar fashion:If R / G = 4, log 2 (R / G) = 2.If R / G = 1/4 = 0.25, log 2 (1/4) = -2.Log normalizes distribution.
11 Finding Significant Genes Fold change: uses a single fold change threshold to select genes; does not take into account the biological and experimental variability.Statistical tests: t test, SAM and ANOVA; require a number of replicates for each condition.
12 Volcano Plot Statistical significance → high (Wolfinger et al., 2001)Larger fold changes does not necessarily mean higher significance levels.
13 Student’s t TestTo test whether there is a significant difference in gene expression measurements between two conditions (A and B):H0: no difference in gene expression,H1: the gene is differentially expressed,Test statistic:Calculate the probability (p value) of the t statistic with degree of freedom, df = nA + nB - 2.Assume a 95% confidence level (i.e., 5% false positive rate). If p ≤ 0.05, reject the null hypothesis.
14 Problem of Multiple Testing Suppose that you have 5,000 genes on your microarray, and you select the genes with p ≤ 0.05 (i.e., 5% false positive rate). Because you have applied 5,000 times of the t test, you may have 5,000 x 0.05 = 250 false positives!
15 Correction for Multiple Testing Bonferroni correction:Set the significance cutoff, p' = α / N, where α is the false positive rate, and N is the number of genes.For example, if you have 5,000 genes in your microarray, and you expect 5% of false positives, the significance cutoff, p' = 0.05 / 5000 = 1.0 E -5.False Discovery Rate (FDR):Rank all the genes by significance (p value) so that the top gene has the most significant p value.Start from the top of the list, and accept the genes ifi: the rank of the gene in the list.N: the number of genes in the array.q: the desired FDR.
16 SAM: Significance Analysis of Microarrays SAM ( is a modified t test.The observed d statistic is computed from the data, and the expected d statistic is assessed by permutation.With a user-defined FDR, SAM derives the significance cutoffs for selecting up- and down-regulated genes.Down-regulatedUp-regulatedExpected d statisticObserved d statisticSAM PlotObserved d = expected dSignificance cutoffs
17 ANOVAANalysis Of VAriance (ANOVA) is used to find significant genes in more than two conditions:For each gene, compute the F statistic.Calculate the p value for the F statistic.Adjust the significance cutoff for multiple testing.GeneDisease ADisease BDisease CA1A2A3B1B2B3C1C2C3g10.91.11.41.220.127.116.11.92.6g18.104.22.168.22.214.171.124.41.5g126.96.36.199.8g42.01.74.03.188.8.131.52∙ ∙ ∙
18 Clustering AnalysisClustering analysis is to partition a dataset into a few groups (clusters) such that:Homogeneity: objects in the samecluster are similar to each other.Separation: dissimilar objects areplaced in different clusters.In microarray data analysis, thismeans to find groups of genes (or samples) with similar gene expression patterns.Two key questions:How to measure similarity of gene expression?How to find these gene clusters?
19 Distance MetricsExpression vector: each gene can be represented as a vector in the N-dimensionalhyperspace, where N is thenumber of samples.Euclidean distance:Vector angle:Pearson correlation coefficient:Sample 1Sample 2Aa2a1Bb2b1dα
20 Z TransformationIf Euclidean distance is used for clustering analysis, z transformation of the gene expression matrix may be necessary.For each gene, calculate the z scores of the expression values:Log (ratio)Samples— Gene A— Gene BdAB = 3.58Z scoreSamples— Gene A— Gene BdAB = 0.36
21 Hierarchical Clustering Initialization: each object is a clusterIterationMerge two clusters which are most similar to each otherUntil all objects are merged into a single clusterbdceaStep 0Step 1Step 2Step 3Step 4a ba b c d ec d ed eAgglomerative approach
22 Hierarchical Clustering (Cont’d) Calculating distances between clusters:Single linkage: takes the shortestdistance between two clusters.Complete linkage: uses the largestAverage linkage: uses the averageThe clustering results are visualized using a tree (called dendrogram) with color-coded gene expression levels.Hierarchical clustering can be applied to genes, samples, or both.CLSLAL
23 Sample ClusteringAlizadeh, et al., Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature, 403:
24 k-Means Clustering Initialization User-defined k (# clusters) Randomly place k vectors(called centroids) in thedata spaceIterationEach object is assigned toits closest centroidRe-compute each centroidby taking the mean ofdata vectors currentlyassigned to the clusterUntil the cluster centroids no longer changeIteration0:1:2:3:k = 2
25 Self-Organizing Map (SOM) The user defines an initial geometry of nodes (reference vectors) for the partitions such as a 3 x 2 rectangular grid.During the iterative “training” process, the nodes migrate to fit the gene expression data.The genes are mapped to the most similar reference vector.
26 k-means SOM 237 genes 194 genes Clustering analysis of a yeast cell cycle time-series datasetk-meansSOM237 genes194 genes
27 Tools for Microarray Data Analysis GenePix ( commercial software for microarray image analysis.GeneSpring ( commercial software for microarray data analysis.TIGR MeV ( free software for clustering, visualization, classification and statistical analysis of microarray data.Bioconductor ( open source, free software for the analysis of genomic data. For microarray data analysis, most of the statistical methods are implemented in R.
28 Microarray DatabasesGene Expression Omnibus (GEO) at NCBI ( a public repository for high throughput gene expression data.ArrayExpress at EBI ( a public repository for microarray gene expression data; MIAME compliant.Stanford Microarray Database (SMD at stores raw and normalized microarray data; provides data retrieval and online data processing.
29 The MIAME StandardMIAME (Minimum Information About a Microarray Experiment) is a microarray data standard proposed by the Microarray Gene Expression Database group (MGED,MIAME ( is needed to interpret the results from a microarray experiment and potentially to reproduce the microarray experiment.MIAME checklist helps authors, reviewers and editors of scientific journals to meet the MIAME requirements and to make microarray data available to the community in a useful way.
30 SummaryImage analysis and data normalization are important preprocessing steps for microarray data analysis.Statistical methods are available for selecting significantly up- or down-regulated genes.Clustering analysis is widely used to explore and visualize microarray data.The resulting significant or co-expressed genes can be further investigated using Gene Ontology annotation and promoter analysis.