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Spotted Microarray Workshop
Microarray Data Preprocessing and
Clustering Analysis
Liangjiang (LJ) Wang
[email protected]
KSU Bioinformatics Center, Biology Division
June, 2005
Outline
• Overview of microarray data analysis.
• Microarray data preprocessing.
• Statistical inference of significant genes.
• Clustering analysis and visualization.
• Microarray databases and standards.
Spotted Microarray
Reference Cells
Experimental Cells
Extract mRNA
Make and
label cDNA
Genes
Samples
Gene
expression
matrix
(ratios)
Array image data
Hybridize
Probes
Overview of Microarray Data Analysis
Microarray
experiment
Image analysis and
data normalization
Statistical inference
of significant genes
Sample
classification
Clustering analysis of
co-expressed genes
List of significant or
co-expressed genes
Promoter analysis, gene function
prediction, and pathway analysis
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.
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.
Global Normalization
• Total intensity normalization:
– A normalization factor is calculated by summing
the measured intensities in both channels and
then taking the ratio:
N
Ri

i 1
 
N
i 1 Gi
– All the intensities in one channel are multiplied by
the normalization factor:
Gi  Gi and Ri  Ri
• A subset of genes (housekeeping genes) may be
also used for the global normalization.
Scatter Plot of Cy3 vs Cy5 Intensities
Intensities from “self-self” hybridization
After normalization
Before normalization
(Quackenbush, 2001)
Lowess Normalization
• Probably 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)
(Quackenbush, 2001)
(Quackenbush, 2001)
After lowess
log ratio, log2(R / G)
log ratio, log2(R / G)
Raw data
0
Mean log intensity,
1
2
log 10 ( R * G)
0
Mean log intensity,
1
2
log 10 ( R * G)
Why Log Transformation?
• Log 2 (R / G) treats up-regulated and downregulated 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.
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.
Statistical significance → high
Volcano Plot
(Wolfinger et al., 2001)
Larger fold changes does not necessarily mean higher significance levels.
Student’s t Test
• To test whether there is a significant difference in
gene expression measurements between two
conditions (A and B):
– H0: no difference in gene expression, X A  X B
– H1: the gene is differentially expressed, X A  X B
• Test statistic:
t
XA  XB
d

XA  XB
 A2
nA

 B2
nB
• 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.
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!
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 if
i
p
q
N
i: the rank of the gene in the list.
N: the number of genes in the array.
q: the desired FDR.
SAM: Significance Analysis of Microarrays
• SAM (http://www-stat.stanford.edu/~tibs/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.
SAM Plot
Observed d statistic
Up-regulated
Observed d
= expected d
Significance
cutoffs
Down-regulated
Expected d statistic
ANOVA
• ANalysis Of VAriance (ANOVA) is used to find
significant genes in more than two conditions:
Disease A
Disease B
Disease C
Gene
A1
A2
A3
B1
B2
B3
C1
C2
C3
g1
0.9
1.1
1.4
1.9
2.1
2.5
3.1
2.9
2.6
g2
4.2
3.9
3.5
5.1
4.6
4.3
1.8
2.4
1.5
g3
0.7
1.2
0.9
1.1
0.9
0.6
1.2
0.8
1.4
g4
2.0
1.2
1.7
4.0
3.2
2.8
6.3
5.7
5.1
∙∙∙
∙∙∙
∙∙∙
∙∙∙
∙∙∙
∙∙∙
∙∙∙
∙∙∙
∙∙∙
∙∙∙
• For each gene, compute the F statistic.
• Calculate the p value for the F statistic.
• Adjust the significance cutoff for multiple testing.
Clustering Analysis
• Clustering analysis is to partition a dataset into a
few groups (clusters) such that:
– Homogeneity: objects in the same
cluster are similar to each other.
– Separation: dissimilar objects are
placed in different clusters.
• In microarray data analysis, this
means 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?
Distance Metrics
Sample 2
• Expression vector: each gene can be represented as
a vector in the N-dimensional
hyperspace, where N is the
B
number of samples.
b2
• Euclidean distance:
d
2
(
a

b
)
i 1 i i
N
• Vector angle:

N

N
2
a
i 1 i
α
a1
ab
i 1 i i
cos  
A
a2
d

b1
Sample 1
N
2
b
i 1 i
• Pearson correlation coefficient:


N
i 1

N
i 1
(ai  a)(bi  b)
(ai  a)
2

N
i 1
(bi  b)
,
2
  [1, 1].
Z Transformation
• If 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:
x
— Gene A
— Gene B
— Gene A
— Gene B
Z score
Log (ratio)
z xi 
xi  x
dAB = 3.58
Samples
dAB = 0.36
Samples
Hierarchical Clustering
Initialization: each object is a cluster
Iteration
Merge two clusters which are most similar to each other
Until all objects are merged into a single cluster
a
ab
b
abcde
c
cde
d
de
Agglomerative
approach
e
Step 0
Step 1
Step 2
Step 3
Step 4
Hierarchical Clustering (Cont’d)
• Calculating distances between clusters:
– Single linkage: takes the shortest
distance between two clusters.
CL
– Complete linkage: uses the largest
distance between two clusters.
– Average linkage: uses the average
distance between two clusters.
SL
AL
• The 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.
Sample
Clustering
Alizadeh, et al.,
2000. Distinct
types of diffuse
large B-cell
lymphoma
identified by
gene expression
profiling. Nature,
403:503-511.
k-Means Clustering
Initialization
Iteration
User-defined k (# clusters)
Randomly place k vectors
(called centroids) in the
data space
Iteration
Each object is assigned to
its closest centroid
Re-compute each centroid
by taking the mean of
data vectors currently
assigned to the cluster
Until the cluster centroids no
longer change
0:
1:
2:
3:
k=2
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.
Clustering analysis of a yeast cell cycle time-series dataset
k-means
237 genes
SOM
194 genes
Tools for Microarray Data Analysis
• GenePix (http://www.axon.com/GN_GenePixSoftware.html):
commercial software for microarray image analysis.
• GeneSpring
(http://www.silicongenetics.com/cgi/SiG.cgi/Products/GeneSpring/index.smf):
commercial software for microarray data analysis.
• TIGR MeV (http://www.tm4.org/mev.html): free
software for clustering, visualization, classification
and statistical analysis of microarray data.
• Bioconductor (http://www.bioconductor.org/): open
source, free software for the analysis of genomic
data. For microarray data analysis, most of the
statistical methods are implemented in R.
Microarray Databases
• Gene Expression Omnibus (GEO) at NCBI
(http://www.ncbi.nlm.nih.gov/geo/): a public repository
for high throughput gene expression data.
• ArrayExpress at EBI (http://www.ebi.ac.uk/arrayexpress/):
a public repository for microarray gene expression
data; MIAME compliant.
• Stanford Microarray Database (SMD at
http://genome-www5.stanford.edu/): stores raw and
normalized microarray data; provides data retrieval
and online data processing.
The MIAME Standard
• MIAME (Minimum Information About a Microarray
Experiment) is a microarray data standard
proposed by the Microarray Gene Expression
Database group (MGED, http://www.mged.org/).
• MIAME (http://www.mged.org/Workgroups/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.
Summary
• Image 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.