Introduction to Microarrays

Kellie J. Archer, Ph.D.Assistant Professor

Department of Biostatisticskjarcher@vcu.edu

Microarrays

A snapshot that captures the activity pattern of thousands of genes at once.  

Custom spotted arrays Affymetrix GeneChip

Spotted Microarray Process

CTRL

TEST

Affymetrix GeneChip® Probe Arrays

24µm

Each probe cell or feature containsmillions of copies of a specificoligonucleotide probe

Image of Hybridized Probe Array

Over 250,000 different probes complementary to geneticinformation of interest

Single stranded, fluorescentlylabeled DNA target

Oligonucleotide probe

* **

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1.28cm

GeneChip Probe Array Hybridized Probe Cell

BGT108_DukeUniv

Applications of microarrays

• Cancer research: Molecular characterization of tumors on a genomic scale; more reliable diagnosis and effective treatment of cancer

• Immunology: Study of host genomic responses to bacterial infections

• Model organisms: Multifactorial experiments monitoring expression response to different treatments and doses, over time or in different cell types

• etc.

Applications of Microarrays

• Compare mRNA transcript levels in different type of cells, i.e., vary– Tissue (liver vs. brain);– Treatment (Drugs A, B, and C);– State (tumor vs. normal);– Organism (yeast, different strains);– Timepoint;– etc.

Affymetrix Design

PM

MM

GCGCCGGCTGCAGGAGCAGGAGGAG

GCGCCGGCTGCACGAGCAGGAGGAG

11 – 20 Probe Pairs interrogate each gene

Image Analysis: Pixel Level Data

6 x 6 matrix of pixels for each PM and MM probeHG-U133A GeneChip

Expression Quantification

PM

MM

GCGCCGGCTGCAGGAGCAGGAGGAG

GCGCCGGCTGCACGAGCAGGAGGAG

PM and MM intensities are combined to form an expression measure for the probe set (gene)

Expression Quantification• Initially, Affymetrix signal was calculated as

where j indexes the probe pairs for each probe set A. This is known as the “Average Difference” method.

• Problems: – Large variability in PM-MM – MM probes may be measuring signal for another

gene/EST– PM-MM calculations are sometimes negative

Expression Quantification

• The mean of a random variable X is a measure of central location of the density of X.

• The variance of a random variable is a measure of spread or dispersion of the density of X.

• Var(X)=E[(X-)2] =E(X2) - 2

• Standard deviation = =

Var(X)

Expression QuantificationIllustration:

Average Difference.xls

Sources of Obscuring Variation in Microarray

Measurements • Sample handling (degree of physical manipulation, time from extripation to freezing)

• Microarray manufacture • Sample processing (extraction procedure, RNA

integrity & purity, RNA labeling) • Processing differences (hybridization chambers,

washing modules, scanners)• Personnel differences • Random differences in signal intensity in a data

set which co vary with the biological process

Normalization• The purpose of normalization is to remove

experimental artifacts of no direct interest, that is, the removal of systematic effects other than differential expression. Normalization procedures often include – background subtraction, – detection of outliers, – and removal of variation due to

• differences in sample preparation, • array differences, • differences in dye labeling efficiencies,

• and scanning differences.

16 Replicate HG-133A GeneChips, Before normalization

16 Replicate HG-133A GeneChips, After normalization

Taxonomy of Microarray Data Analysis Methods

• Unsupervised Learning: The statistical analysis seeks to find structure in the data without knowledge of class labels.

• Supervised Learning: Class or group labels are known a priori and the goal of the statistical analysis pertains to identifying differentially expressed genes (AKA feature selection) or identifying combinations of genes that are predictive of class or group membership.

Unsupervised Learning• Unsupervised learning or clustering involves the

aggregation of samples into groups based on similarity of their respective expression patterns without knowledge of class labels.

• Examples of Unsupervised Learning methods include– Hierarchical clustering– k-means– k-medoids– Self Organizing Maps– Principal Components– Multidimensional Scaling

Supervised Learning• Example methods for Class comparison/ Feature

selection include– T-test / Wilcoxon rank sum test– F-test / Kruskal Wallis test– etc.

• Example methods for Class Prediction include– Weighted voting– K nearest neighbors– Compound Covariate Predictors– Classification trees– Support vector machines– etc.

Supervised Learning: Class Prediction

• Risk of over-fitting the data: may have a perfect discriminator for the data set at hand but the same model may perform poorly on independent data sets.

• Most prediction methods are intended for large ‘n’ (samples) small ‘p’ (covariates) datasets.

• Process is to– Fit model– Check model adequacy– Make an inference

Class Prediction: Checking model Adequacy

• Regardless of algorithm used, it is essential that once the prediction rule has been defined, an unbiased estimate of the true error rate must be calculated.

Class Prediction: Checking Model Adequacy

• In a data rich situation,– randomly divide the dataset into two

parts, representing a training and test dataset.

– Build the prediction algorithm using the training dataset

– Once a final model has been developed, the prediction rule is applied to the test dataset to estimate the misclassification error

Class Prediction: Checking Model Adequacy

• For small sample sizes, withholding a large portion of the data for validation purposes may limit the ability of developing a prediction rule. Therefore, use cross-validation techniques to assess the error.

Class Prediction: Checking Model Adequacy

• K-fold cross-validation requires one to randomly split the dataset into K equally sized groups.

• Thereafter, the model is fit to K-1 parts of the data and the generalization error is calculated using the Kth remaining part of the data.

• This procedure is repeated so that the generalization error is estimated for each of the K parts of the data, providing an overall estimate of the generalization error and its associated standard error.

Class Prediction: Checking Model Adequacy

1 2 3 4 5 6 7 8 9 10

• Leave out data in group 3• Fit the model to the data in groups 1 – 2, 4 – 10 (learning dataset)• Calculate the error using observations in group 3 as the test dataset• Do this for each of the 10 partitions