Pabio590B – week 1

Microarrays

Overview

Design & hybridization

Data analysis

Overview

Affix/synthesize probes of known sequence to chip

Hybridize with labeled sample

Quantify level of hybridization to each probe

Normalization

Statistics

Clustering & more

Experiments you might do

Measure RNA expression

Changes in gene expression over time / lifecycle

Compare differences between tissues/cell types

Comparisons between species/strains/conditions

Whole genome transcript mapping (tiling arrays)

Measure DNA contentPresence or absence of region

Copy number via Comparative Genomic Hybridization

SNP Genotyping/Re-sequencing

OtherChIP on chip arrays

RIP on chip

Microarray Design

Affix/synthesize probes of known sequence to chip

Hybridize with labeled sample

Quantify level of hybridization to each probe

Normalization

Statistics

Clustering & more

RNA Expression Chip Designs

Expression Array:- N number of probes per gene of interest- Trade-off between accuracy and number of features

Tiling array:- Place probe of X nt every Y bases - Biased vs unbiased

50 nt 50 nt

70 nt tiling window

20 nt

Probe considerations

Number of probes per region of

interest

Specificity of probes

Distance between probes (tiling)

Mismatch probes (Affymetrix)

Hybridization

Affix/synthesize probes of known sequence to chip

Hybridize with labeled sample

Quantify level of hybridization to each probe

Normalization

Statistics

Clustering & more

Two-color vs One-color

Two-color • Two samples one each slide• cy3 - green - 532nm• cy5 - red - 635nm

One-color• One sample per slide• cy3

No significant difference in accuracy or reproducibility

Designs for Two-color Array

Experiment Replicatescy3 cy5WT MuWT MuWT Mu

cy3 cy5WT1 Mu1WT2 Mu2WT3 Mu3

Biological Replicates

Dye Swapscy3 cy5WT MuMu WTWT MuMu WT

cy3 cy5ref Aref Bref Cref Dref Eref F

Common Reference

cy3 cy5A BB CC DD EE FF A

Round Robin

Data Normalization

Affix/synthesize probes of known sequence to chip

Hybridize with labeled sample

Quantify level of hybridization to each probe

Normalization

Statistics

Clustering & more

Within-Array Normalization

Lowess Normalization

Before After

Signal intensity

Cy3

/Cy5

Between-Array Normalization

RNA Spike-in Random Probes Median Scaling Quantile Scaling

Median and quantile normalization are predicated upon the arrays in question having the same distribution. That is to say, if you can safely assume that the bulk of genes have the same expression across the arrays, only then you can use those methods.

Quantile Normalization

Before After

Statistical Analysis

Affix/synthesize probes of known sequence to chip

Hybridize with labeled sample

Quantify level of hybridization to each probe

Normalization

Statistics

Clustering & more

Some Advice About Statistics

Don’t get too hung up on p-values [or any other stat].

Ultimately what matters is biological relevance and external knowledge and other heterogeneous measures (related functions, pathways, other data types) that are not easily measured by statistics alone.

P-values should help you evaluate the strength of the evidence, rather than being used as an absolute yardstick of significance.

Statistical significance is not necessarily the same as biological relevance and vice-versa.

John Quackenbush

Is this gene differentially expressed between the two conditions?

SampleA

SampleB

Pro

be S

igna

l

To rephrase the question

Is the mean probe value different between Samples A & B• Null Hypothesis = H0 = means are the same• Alternate Hypothesis = Ha = means are different

What affects our ability to test the hypothesis?

Difference in means Number of sample points Standard deviations of sample

The T-statistic

Directly proportional to difference in means Inversely proportional to standard deviation Directly proportional to sample size

The T-test calculates how likely the T-statistic is, given the null hypothesis that the means are actually the same.

T-statistic and P-values

P-values can be determined from theoretical distributions or permutation testing

• Theoretical distributions rely on a set of assumptions that array experiments do not necessarily follow

• Permutation tests do not rely on any assumptions

Permutation Testing

GeneA

GeneB

Pro

be S

igna

l

Original

Group1

Group2

Pro

be S

igna

l

Permutation 2

Group1

Group2

Pro

be S

igna

l

Permutation 1

1) Permute n times by random shuffling

2) Calculate T-statistic for each permutation

3) Calculate probability of original T-statistic

Interpreting P-values

T-test tests the null hypothesis that sample means are equal

Gene X has p-value of 5% from T-test 95% chance it is differentially expressed 5% chance that is NOT differentially

expressed

= False Positive Rate = 5%

T-Test Refinements

Equal vs unequal variance of samples

Equal vs unequal sample size Dependant vs independent

samples

CAVEAT:

As sample sizes get smaller, the validity of p-values calculated via permutation diminishes. Microarrays typically have few probes per gene, so sample size is smallish.

Multiple Testing Problem

If there is a 5% chance of false positives in one experiment, what happens when we are testing 10,000 genes. • The majority of those genes are not

differentially expressed, but• a 5% p-value means we will have 500

false-positives.

Family-Wise Error Rate (FWER)

One comparison: FWER = p-value

10,000 comparisons: FWER ~ 1.0

That means that when making 10,000 comparisons you are sure to make at least one error.

FWER is the probability of making one or more false discoveries (type I errors) among all the hypotheses when performing multiple pair-wise tests.

Bonferroni Correction

What if you want to keep the FWER at 5%

• 0.05 / 10,000 = 0.000005 = 5e-6

• Only those genes with T-test p-value of < 5xe-6 are called differentially expressed

• Leads to experiment-wide of 0.05

The Standard Bonferroni correction is considered very conservative

Adjusted Bonferroni

Rank all genes by ascending order of p-value

Assign gene with smallest p-value a corrected p-value of / N (0.5/10,000)

Assign gene with second smallest p-value a corrected p-value of / N-1

Etc…The Adjusted Bonferroni correction is less conservative

False Discovery Rate

Measures the likely number of false positives amongst “discovered” genes

Factors affecting FDR:• Proportion of actual differentially

expressed genes• Distribution of the true differences• Measurement variability• Sample size

Analysis of Variance (ANOVA)

Microarray testing across ≥ 3 conditions

Is a gene expressed equally across all conditions?

F-ratio for given gene X:(variability within conditions) / (variability across

conditions)

Calculate p-value• Look up probability of F-ratio• Determine probability by permutation testing

Significance Analysis of Microarrays (SAM)

Gene-specific T-tests Computes statistic (dj) for each gene j

• measures the relationship between gene expression and a response variable

• describes and groups the data based on experimental conditions

• uses non-parametric statistics

• repeated permutations are used to determine FDR

Accounts for correlations in genes and avoids parametric assumptions about the (normal vs non-normal) distribution of individual genes

Clustering

Affix/synthesize probes of known sequence to chip

Hybridize with labeled sample

Quantify level of hybridization to each probe

Normalization

Statistics

Clustering & more

Why do clustering?

Identify groups of possibly co-regulated genes (e.g. so you can look for common sequence motifs)

Identify typical temporal or spatial gene expression patterns (e.g. cell-cycle data)

Arrange a set of genes in a linear order that is at least not totally meaningless

Can also cluster experiments

Quality control• detect bad/outlying experiments

Identify or categorize classes of biological samples • sorting by tumor sub-type

How you cluster?

Define a distance measure Group genes (or experiments)

based on that measure

Objects are placed into groups. Objects within a group are more similar to each other than objects across groups.

In some cases groups are hierarchically organized based on the intra-group similarity

Distance Metrics

Correlation (X,Y) = 1 Distance (X,Y) = 4

Correlation (X,Z) = -1 Distance (X,Z) = 2.83

Correlation (X,W) = 1 Distance (X,W) = 1.41

Correlation Euclidean

Clustering considerations

Euclidean clustering• Magnitude & direction• ≥ 2 conditions

Correlation clustering • Direction only• ≥ 3 conditions

Array data is noisy, so you probably need multiple data points per condition

Clustering methods• Hierarchical• Partitional• Other

Hierarchical clustering

Initial state - each item is a cluster

Iterate- join two most similar cluster

Stop- when number of clusters reaches user-defined value

Agglomerative, bottom-up method

Linkage methods

Single Link:Similarity of two most similar members

Complete Link:Similarity of two most similar members

Average Link:Average similarity of all members

Ways to determine cluster similarity

Comparing linkage methods

Single AverageComplete

Partitional (K-means) clustering

Partition data into K random clusters

Assign each point to nearest cluster

Calculate centroid of each cluster

GOTO step 2

Divisive, top-down method

Other methods

Support Vector Machines (SVM) K-nearest Neighbor (KNN) Self Organizing Maps (SOM) Self Organizing Tree Algorithm (SOTA) Cluster Affinity Search Technique

(CAST) QT Cluster (QTC) Discriminant Analysis Classifier (DAM) Principal Component Analysis (PCA) Etc.

Warnings and Limitations

Clusters are like statisticsIdeally they mirror reality, but they should only be taken seriously in conjunction with confirmatory data from other sources.

Clustering software clusters thingsIf you tell it to find 4 clusters, it will find 4 clusters in anything!

Garbage In, Garbage OutClustering typically relies on a set of input parameters that can be hard to evaluate except for empirically evaluating the outputs for a given set of input parameters.

Clusters Interpretation - EASE

(Expression Analysis Systematic Explorer)

Population Size: 40 genesCluster size: 12 genes

10 genes, shown in green, have a common biological theme and 8 occur within the cluster

Microarray Analysis Software

TIGR MEVLimmaSAMEDGE

• These software packages are free and open-source

• Each has different strengths/weaknesses and makes different assumptions about your data

$$ Analysis Platforms

Gene Sifter

Rosetta Resolver

Bio Discovery

Microarray Data Sources

Gene Expression Omnibus

(NCBI)

ArrayExpress (EBI)

Stanford Microarray Database

Yale Microarray Database

Microarray Data Standards

Microarray Gene Expression Data Society (MGED)• MIAME• MAGE - OM• MAGE ML

RNA Abundance Database (RAD)• Integrating data from various types of

expression experiments