Statistical Analysis of

Microarray Data

ByH. Bjørn Nielsen & Hanne Jarmer

Sample PreparationHybridization

Array designProbe design

QuestionExperimental Design

Buy Chip/Array

Statistical AnalysisFit to Model (time series)

Expression IndexCalculation

Advanced Data AnalysisClustering PCA Classification Promoter AnalysisMeta analysis Survival analysis Regulatory Network

ComparableGene Expression Data

Normalization

Image analysis

The DNA Array Analysis Pipeline

What's the question?

Typically we want to identify differentially expressed genes

Example: alcohol dehydrogenase is expressed at a higher level when alcohol is added to the media

without alcohol with alcohol

alcohol dehydrogenase

He’s going to say it

However, the measurements contain stochastic noise

There is no way around it

Statistics

Noisymeasurements p-value

statistics

You can choose to think of statistics as a black box

But, you still need to understand how to interpret the results

P-valueThe chance of rejecting the null hypothesis by coincidence----------------------------For gene expression analysis we can say: the chance that a gene is categorized as differentially expressed by coincidence

The output of the statistics

The statistics gives us a p-value for each gene

We can rank the genes according to the p-value

But, we can’t really trust the p-value in a strict statistical way!

Why not!

For two reasons:

1. We are rarely fulfilling all the assumptions of the statistical test

2. We have to take multi-testing into account

The t-test Assumptions

1. The observations in the two categories must be independent

2. The observations should be normally distributed

3. The sample size must be ‘large’(>30 replicates)

Multi-testing?

In a typical microarray analysis we test thousands of genes

If we use a significance level of 0.05and we test 1000 genes. We expect 50 genes to be significant by chance

1000 x 0.05 = 50

Correction for multiple testing

Benjamini-Hochberg:

P ≤ iN 0.01

Bonferroni:

P ≤ 0.01N

N = number of genesi = number of accepted genes

Confidence level of 99%

But really, those methods are too strict

What we can trust is the ability of the statistical test to rank the genes according to their reliability

If we permute the samples we can get an estimate of the False Discovery Rate (FDR) in this set

The number of genes that are needed or can be handled in downstream processes can be used to set the cutoff

log2 fold change (M)

P-value

Volcano Plot

What's inside the black box ‘statistics’

t-test or ANOVA

The t-test

Calculate T

Lookup T in a table

The t-test II

The t-test tests for difference in means ()

Intensityof gene x

Density wt wt mut mutant

t

The t statistic is based on the sample mean and variance

The t-test III

ANOVA

ANalysis Of Variance

Very similar to the t-test, but can test multiple categories

Ex: is gene x differentially expressed between wt, mutant 1 and mutant 2

Advantage: it has more ‘power’ than the t-test

ANOVA II

Intensity

Density

Variance between groups

Variance within groups

Blocks and paired tests

Some undesired factors may influence the experiments, the effect of such can be greatly reduced if they are blocked out or if the experiment is paired.

Some possible blocks: - Dye - Patient - Technician - Batch - Day of experiment - Array

Paired t-test

Hypothesis: There is no difference between the mean BLUE and RED

Block 1

Block 3Block 2

An example: (2-way ANOVA with blocks)

Experimental Design: A187 CreA

Glucose Ethanol Glucose Ethanol

3x

Everything was done in batches to capture the systematic noise

Example: Batch to batch variation

Within batch variation is lower than the between batch variation

Example: Data analysis - Blocking

• We can capture the batch variation by blockingTwo-way ANOVA

Glucose

Ethanol

A187 CreA

Effect 1

Effect 2

Batch A B C

Ex: Result of the 2-way ANOVA(3 p-values)

Two-way ANOVA

Ethanol

Glucose

A187 CreA

Media effect

Genotypeeffect

Batch A B C

A genotype p-valueA growth media p-valueAn interaction p-value

Conclusion

• Array data contains stochastic noise– Therefore statistics is needed to conclude on

differential expression

• We can’t really trust the p-value• But the statistics can rank genes• The capacity/needs of downstream

processes can be used to set cutoff• FDR can be estimated• t-test is used for two category tests• ANOVA is used for multiple categories