Statistical Analysis of

Microarray Data

ByH. Bjørn Nielsen

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

without alcohol with alcohol

alcohol dehydrogenase

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

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

log2 fold change (M)

P-v

alu

e

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

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