1. Statistical Analysis of Microarray DataBy
H. Bjørn Nielsen & Hanne Jarmer

2. The DNA Array Analysis Pipeline
Question
Experimental Design
Array design
Probe design
Sample Preparation
Hybridization
Buy Chip/Array
Image analysis
Normalization
Expression Index
Calculation
Comparable
Gene Expression Data
Statistical Analysis
Fit to Model (time series)
Advanced Data Analysis
Clustering PCA Classification Promoter Analysis
Meta analysis Survival analysis Regulatory Network

3. What's the question? without alcohol with alcohol
Typically we want to identify differentially expressed genes
Example:
alcohol dehydrogenase is expressed at a higher level when alcohol is added to the media
alcohol dehydrogenase
without alcohol
with alcohol

4. Statistics However, the measurements contain stochastic noise
There is no way around it
He’s going to say it
Statistics

5. You can choose to think of statistics as a black box
Noisy
measurements
p-value
statistics
But, you still need to understand how to interpret the results

6. The output of the statistics
P-value
The 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

7. 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!

8. Why not! For two reasons:
We are rarely fulfilling all the assumptions of the statistical test
We have to take multi-testing into account

9. 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)

10. Multi-testing?
In a typical microarray analysis we test thousands of genes
If we use a significance level of 0.05
and we test 1000 genes. We expect 50 genes to be significant by chance
1000 x 0.05 = 50

11. Correction for multiple testing
Bonferroni:
P ≤
0.01 N
Confidence level of 99%
Benjamini-Hochberg:
P ≤ i N
0.01
N = number of genes
i = number of accepted genes

12. 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
The number of genes that are needed or can be handled in downstream processes can be used to set the cutoff
If we permute the samples we can get an estimate of the False Discovery Rate (FDR) in this set

13. Volcano Plot
log2 fold change (M)
P-value

14. What's inside the black box ‘statistics’
t-test or ANOVA

15. The t-test
Calculate T
Lookup T in a table

16. The t-test II The t-test tests for difference in means () wt wt
mut mutant
Intensity
of gene x
Density

17. The t-test III
The t statistic is based on the sample mean and variance t

18. 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

19. ANOVA II Density Intensity Variance between groups
Variance within groups
Density
Intensity

20. 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

21. Paired t-test Block 1 Block 2 Block 3 Hypothesis:
There is no difference between the mean BLUE and RED
Block 1
Block 2
Block 3

22. An example: (2-way ANOVA with blocks)
Experimental Design:
A CreA
Glucose Ethanol Glucose Ethanol 3x
Everything was done in batches to capture the systematic noise

23. Example: Batch to batch variation
Within batch variation is lower than the between batch variation

24. Example: Data analysis - Blocking
We can capture the batch variation by blocking
Two-way ANOVA
Glucose
Ethanol
A CreA
Effect 1
Effect 2
Batch A B C

25. Ex: Result of the 2-way ANOVA (3 p-values)
A genotype p-value
A growth media p-value
An interaction p-value
Two-way ANOVA
Ethanol
Glucose
A CreA
Media effect
Genotype
effect
Batch A B C

26. 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