1. Linear Models for Microarray Data
LIMMA
Linear Models for Microarray Data

2. Difficulties with microarray data
Variability of the expression values differs between genes
Non-identical and dependent distribution between genes
Multiple testing of tens of thousands of genes

3. Correct for multiple comparisons
Multiple testing - Family-wise error rate
- False Discovery Rate etc.
Parallel nature of the inference allows for compensating possibilities
Borrowing information from the ensemble of genes to assist in inference from individual genes

4. Empirical Bayes
Frequentist methods, a hypothesis is typically rejected or not rejected without directly assigning a probability
Bayesian methods, specifies some prior probability, which is then updated in the light of new data.
For Bayesian techniques, the prior distribution is assigned independent of the data and fixed before any data is observed.

5. Empirical Bayes
Superficially similar to Bayesian methods in that a prior distribution is assigned.
However, prior distribution is estimated from the data
Therefore Empirical Bayes is a frequentist technique

6. LIMMA
Empiricial Bayes techniques have previously been applied to microarray data
Analysis specific to experiment and very difficult to implement
LIMMA - Simple model with simple expression of posterior odds
Allows linear modelling to be applied to microarray data

7. Estrogen Data
2x2 factorial experiment on MCF7 breast cancer cells using Affymetrix HGU95av2 arrays
Factors : Estrogen (Presence/Absence)
Length of exposure (10hr/48hr)
The idea of the study is to identify genes that respond to estrogen treatment

8. Read in the Data Load in the estrogen data Normalise the data
Define the targets (factors) for the linear model

9. Design Matrix Eight arrays Four pairs of replicates
1 low10-1.cel absent 10
2 low10-2.cel absent 10
3 high10-1.cel present 10
4 high10-2.cel present 10
5 low48-1.cel absent 48
6 low48-2.cel absent 48
7 high48-1.cel present 48
8 high48-2.cel present 48
Eight arrays
Four pairs of replicates
Four parameters in the linear model

10. Contrast Matrix Estrogen effect at 10 hours
1 low10-1.cel absent 10
2 low10-2.cel absent 10
3 high10-1.cel present 10
4 high10-2.cel present 10
5 low48-1.cel absent 48
6 low48-2.cel absent 48
7 high48-1.cel present 48
8 high48-2.cel present 48
Estrogen effect at 10 hours
Time effect without estrogen
Estrogen effect at 48 hours

11. Differential Expression
Extract linear model fit for contrasts
Obtain list of differentially expressed genes for contrasts
Look for overlap among differentially expressed genes

12. Linear Model Fit
logFC - Estimate of the log2-fold-change corresponding to the effect or contrast
AveExpr - Average log2-expression for the probe over all arrays/channels
t - moderated t-statistic
P.Value - Raw p-value
adj.P.Value -Adjusted p-value
B - log odds that the gene is differentially expressed

13. Annotating Data Probe arrays can be annotated with external data
Multiple sources of gene annotations

14. Gene Set Enrichment
All biochemical pathways are determined by sets of genes
Gene sets are determined by prior biological knowledge relating to co-expression, function, location or known biochemical pathways.
If a pathway is in any way related to a biological trait then the co-functioning genes should display a higher degree of enrichment compared to the rest of the transcriptome.
Gene Set Enrichment (GSE) is a computational technique which determines whether a priori defined set of genes show statistically significant overlap

16. Estrogen receptor (ER) gene set
If estrogen is present, ER genes will bind the estrogen and become activated
Gain ability to regulate gene expression and result in differential expression between the cells with and without estrogen
Should lead to up regulation of ER genes