Linear models for Microarray analysis

Overview of Limma package for R

• Fits a linear model for each spot (gene)
• An open source software package for the R programming environment
• Focus on normalization and statistical analysis of cDNA microarray gene expression data
• OOP environment for handling information in a microarray experiment
• Statistical analysis approach can be used for Affymetrix microarray experiments

---

Origin

• Written and maintained by Gordon Smyth with contributions From WEHI, Melbourne, Australia
• Software made public at the Australian Genstat Conference, Perth, in Dec 2002
• Became available in the Bioconductor open source bioinformatics project April 2003
• Limma integrates with other Bioconductor software packages, affy, marray, using convert package
• Active development cycle

File:Limma versions.tiff

---

Statistical approach

• Parallel inference for each gene
• Computationally fast/robust
• Handles missing information/use defined flag information
• Linear models are essentially t-statistics for each spot/gene (signal/noise)
• Also makes use of between gene information (moderated t-statistics)

---

Object orientated programming environment

File:OOP.png

• Uploading data into the R programming language automatically populates elements of RGList
  • R (Red foreground)
  • G (Green foreground)
• Foreground intensities range ~ 1 → 65535
  • Rb (Red background)
  • Gb (Green background)
• Background intensities range ~ 1 → 1000
  • genes (Spot annotation list)
  • weights (prior weights weights given to each spot)

• MAList data transformation
  • M = log2(R) - log2(G) (minus)
  • A = (log2(R) + log2(G))/2) (add - abundance)

• Backtransforming to Normalized R', G' values
  • log2(R') = A + M/2
  • log2(G') = A - M/2

---

Advantages using Limma

• Nice organisational framework for handling cDNA expression data using object orientated programming
• Flexible methods to handle weighting of poor quality spots
• Encorporates cDNA normalization routines with a proven track record
• Robust statistical analysis approach

Can analyze cDNA microarray slides possessing large amounts of missing information

• Analysis methods able to encorporate duplicate spots from either technical or biological sources

---

Limitations

• Experiments with different spotting templates cannot easily be combined for analysis
• Statistical analysis cannot pool information together when there are variable numbers of the same replicated spots

Must analyze spot information about the same transcript independently

• Linear models cannot encorporate error model structures from time series designs

---

Microarray workshop experiment

• Dye swap experiment
• Directed graph

File:Dyeswap.png

FileName SlideNumber   Cy3   Cy5 Design
BE34.gpr          34  Leaf Fruit     -1
BE35.gpr          35 Fruit  Leaf      1
BE36.gpr     	  36 Fruit  Leaf      1
BE37.gpr   	  37  Leaf Fruit     -1

• Fruit versus Leaf comparisons M value multipliers -1, 1, 1, -1
• Determining design questions of interest is the hardest part