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Introduction to Statistical Analysis of Gene Expression Data
Feng HongBeespace meetingApril 20, 2005
The Central Dogma
DNA Transcription
RNA Translation
Protein
Source: http://www.accessexcellence.org/
A gene is a sequence of nucleotides that codes for a protein
All cells contain the same gene information in DNA, but only a few genes are expressed in certain cell
The presence of mRNA in a cell indicates that a gene is active;
Microarray Technololgy
http://www.accessexcellence.org/RC/VL/GG/microArray.html
Microarray
Examine how active the thousands of genes are at once
Florescent-dye-labeled mRNA from different samples hybridize to the DNA on the array
Intensity of florescent indicates the expression level of the gene in the sample
Steps in Microarray experiment Experimental Design Signal Extraction
Image Analysis Normalization: remove the artifacts across arrays
Data Analysis Selection of Genes differentially expressed Clustering and classification
Experimental Design
For two-color cDNA experiment, only two sample mRNA can be hybridized on the one array
Factors influencing choice of experimental design Number of different samples Aim of the experiment: which comparisons are of
primary interest Constraint of resources Power of the experiment
Experimental Design Direct Comparison :
compare only two mRNA samples Dye-swap is recommended to minimize the
Reference Sample: Compare several samples with reference Indirect comparison between the samples
Saturated Design More than two MRNA samples All comparison are of interest
Loop Design Used in time couse
More complicated designs
Design used in Whitfield et al.(2003)
Source: Whitfield, Cziko, Robinson, 2003, Gene Expression Profiles in the brain predict behavior in individual honey bees, Science, supplement materials
Gene expression measurements Gene expression data are noisy Source of errors
Microarray manufacturing Preparation of mRNA from biological samples Hybridization Scanning Imaging
Image Analysis
Preprocess the raw scanned image Gridding, edge detection, segmentation,
summarization of pixel intensities Output: foreground intensities (R, G),
background intensities(Rb, Gb), “flagged” spots
Statistical Data Analysis of the data Objective: identifying as many genes that are
differentially expressed across conditions as possible while keeping the probability of making false declarations of expression acceptably low
Software for statistical microarray analysis Generic statistical plat form
SAS Splus R Matlab
Specific packages for microarray data analysis Maanova Bioconductor (www.bioconductor.org): limma, Etc. etc. Our own programs
Visualize data and check quality Look at original image Use MA plot(log fold change vs log intensity)
y-axis: M = log2 (R) - log2 (G) x-axis: A = log2 (R) + log2 (G)
Raw image
MA plot
Normalization “to adjust micro array data for effects which arise from
variation in the technology rather than from biological differences between RNA samples” (Smyth and Speed, 2003)
“an iterative process of visualization, identification of likely artifacts and removal of artifacts when feasible” (Parmgiani et al. 2003)
Two places Within-array normalization Across-array normalization
Method: check MA plot, transform the data: loess transformation, lin-log transformation, etc.
Examples of Normalization
ANOVA (Analysis of Variance)ModelLet yijkg be the fluorescent intensity measured from Array i,
Dye j, Variety k, and Gene g, on the appropriate scale (such as log). A typical analysis of variance (ANOVA) model is:
yijkg = µ + Ai + Dj + Vk + Gg + (AG)ig + (DG)jg + (VG)kg + ijkg
• µ, A, D, V are “normalization” terms• G are the overall gene effects• AG’s are “spot” effects• DG’s are gene-specific dye effects• VG’s are the effects of interest. The capture the expression of
genes specifically attributable to varieties.• is random error
Two stage ANOVA
Global ANOVA model
yijkgr = µ + Ai + Dj + Vk + Gg + (AG)ig + (DG)jg + (VG)kg + εijkg
However, fitting the global model is computationally prohibitive. In stead, breaking the model into two stages
Two stage ANOVA Fit the “normalization model”
yijkg = µ + Ai + Dj + Vk + rijkgr
Fit residuals on per gene basis
rijkr = G + (AG)i + (DG)j + (VG)k + εijk
Report significant genes: Multiple Test Adjustment P-values
P-value = if gene is not differentially expressed, the chance that we will observe more extreme case than what we observed. The smaller p-value, the more significant the result.
If we set the cutoff point at 0.05, and we test on 8000 genes, and assume that none of the gene is differentially expressed, we will expect to declare 400 genes are significant.
adjusted p-values Posterior probability False Discovery Rate (FDR)
FDR = E(#genes falsely declared diff. expr. / # genes decleared diff. expr.)
Ranking the genes
Clustering
After selecting the list of differentially expressed genes, we want to investigate the relationship between these genes
Look at “profile” of gene expressions across the samples
Cluster the selected genes into clusters, genes with similar profiles are clustered together Kmeans Hierarchical clustering
Example of Clustering from Whitfield et al 2003.
Principal Component Analysis Reduce the high dimension data into a small
number of summary variables (principal components).
Use correlation matrix 1st component is the direction along which there is
greatest variation in the data 2nd component is orthogonal to 1st component, which
represent the greatest variation in data after controlling 1st component
Can be used to visually identify clusters or assist classifications. (for example, Whitfield 2003)
Example of PCA
Source: Whitfield, Cziko, Robinson, 2003, Gene Expression Profiles in the brain predict behavior in individual honey bees, Science