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