Gene Expression Data Analysis II

Yan Cui (ycui2@uthsc.edu)

The address of this webpage:

http://compbio.uthsc.edu/microarray/lecture2.htm

Two Algorithms for Identifying Differentially Expressed Genes

1. T-Test

2. SAM: Significance Analysis of Microarray Data

Differential gene expression

Each cell of an organism contains a complete copy of the organism's genome.

Cells are of many different types and states, e.g. blood, nerve, and skin cells, dividing cells, etc.

What makes the cells different?

Differential gene expression, i.e., when, where, and in what quantity each gene is expressed.

(Statistics for Microarray Data Analysis by Terry Speed)

The differentially expressed genes are the genes whose expression levels are significantly different between two groups of experiments (or samples).

3. Calculate the observed t-statistic for each gene

, where

The idea is to compare between-group difference (the numerator) and within-group difference (the denominator).

4. Calculate probability value (p-value) of the t-statistic for each gene from t-distribution.

The output of the analysis: A p-value for each gene. The p-value is the chance of getting the t-statistic as large as, or larger than the observed one, under the hypothesis of no differential expression (null hypothesis). A small p-value indicates that the hypothesis of no differential expression is not true and the gene is differentially expressed.

SAM: Significance Analysis of Microarray Data

The purpose of this analysis is also to pick out genes whose expression level is significantly different between two groups of samples.

3. For each gene, compute d-value (analogous to t-statistic).

This is the observed d-value.

Theterm is here to deal with cases when the variance gets too close to zero (numerically stable).

(Adapted from “SAM: Significance Analysis of Microarray Data” by Paul Delmar)

4. Randomly shuffle the values of the gene between groups A and B, such that the reshuffled groups A and B respectively have the same number of elements as the original groups A and B. Compute the d-value for each randomized grouping:

Repeat step 4 many times, so that each gene has many randomized d-values. Take the average of the randomized d-values for each gene. This is the expected d-value of that gene.

The program plots the observed d-values vs. the expected d-values (horizontal axis = the expected d-values, vertical axis = observed d)

It is a very interactive algorithm – allows users to dynamically change thresholds for significance (through the tuning parameter delta) after looking at the distribution of the d-value.

(Adapted from documentation of MeV, http://www.tigr.org/software/tm4/mev.html)

Perform T-test and SAM analysis with MeV

Data File: Stanford_Large.txt

TTEST: T-test

Specify Options:

The Expression Image of the Significant Genes:

Click on the header of a column to sorting rows in ascending order based on the contents of the column

SAM: Significance Analysis of Microarray Data

Specify Options:

SAM Graph:

Significant Genes:

Further Reading

1. Pan, W. (2002) A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments. Bioinformatics 2002 18: 546-554. (http://bioinformatics.oupjournals.org/cgi/reprint/18/4/546.pdf)

2. Cui, X. and Churchill, G.A. (2003) Statistical tests for differential expression in cDNA microarray experiments. Genome Biology 4:210. (http://www.pubmedcentral.gov/picrender.fcgi?artid=154570&blobtype=pdf)

3. Stockburger D.W., The t distribution, http://www.psychstat.missouristate.edu/introbook/sbk24.htm

Gene Expression Databases

Stanford Microarray Database

Gene Expression Omnibus

Homework

Due Date: Wednesday, February 22. Submit to Dr. Yan Cui via email (ycui2@uthsc.edu). The solution will be posted here on February 23.

Data: Download the dataset from http://compbio.uthsc.edu/MSCI814/Homework2.txt (Right click on the link and select Save Target As). The dataset contains gene expression profiles of 8 breast cancer samples (BC1-8) and 8 ovarian cancer samples (OC1-8).

Identify the genes that are differentially expressed between the two groups (8 breast cancer samples vs. 8 ovarian cancer samples) using:

1. T-test

a. How many significant genes are identified using the default options?

b. Which gene has the smallest p-value?

2. SAM

a. Set the delta value = 1.0, how many significant genes are identified? What is the median number of false significant genes?