Statistical Analysis of cDNA microarrays II
-
Upload
inez-robles -
Category
Documents
-
view
43 -
download
1
description
Transcript of Statistical Analysis of cDNA microarrays II
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Statistical Analysis of cDNA microarrays II
Terry Speed
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Outline
Different types of questions asked in microarray experiments
Cluster analysis
Single gene method
A synthesis
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Gene Expression DataGene expression data on p genes for n samples
Genes
mRNA samples
Gene expression level of gene i in mRNA sample j
=Log( Red intensity / Green intensity)Log(Avg. PM - Avg. MM)
sample1 sample2 sample3 sample4 sample5 …
1 0.46 0.30 0.80 1.51 0.90 ...2 -0.10 0.49 0.24 0.06 0.46 ...3 0.15 0.74 0.04 0.10 0.20 ...4 -0.45 -1.03 -0.79 -0.56 -0.32 ...5 -0.06 1.06 1.35 1.09 -1.09 ...
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Experiments, horses for courses
mRNA levels compared in many different contexts
—Tumour cell lines
—Different tissues, same organism
—Same tissue, different organisms (wt, ko, tg)
—Same tissue, same organism (trt vs ctl)
—Time course experiments
No single method of analysis can be appropriate for all. Rather, each type of experiment requires its own analysis.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Cluster Analysis
Can cluster genes, cell samples, or both.
Strengthens signal when averages are taken within clusters of genes (Eisen).
Useful (essential ?) when seeking new subclasses of cells, tumours, etc.
Leads to readily interpreted figures.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Clusters
Taken from Nature February, 2000Paper by Allzadeh. A et alDistinct types of diffuse large B-cell lymphoma identified by Gene expression profiling,
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Discovering sub-groups
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Which genes have changed?This is a common enough question. We will illustrate one
approach when replicates are available.
GOAL: Identify genes with altered expression in the livers of one line of mice with very low HDL cholesterol levels compared to inbred control mice.
Experiment: Apo AI knock-out mouse model
8 knockout (ko) mice and 8 control (ctl) mice (C57Bl/6).
16 hybridisations: mRNA from each of the 16 mice is labelled with Cy5, pooled mRNA from control mice is labelled with Cy3.
Probes: ~6,000 cDNAs, including 200 related to lipid metabolism.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Which genes have changed?
1. For each gene and each hybridisation (8 ko + 8 ctl), use M=log2(R/G).
2. For each gene form the t statistic:
average of 8 ko Ms - average of 8 ctl Mssqrt(1/8 (SD of 8 ko Ms)2 + (SD of 8 ctl Ms)2)
3. Form a histogram of 6,000 t values.
4. Do a normal Q-Q plot; look for values “off the line”.
5. Adjust for multiple testing.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Histogram
ApoA1
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Plot of t-statistics
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Assigning p-values to measures of change
• Estimate p-values for each comparison (gene) by using the permutation distribution of the t-statistics.
• For each of the possible permutation of the trt / ctl labels, compute the two-sample t-statistics t* for each gene.
• The unadjusted p-value for a particular gene is estimated by the proportion of t*’s greater than the observed t in absolute value.
816( ) =12,870
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Multiple Testing
Problem: We have just performed ~6000 tests!=> need to control the family-wise false positive rate (Type I
error).=> use adjusted p-values.
Bonferroni adjustment. Multiply p-values by number of tests.
Too conservative, doesn’t take into account the dependence structure between the genes.
Westfall & Young. Estimate adjusted p-values using the permutation distribution of statistics which take into account the dependence structure between the genes. Less conservative.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Apo A1: Adjusted and Unadjusted p-values for the 50 genes with the larges absolute t-statistics.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Apo AI. Genes with adjusted p-value < 0.01
Gene Adjustedp
t Num Den
ApoAI 0.00 -22.85 -3.19 0.14
Sterol C5-desaturase 0.00 -13.14 -1.06 0.08
Catechol O-methyltransferase
0.00 -12.21 -1.90 0.16
Apo CIII 0.00 -11.88 -1.02 0.09
ApoAI 0.00 -11.44 -3.09 0.27
EST 0.00 -9.11 -1.02 0.11
Apo CIII 0.00 -8.36 -1.04 0.12
Sterol desaturase 0.01 -7.72 -1.04 0.13
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
LimitationsCluster analyses:
1) Usually outside the normal framework of statistical inference;
2) less appropriate when only a few genes are likely to change.
3) Needs lots of experiments
Single gene tests:
1) may be too noisy in general to show much
2) may not reveal coordinated effects of positively correlated genes.
3) hard to relate to pathways.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
A synthesis
We and others (Stanford) are working on methods which try to combine the best of both of the preceding approaches.
Try to find clusters of genes and average their responses to reduce noise and enhance interpretability.
Use testing to assign significance with averages of clusters of genes as we did with single genes.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Clustering genes
1 2 3 4 5
Cluster 6=(1,2)
Cluster 7=(1,2,3)Cluster 8=(4,5)
Cluster 9= (1,2,3,4,5)
Let p = number of genes.
1. Calculate within class correlation.
2. Perform hierarchical clustering which will produce (2p-1) clusters of genes.
3. Average within clusters of genes.
4 Perform testing on averages of clusters of genes as if they were single genes.
E.g. p=5
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Data - Ro1Transgenic mice with a modified Gi coupled receptor (Ro1).
Experiment: induced expression of Ro1 in mice.
8 control (ctl) mice
9 treatment mice eight weeks after Ro1 being induced.
Long-term question: Which groups of genes work together.
Based on paper: Conditional expression of a Gi-coupled receptor causes ventricular conduction delay and a lethal cardiomyopathy, see Redfern C. et al. PNAS, April 25, 2000.
http://www.pnas.org also
http://www.GenMAPP.org/ (Conklin lab, UCSF)
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Histogram
Cluster of genes(1703, 3754)
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Top 15 averages of gene clusters
-13.4 7869 = (1703, 3754)
-12.1 3754
11.8 6175
11.7 4689
11.3 6089
11.2 1683
-10.7 2272
10.7 9955 = (6194, 1703, 3754)
10.7 5179
10.6 3916
-10.4 8255 = (4572, 4772, 5809)
-10.4 4772
-10.4 10548 = (2534, 1343, 1954)
10.3 9476 = (6089, 5455, 3236, 4014)
Might be influenced by 3754
1 0.7 0.7
0.7 1 0.8
0.7 0.8 1
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
Correlation1 0.5 0.5
0.5 1 0.8
0.5 0.8 1
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
T Group ID
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Limitation
Hard to extend this method to negatively correlated clusters of genes. Need to consider together with other methods.
Need to identify high averages of clusters of genes that are due to high averages from sub-clusters of those genes.
Department of Statistics, University of California, Berkeley , and Division of Genetics and Bioinformatics, Walter and Eliza Hall Institute of Medical Research
Acknowledgments
Yee Hwa YangYee Hwa Yang
Sandrine DudoitSandrine Dudoit
Natalie RobertsNatalie Roberts
Ben BolstadBen Bolstad
Ingrid LonnstedtIngrid Lonnstedt
Karen VranizanKaren Vranizan
WEHI Bioinformatics groupWEHI Bioinformatics group
Matt Callow (LBL)
Bruce Conklin (UCSF)