Correlation Matrix Diagonal Segmentation (CMDS)

A Fast Genome-wide Approach for Identifying Recurrent DNA Copy Number Alterations

across Cancer Patients

Qunyuan Zhang(1), Li Ding(2), Aldi Kraja(1) Ingrid Boreki(1), Michael A. Province(1)

(1)Division of Statistical Genomics, (2)Genome Center

Washington University School of Medicine, USA

IGES, Sept. 2008, St. Louis IGES, Sept. 2008, St. Louis

1

Introduction

DNA copy number alteration (CNA) is one of the significant hallmarks of genomic

abnormality in tumor cells. Identification of recurrent CNA (RCNA) across a cohort of cancer

patients may provide an important insight into the molecular mechanism of oncogenesis

and produce useful information for the diagnosis and treatment of cancers. Most of current

methods for RCNA identification adopt a two-step strategy, which requires discretization

(binarization, segmentation or incontinuous smoothing) for each individual sample’s data

before searching RCNA regions across multiple samples. Although disretization provides

useful CNA pattern or profile for individual samples, it may lose original distribution

information when converting raw continuous signals into discretized data, and therefore

may deteriorate the overall statistical power of RCNA detection. Besides, individual sample

discretization, along with the following multiple sample analysis, may produce in total a

heavy computational burden which could impedes the application, especially in the

genome-wide studies with high density signals and large sample sizes.

2

Purpose

To develop a fast genome-wide approach, Correlation Matrix Diagonal

Segmentation (CMDS), for identifying recurrent DNA copy number alterations

(RCNAs) in large scale genome-wide studies at the population level. The approach

needs no data discretization for individual samples and directly analyzes the raw

data of the entire samples. Here we present:

Statistical power (or receiver operating characteristic, ROC) of CMDS under a

variety of configurations of multiple factors;

Comparison of statistical power and computational efficiency with existing

typical discretization-based approach;

Application of CMDS to real data from the Tumor Sequencing Project (TSP).

3

The CMDS Approach (Rationale)

Due to the copy number (CN) changes in the same chromosomal

region across individuals (slide 6, fig a), RCNA causes co-variation

(or correlations) between chromosomal sites within the

recurrent region, and therefore diagonally forms a correlation

block in the CN correlation matrix of chromosomal sites (slide 6,

fig b). As each correlation block corresponds to a RCNA region,

RCNA can be identified by detecting correlation blocks along the

diagonal of correlation matrix.

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1. Prepare copy number (log2 ratio) data as a n×m matrix (X). n=number of samples,

m=number of chromosomal sites; (see slide 6, fig a)

2. Calculate Pearson’s correlation coefficients between chromosomal sites i and j (rij);

3. Normalize rij through Fisher’s transformation ( ) and obtain

normalized correlation matrix (Z); (see slide 6, fig b)

4. Specify a small square block size b (e.g. b=10) and slide the block along the diagonal of

matrix Z . For each block h, calculate: (see slide 6, fig c)

5. Under the null hypothesis that there is no CNA (i.e. no correlation between chromosomal

sites), will randomly follow a normal distribution with a mean of 0 and a variance of

. Based on this, p-value for each chromosomal block under the null hypothesis can be

calculated and then used to determine the significance of RCNA regions. (see slide 6, fig d)

The CMDS Approach (Procedure)

5

ij

ijij r

rnz

1

1log

2

3

2 1

1)1(

2 bh

hj

bh

jkjkh z

bbz

hz )/(2 2 bb

Illustration of CMDS

a. Raw copy number data of 100 samples and 500 chromosomal sites (red denotes copy number higher than 2)

b. Correlation matrix of 500 sites (white block indicates high correlation RCNA region)

c. Diagonal transformed values

d. Negative log10(P) values for the tests of

6

hz

hz

RCNA region

RCNA region RCNA region

RCNA region

Factors Affecting the Power of CMDS

7

The statistical power of CMDS depends on multiple factors,

including:

Block size (b) chosen for diagonal transformation

Sample size (n)

Frequency of RCNA among population (f)

Amplitude (i.e. copy number) of RCNA region (c)

Total number of chromosomal sites (m) involved in analysis

Number of sites within RCNA region (t)

Expected and Observed Type I errors

Result is based on 1000

replications of simulation

(b=20,n=50,f=0.1,c=3,m=5000,

t=50)

Conclusion: the P value

calculation in CMDS is very

close to the expected, which

allows a quick test without

using re-sampling or

permutation technique.

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ROC Curves of CMDS Under Multiple Configurations

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Simulation parameters:

a) n=50,f=0.1,c=3,m=1000,t=10~

50(random)

b) b=20,f=0.1,c=3,m=1000,t=30

c) b=20,n=50,c=3,m=1000,t=30

d) b=20,n=50,f=0.1,m=1000,t=30

e) b=20,n=50,f=0.1,c=3,m=1000

f) b=20,n=50,f=0.1,c=3,t=30

Results are based on 500

replications of Simulation

TPR: ture positive rate; FPR: false positive rate

Comparison with Other Approach

The figure above shows the ROC curves of CMDS and a typical discretization-based approach, STAC (Diskin et al.,2006). Before STAC analysis, GLAD (Hupe et al., 2004) was used to smooth and discretize individual sample data. Result is based on 500 replications of simulation (b=20; n=50,f=0.1,c=3~4,m=300,t=30)

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PowerComputer Time

GLAD-STAC: 2820 seconds (47 min)CMDS: 15 seconds

Comparison was performed on DELL OPTIPLEX 755 PC. Both GLAD and CMSD were implemented in R 2.5.1, STAC (permutation number= 10000) was run in JAVA (under Windows XP 5.1). The same data set was used (containing 10000 chromosomal sites and 100 samples). In GLAD-STAC analysis, most time was spent by GLAD.

Conclusion: Compared with discretization-based approach, CMDS can obtain higher power with much smaller computer burden.

Application of CMDS

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We apply CMDS to a real data set from the NHGRI Tumor Sequencing

Project (TSP), which contains the DNA copy number data of tumor tissues

from 371 lung cancer (adenocarcinoma) patients, measured by the

Affymetrix Human Mapping 250K STY SNP array. This data set has been

analyzed using another discretization-based method (GISTIC) and

published elsewhere (Weir et al., 2007). It is now publicly available at

www.broad.mit.edu/cancer/pub/tsp/

Our results show that CMDS can identify most of the interesting, important

regions that have been reported previously, as well as some novel,

unreported regions. (see slides 12~15)

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CMDS Analysis of TSP Data (1)

EGFRMYC

Reported regions with interesting candidate oncogenes

13

CCND1KRAS

CMDS Analysis of TSP Data (2)

Reported regions with interesting candidate oncogenes

14

CDK4 NKX2-1,MBIP

CMDS Analysis of TSP Data (3)

Reported regions with interesting candidate oncogenes

15

CMDS Analysis of TSP Data (4)

Unreported novel regions

Summary

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CMDS directly analyses raw copy number (log2 ratio) data at the population level;

CMDS needs no discretization of individual sample data and adopts an easily

implemented and fast diagonal transformation technique, which substantially reduces

the computer burden;

CMDS exploits correlation information between chromosomal sites, which

increases the statistical power of the RCNA identification;

CMDS is particularly suitable for the quick search of RCNA regions through genome-

wide data from large population;

The R code for CMDS analysis (test version, unpublished) can be obtained by E-mail

Qunyuan Zhang qunyuan@wustl.edu

References

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1. Diskin S J et al. (2006) STAC: A method for testing the significance of DNA copy number aberrations across multiple array-CGH experiments. Genome Research, 16:1149–1158.

2. Hupé P et al. (2004) Analysis of array CGH data: from signal ratio to gain and loss of DNA regions. Bioinformatics, 20:3413–3422.

3. Shah S P et al. (2007) Modeling recurrent DNA copy number alterations in array CGH data. Bioinformatics , 23:450–458.

4. Weir B A et al. (2007) Characterizing the cancer genome in lung adenocarcinoma. Nature, 450: 893-898.