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BIOINFORMATICSORIGINAL PAPER

Vol. 27 no. 11 2011, pages 1473–1480

doi:10.1093/bioinformatics/btr183

Genome analysis

BACOM: in silico detection of genomic deletion types and

correction of normal cell contamination in copy number data

Guoqiang Yu1,†, Bai Zhang1,†, G. Steven Bova2,3,4,5,6, Jianfeng Xu7, Ie-Ming Shih3,8

and Yue Wang1,∗

1Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University,

Arlington, VA 22203,2Department of Urology,3Department of Oncology,4Department of Pathology,5Department of

Genetic Medicine,6Department of Health Sciences Informatics, Johns Hopkins University School of Medicine,

Baltimore, MD 21231,7Center for Cancer Genomics, Wake Forest University School of Medicine, Winston-Salem,

NC 27157 and8Department of Gynecology and Obstetrics, Johns Hopkins University School of Medicine, Baltimore,

MD 21231, USA

Associate Editor: Martin Bishop

Advance Access publication April 15, 2011

ABSTRACT

Motivation: Identification of somatic DNA copy number alterations

(CNAs) and significant consensus events (SCEs) in cancer genomes

is a main task in discovering potential cancer-driving genes such

as oncogenes and tumor suppressors. The recent development

of SNP array technology has facilitated studies on copy number

changes at a genome-wide scale with high resolution. However,

existing copy number analysis methods are oblivious to normal

cell contamination and cannot distinguish between contributions

of cancerous and normal cells to the measured copy number

signals. This contamination could significantly confound downstream

analysis of CNAs and affect the power to detect SCEs in clinical

samples.

Results: We report here a statistically principled in silico approach,

Bayesian Analysis of COpy number Mixtures (BACOM), to accurately

estimate genomic deletion type and normal tissue contamination,

and accordingly recover the true copy number profile in cancer

cells. We tested the proposed method on two simulated datasets,

two prostate cancer datasets and The Cancer Genome Atlas

high-grade ovarian dataset, and obtained very promising results

supported by the ground truth and biological plausibility. Moreover,

based on a large number of comparative simulation studies, the

proposed method gives significantly improved power to detect SCEs

after in silico correction of normal tissue contamination. We develop

a cross-platform open-source Java application that implements the

whole pipeline of copy number analysis of heterogeneous cancer

tissues including relevant processing steps. We also provide an R

interface, bacomR, for running BACOM within the R environment,

making it straightforward to include in existing data pipelines.

Availability: The cross-platform, stand-alone Java application,

BACOM, the R interface, bacomR, all source code and the simulation

data used in this article are freely available at authors’ web site:

http://www.cbil.ece.vt.edu/software.htm.

Contact: yuewang@vt.edu

Supplementary Information: Supplementary data are available at

Bioinformatics online.

∗To whom correspondence should be addressed.

†The authors wish it to be known that, in their opinion, the first two authors

should be regarded as joint First Authors.

Received on January 21, 2011; revised on March 23, 2011; accepted

on April 4, 2011

1

DNA copy number change is an important form of structural

variation in the human genome. Somatic copy number alterations

(CNAs) are key genetic events in the development and progression

of human cancers, and frequently contribute to tumorigenesis

(Pollack et al., 2002). The coverage of copy number changes varies

from a few hundred to several million nucleotide bases, and somatic

CNAs in tumors exhibit highly complex patterns. The advance of

oligonucleotide-basedsinglenucleotidepolymorphism(SNP)arrays

provides a high-density and allelic-specific genomic profile and

enables researchers to study copy number changes on a genome-

wide scale. For instance, Affymetrix offers several DNA analysis

arrays for SNP genotyping and copy number variation (CNV)

analysis, and the newest Affymetrix Genome-Wide Human SNP

Array 6.0 features 1.8 million genetic markers, including more than

906600 SNPs and more than 946000 probes for detecting CNVs or

CNAs.

Quantitative analysis of somatic CNAs has found broad

application in cancer research. Although molecular analysis of

tumors in their native tissue environment provides the most accurate

picture of their in vivo state, tissue samples often consist of mixed

cancerandnormalcells,andaccordingly,theobservedSNPintensity

signals are the weighted sum of the copy numbers contributed

from both cancer and normal cells. This tissue heterogeneity

inherited in the measured copy number signals could significantly

confound subsequent marker identification and molecular diagnosis

rooted in cancer cells, e.g. true copy number estimation, consensus

region detection, CNA association studies and detection of loss of

heterozygosityandhomozygousdeletion.Experimentalmethodsfor

minimizing normal cell contamination, such as cell enrichment or

purification, are prohibitively expensive, inconvenient and prone to

errors (Clarke et al., 2008).

Here we ask whether it is possible to computationally correct

normaltissuecontaminationbyestimatingtheproportionsofnormal

and cancer cells and recovering the true copy number profiles of

cancer cells, based on the observed SNP intensity signals from

INTRODUCTION

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cell mixtures. Albeit with limited success, some initial efforts

have been recently made to address the impact of normal tissue

contamination in copy number analysis (Assie et al., 2008; Lamy

et al., 2007; Nancarrow et al., 2007; Peiffer et al., 2006) or to

estimate the fraction of normal cells in tumor samples (Goransson

et al., 2009; Yamamoto et al., 2007). Nancarrow et al. (2007)

developed a visual inspection toolkit that allows users to determine

the presence of stromal contamination. Yamamoto et al. (2007) and

Goranssonetal.(2009)proposedcomputationalmethodstoestimate

the proportion of normal cells by matching to the experimental or

simulated histograms of different mixtures. However, given the fact

that the noise level in the raw copy number data is often quite high

and varies from sample to sample, neither visual inspection nor

simulated histogram matching will be able to produce an accurate

and stable estimate of the fraction of normal cells in the tumor

sample. An additional limitation associated with these methods

is the lack of rigorous statistical principles in driving algorithm

development.

In this study, we report a statistically principled in silico

approach to accurately detect genomic deletion type, estimate

normal tissue contamination and accordingly recover the true copy

number profile in cancer cells. By exploiting the allele-specific

information provided by SNP arrays, we introduce a series of

definitions and theorems to illustrate the detectability and its

conditions, and propose a Bayesian Analysis of COpy number

Mixtures (BACOM) method. The BACOM algorithm is based on

a statistical mixture model for copy number deletion segments

in heterogeneous tumor samples, whose parameters are estimated

using Bayesian differentiation between hemizygous deletion (hemi-

deletion, where one allele is absent) and homozygous deletion

(homo-deletion, where both alleles are absent) and plug-in sample

averaging. Subsequently, the weighted average of estimated normal

tissue fraction coefficients across multiple segments is used to

estimate the true copy numbers rooted in cancer cells across all

loci on the genome.As shown in the Section 4, this method not only

produces cancer-specific copy number profiles but also substantially

improves significant consensus events (SCEs) detection power.

To better serve the research community, we have developed

a cross-platform Java application, which implements the whole

pipeline of copy number analysis of heterogeneous cancer tissues.

The BACOM software instantiates the algorithms described in this

report and other necessary processing steps. To take advantage of

many widely used packages in R to perform DNA copy number

analysisandR’spowerfulandversatilevisualizationcapabilities,we

also provide an R interface, bacomR, that enables users to smoothly

incorporate BACOM into their specific copy number analysis or

to integrate BACOM with other R or Bioconductor packages. We

expect this newly developed software to be a useful tool in routine

copy number analysis of heterogeneous tissues.

2

We first discuss a deletion-focused latent variable model for the copy

numbersignalinheterogeneoustumorsamples.Then,weproposeaBayesian

approach to statistically characterize distinctive copy number signals due

to homo-deletion or hemi-deletion, supported by a novel summary statistic

derived from allele-specific information. Next, we estimate the fraction of

normal cells in the sample based on the deletion type-specific segments,

and subsequently recover the cancer-specific DNA copy number profile.

THEORY AND METHOD

Fig. 1. The flow chart of BACOM.

Figure 1 gives the flowchart of BACOM consisting of three major steps:

(i) inference of deletion types, (ii) estimation of the normal tissue fraction

and (iii) recovery of the copy number profile in cancer cells.

2.1

Supplementary Figure S17 shows SNP array intensity signals that serve as

the raw data to study copy number changes, where observed non-integer

copy numbers suggest the presence of normal cells in the tumor sample.

In heterogeneous tumor samples, the measured array intensity is a mixture

of DNA copy number signals from both normal and cancer cells, given

mathematically by

Copy number signal model

Xi=α×Xnormal,i+(1−α)×Xcancer,i.

(1)

whereXiistheobservedDNAcopynumbersignalatlocusi,αistheunknown

fraction of normal cell subpopulation in the sample and Xnormal,iand Xcancer,i

are the unknown latent DNAcopy number signals in normal and cancer cells

at locus i, respectively. It should be noted that, in model (1), we have chosen

not to consider CNVs in normal cells, because these are much rarer than

CNAs in cancer cells.

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BACOM

Since human somatic cells are diploid, the expected DNA copy number

at locus i in normal cells is two, i.e. E[Xnormal,i]=2. In contrast, if there

is a homo-deletion or hemi-deletion at locus i in cancer cells, then the

expected DNA copy number becomes zero or one, i.e. E[Xcancer,i]=0 or 1.

By focusing on deletion-only CNA loci and taking the expectations on both

sides of Equation (1), we have

?E[Xi]=α×2+(1−α)×0=2α,

Equation (2) indicates that, as a function of normal cell fraction α, the

expected copy number at a deletion locus depends on the deletion type and

is distinctive except when α=1. Inspired by this observation, we propose

to explore a statistically principled solution (detectability): if a Bayesian

hypothesis test can be constructed to differentiate between homo-deletion

and hemi-deletion segments based on allele-specific signals, we could, in

principle, estimate α by the sample average over the deletion segments.

if homo-deletion,

E[Xi]=α×2+(1−α)×1=1+α, if hemi-deletion.

(2)

2.2

Affymetrix SNP chips provide both allele-specific signals (A allele and B

allele) and their summed intensity (observed DNA copy number signal).

If we denote the signals of alleles A and B at locus i by XA,i and XB,i,

respectively, then the observed DNA copy number signal Xiin model (1)

can be rewritten as

Xi=XA,i+XB,i.

To fully exploit allele-specific information readily provided by the SNP

arrays and associated genotype calling algorithms, our method will focus

solely onAB genotype (not consideringAAor BB genotypes). For a length-

L homo/hemi-deletion segment {Xi|i=1,2,···,L}, we make the following

realistic assumption on the allele-specific signals.

Inference of deletion type

(3)

Assumption 1.

1,2,···,L}, each of the allele-specific signals XA,iand XB,iare independently

distributed Gaussian random variables with distinct means but common

variance, σ2, for i=1,2,···,L.

For a length-L homo/hemi-deletion segment {Xi|i=

It should be noted that XA,i and XB,i are not statistically independent

but, rather often correlated, referred to as the cross-talk between alleles A

and B (Bengtsson et al., 2008). Thus, under Assumption 1, the observed

copy number signals Xiare independent and identically distributed random

variables following a normal distribution N(µA+B,σ2

and variance σ2

A+Bcan be readily estimated by using the observed signals Xi

for i=1,2,...,L.

To statistically differentiate between hemi-deletion and homo-deletion,

we define a novel summary statistic, given mathematically by the following

newly defined random variable

A+B) whose mean µA+B

Y =σ−2

A−B

L

?

i=1

(XA,i−XB,i)2,

(4)

where σ2

shown that Y follows either a non-central or a standard χ2distribution,

depending upon the deletion type. We, therefore, present the following two

lemmas with proofs to show that the key parameter associated with these χ2

distributions can be estimated using signals Xi, XA,iand XB,i.

A−Bis the variance of XA,i−XB,i. Under Assumption 1, it can be

Lemma 1. Suppose that, within a length-L hemi-deletion segment, each

of the allele-specific signals XA,i and XB,i are independently distributed

Gaussian random variables with distinct means and common variance.

Then, the summary statistic random variable Y defined in (4) follows an L

degreesoffreedomnon-centralχ2distributionwithnon-centralityparameter

λ=L(2−µA+B)2σ−2

between XA,iand XB,i.

A+B(1+ρ)/(1−ρ), where ρ is the correlation coefficient

Proof. Applying Equation (1) to the loci within a hemi-deletion segment,

where one of the alleles (but not both) is deleted, we have, for i=1,2,...,L

µA−B=E[XA,i−XB,i]

=E[α×(Xnormal,A,i−Xnormal,B,i)

+(1−α)×(Xcancer,A,i−Xcancer,B,i)]

=α×E[Xnormal,A,i−Xnormal,B,i]

+(1−α)×E[Xcancer,A,i−Xcancer,B,i]

=α×(1−1)±(1−α)×(1−0)

=±(1−α),

While from Equation (2), we have µA+B=E[Xi]=1+α which implies

α=µA+B−1.

Thus, µA−Bcan be expressed in terms of µA+Bas

µA−B=±(1−α)=±[1−(µA+B−1)]=±(2−µA+B).

Furthermore, Assumption 1 implies that

i=1,2,···,L.

σ2

A+B=2σ2(1+ρ) and

σ2

A−B=2σ2(1−ρ).

A−Bis a non-trivial task, simple

A−Bcan be expressed in terms of

Although direct estimation of σ2

mathematical manipulation shows that σ2

σ2

A+Bas

σ2

A−B=σ2

A+B(1−ρ)/(1+ρ).

By the definition of the non-centrality parameter λ and Equation (4), we

conclude

?µA−B,i

λ=

L

?

L

?

i=1

σA−B,i

?2

=

i=1

[±(2−µA+B)]2(1+ρ)

σA+B(1−ρ)

=L(2−µA+B)2σ−2

A+B(1+ρ)/(1−ρ).

Accordingly, the conditional L degrees of freedom non-central χ2

distribution of Y under hemi-deletion is given by

⎧

⎪⎩

where ? denotes the Gamma function.

Q.E.D.

χ2(y;L,λ)=

⎪⎨

e−(y+λ)/2

2L/2

∞

?

k=0

yL/2+k−1λk

?(k+L/2)22kk!

for y>0,

0 for y≤0.

(5)

Lemma 2. Suppose that, within a length-L homo-deletion segment, each

of the allele-specific signals XA,i and XB,i are independently distributed

Gaussianrandomvariableswithdistinctmeansandcommonvariance.Then,

the summary statistic random variable Y defined in (4) follows an L degrees

of freedom standard χ2distribution.

Proof. ApplyingEquation (1)tothelociwithinahomo-deletionsegment,

where both alleles are deleted, we have, for i=1,2,...,L

µA−B=E[XA,i−XB,i]

=E[α×(Xnormal,A,i−Xnormal,B,i)

+(1−α)×(Xcancer,A,i−Xcancer,B,i)]

=α×E[Xnormal,A,i−Xnormal,B,i]

+(1−α)×E[Xcancer,A,i−Xcancer,B,i]

=α×(1−1)+(1−α)×(0−0)

=0.

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Thus, Equation (4) implies that, under homo-deletion, the summary

statistic random variable Y defined in (4) follows an L degrees of freedom

standard χ2distribution, given by

⎧

⎩

where ? denotes the Gamma function.

Q.E.D.

χ2(y;L)=

⎨

1

2L/2?(L/2)y(L/2)−1e−y/2

0

for y>0,

for y≤0,

(6)

Lemmas 1 and 2 suggest the possibility of constructing a Bayesian

hypothesis testing strategy to differentiate between the two deletion types

(i.e. hemi-deletion and homo-deletion). The novel and powerful feature of

this approach is that the parameter value of the underlying deletion type-

conditioned probability density function can be readily estimated using the

available signals Xi, XA,i and XB,i without the knowledge of the deletion

type associated with Xi, XA,iand XB,i. Furthermore, having determined the

deletion type-conditioned probability density functions, we can then identify

the deletion type of the segment using Bayesian hypothesis testing. The

conclusion is summarized in the following theorem.

Theorem 1 (deletion-type identifiability). Suppose that, within a length-

L deletion segment, each of the allele-specific signals XA,i and XB,i are

independently distributed Gaussian random variables with distinct means

and common variance. Then, the summary statistic random variable Y =

σ−2

A−B

under homo-deletion, and a non-central L degrees of freedom χ2distribution

under hemi-deletion, with a parameter that can be estimated based on

signalsXA,iandXB,i.Accordingly,thesegmentdeletiontypecanbeoptimally

determined by Bayesian hypothesis testing.

?L

i=1(XA,i−XB,i)2follows an L degrees of freedom χ2distribution

Proof. From Lemma 1, the summary statistic random variable Y under

hemi-deletion follows an L degrees of freedom non-central χ2distribution.

From Lemma 2, the summary statistic random variable Y under homo-

deletion follows an L degrees of freedom standard χ2distribution. Again,

from Lemma 1, we have

λ=L(2−µA+B)2σ−2

A+B(1+ρ)/(1−ρ)

which can be estimated using readily available signals.

Then,astraightforwardapplicationofBayesianhypothesistestingimplies

that the deletion type of the segment can be optimally determined by

?

homo-deletion,if P(hemi-deletion|y)<P(homo-deletion|y),

where P(·|·) denotes the posterior probability of the segment deletion type

given the observed segment signals.

Q.E.D.

hemi-deletion,if P(hemi-deletion|y)≥P(homo-deletion|y),

(7)

2.3

We now complete the description of the BACOM algorithm by considering

the estimation of the model parameters µA+B, σA+Band ρ. Note that µA+B

and σA+B are segment specific. For each segment, they can be readily

estimated from the observed copy number signals by

Implementation of BACOM algorithm

µA+B=1

L

L

?

1

L−1

i=1

Xi,

(8)

σ2

A+B=

L

?

i=1

(Xi−µA+B)2.

(9)

Moreover, we assume that ρ is identical across all the loci within one

subject profile, and hence we conveniently estimate its value based on only

the signals at the Nnormalloci within all normal segments, as given by

Nnormal

?

?Nnormal

i=1

Having determined the parameters of the deletion-type conditional

models, we can infer the type of each deletion segment by applying Bayesian

hypothesistestingbasedon (7).Subsequently,wecanestimatethefractionof

normal cells in the sample specified by (2), i.e., αj=µj−1 for hemi-deletion

and αj=µj/2 for homo-deletion, where µjis the sample average of the copy

number signals of the j-th deletion segment. Moreover, assume that there are

K deletion segments, we can calculate the ensemble estimate of the normal

cell proportion via segment-length weighted average

?K

where Ljis the length of the j-th deletion segment.

Finally, the estimated normal cell fraction can be used to recover the true

copy numbers in cancer cells in the sample. Since Xnormal,i=2 and based on

(1), it is straightforward to estimate the DNA copy number of pure cancer

cells by

ˆXcancer,i=Xi−2α

µA=

i=1

XA,i,µB=

Nnormal

?

i=1

XB,i,

(10)

ρ=

i=1

(XA,i−µA)(XB,i−µB)

(XA,i−µA)2?Nnormal

??Nnormal

i=1

(XB,i−µB)2

.

(11)

α=

j=1αj×Lj

?K

j=1Lj

,

(12)

1−α

.

(13)

3BACOM SOFTWARE

3.1

To better serve the research community, we developed a cross-

platform and open-source BACOM Java application, which

implements the entire pipeline of copy number change analysis

for heterogeneous cancer tissues (Supplementary Material). The

BACOM software instantiates not only the novel algorithms

described here but also other relevant processing steps, including

extraction of raw copy number signals from CEL files,

iterative data normalization, identification of AB loci, copy

number detection and segmentation, probe sets annotation,

differentiation of deletion types, estimation of the normal tissue

fraction and correction of normal tissue contamination. Interested

readers can freely download the software and source code at

http://www.cbil.ece.vt.edu/software.htm.

Stand-alone Java application

3.2

To take advantage of many widely used packages in R and its

associated powerful and versatile visualization capabilities, we

also implemented an R interface, bacomR, that enables users to

smoothly incorporate BACOM into their routine copy number

analysispipelineorintegrateBACOMwithotherRorBioconductor

packages. Users can use their preferred methods to perform

routine tasks such as array normalization and DNA copy number

segmentation and estimation, while using the newly added BACOM

toestimatethenormalcellfractionandsubsequentlyrecoverthetrue

copy number profiles in pure cancer cells.

Running BACOM in R environment

4 RESULTS

4.1

We first consider a realistic synthetic dataset from a mixture of

normal and simulated cancer copy number profiles, as shown in

Simulation studies

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BACOM

AB

Fig. 2. The DNA copy number profile and Bayesian analysis of the deletion segment of the simulation dataset 1 when α=0.7. (A) Copy number profile and

correction results. (B) Bayesian analysis to determine the deletion type of the deletion segment.

Figure 2a.The cancer copy number profile is simulated based on the

real DNA copy number profile of a normal tissue sample assayed

on the Affymetrix Genome-Wide 6.0 SNP array, consisting of

two simulated four-copy amplification segments and one simulated

hemi-deletionsegment.Thenormalandcancercopynumberprofiles

are numerically mixed based on known proportions to produce the

observed copy number signal. Since there is only one deletion

segment (loci 25k∼30k), it is theoretically impossible to tell the

deletion type by examining the observed copy number signal, given

the fact that the cancer copy number signal has been severely

contaminated by a normal copy number signal. The single deletion

inclusion in this dataset has been chosen in order to illustrate the

unsupervised learning ability of BACOM in determining deletion

types.

To determine the deletion type, we first estimate the posterior

probability models of the summary statistic using allele-specific

signals provided by SNP chips, and plot the observed value of the

summary statistic associated with the deletion segment, shown in

Figure 2b. The plot clearly suggests the hemi-deletion type of the

deletion segment. We then estimate the normal tissue fraction in

the sample based on the sample average of the deletion segment α=

µA+B−1.Thisleadstoanestimateofα=0.692andtheaccordingly

corrected cancer copy number profile shown in Figure 2a. The

results show the effectiveness of the BACOM approach in that

the deletion type is correctly determined, the estimated normal

tissue fraction is very close to the true value α=0.7 and the

recovered amplification signals indicate the two expected four-copy

segments.

As an example of a more complex simulation, we consider

a dataset from a mixture of normal and simulated cancer copy

number profiles, as shown in Figure 3a. The cancer copy number

profile includes one homo-deletion, two hemi-deletions and three

different amplification (copy numbers 3, 4 and 5) segments. The

simulated cancer copy number signal, with a total of six altered

copynumbersegments,notonlyretainsthestatisticalcharacteristics

of real SNP array intensity data, but also provides a more complete

picture of copy number alterations and genomic instability in cancer

cells. Once again, the normal and cancer copy number profiles

are numerically mixed based on known proportions to produce the

observed copy number signal. The multiple type-deletion inclusions

in this dataset have been chosen in order to illustrate the consistency

and applicability of BACOM in estimating normal tissue fraction

and cancer-associated copy number alterations.

We first estimate separately the individual normal tissue fractions

αj from one homo-deletion and two hemi-deletion segments,

where the posterior probability models and observed values of the

summary statistic associated with the deletion segments are shown

in Figure 3b. We then use the average value α to recover the

cancer-associated copy number profile, shown in Figure 3a, where

the solid line segments are the recovered cancer-associated copy

number changes. We tested BACOM on six simulation datasets

with different α values, as given in Table 1. The BACOM approach

again achieved very promising results in which the deletion types

are correctly determined, the estimated normal tissue fractions from

different deletion segments are highly consistent, with the average

value very close to the true value and the recovered signals of all six

deletion and amplification segments indicate the expected integer-

valued copy number changes. Table 1 summarizes the experimental

results from all 12 simulated copy number profiles.

4.2

To test the applicability of our proposed method, we consider a

real copy number profile for a prostate cancer sample assayed on

the Affymetrix SNP 500K array. We first applied the BACOM

algorithm to estimate the fraction of normal cell population in

the sample, resulting in α=0.784, which indicates significant

normal tissue contamination. We then used the estimated α value

to recover cancer-specific copy number signal by Equation (13).

The resulting corrected copy number profile for Chromosome 10

is shown in Figure 4, where dotted signals are the mixed copy

number signals arising from the tumor sample with blue-colored

regions being the detected deletion segments, green solid lines are

the normal copy number segments and blue solid lines are the

corrected cancer-specific deletion segments. In this experiment, our

analysis readily reveals and distinguishes both deletion types and

their occurred genomic locations. It is worth noting that BACOM

algorithm identified a homo-deletion segment around locus 18500

in Chromosome 10, that contains the well-known tumor suppressor

gene PTEN.

Analysis of real DNA copy number data

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