Mermel CH, Schumacher SE, Hill B, Meyerson ML, Beroukhim R, Getz GGISTIC2.0 facilitates sensitive and confident localization of the targets of focal somatic copy-number alteration in human cancers. Genome Biol 12: R41

Cancer Program, The Broad Institute of MIT and Harvard, 7 Cambridge Center, Cambridge, MA 02142, USA.
Genome biology (Impact Factor: 10.81). 04/2011; 12(4):R41. DOI: 10.1186/gb-2011-12-4-r41
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We describe methods with enhanced power and specificity to identify genes targeted by somatic copy-number alterations (SCNAs) that drive cancer growth. By separating SCNA profiles into underlying arm-level and focal alterations, we improve the estimation of background rates for each category. We additionally describe a probabilistic method for defining the boundaries of selected-for SCNA regions with user-defined confidence. Here we detail this revised computational approach, GISTIC2.0, and validate its performance in real and simulated datasets.


Available from: Steven Schumacher, Dec 04, 2014
MET H O D Open Access
GISTIC2.0 facilitates sensitive and confident
localization of the targets of focal somatic
copy-number alteration in human cancers
Craig H Mermel
, Steven E Schumacher
, Barbara Hill
, Matthew L Meyerson
, Rameen Beroukhim
and Gad Getz
We describe methods with enhanced power and specificity to identify gen es targeted by somatic copy-number
alterations (SCNAs) that drive cancer growth. By separating SCNA profiles into underlying arm-level and focal
alterations, we improve the estimation of background rates for each category. We additionally describe a
probabilistic method for defining the boundaries of selected-for SCNA regions with user-defined confidence. Here
we detail this revised computational approach, GISTIC2.0, and validate its performance in real and simulated
somatic genetic alterations, including point mutations,
copy-number changes, and fusion events , that affect the
function of critical genes regulating cellul ar growth and
survival [1]. The identifica tion of oncogen es and tumor
suppressor genes being targeted by these alterati ons ha s
greatly acceler ated progress in both the understanding
of cancer pathogenesis and the identification of novel
therapeutic vulnerabilities [2]. Genes targeted by somatic
copy-number alterations (SCNAs), in particular, play
central roles in oncogenesis and cancer therapy [3]. Dra-
matic improvements in both array and sequencing plat-
forms have enabled increasingly high-resolution
characterization of the SCNAs present in thousands of
cancer genomes [4-6].
However, the discovery of new cancer genes being tar-
geted by SCNAs is complicated by two fundamental
challenges. First, somatic alteratio ns are acquired at ran-
dom during each cell division, only some of which (dri-
ver alterations) promote cancer development [7].
Selectively neutral or weakly deleterious passenger
alterations may nonetheless become fixed whenever a
subclone ca rrying such alterations acquires selectively
benefic ial mutations that promote clonal dominance [8].
sands of genes, but the selective benefits of driver altera-
tions are likely to be mediated by only one or a few of
these genes. For these reasons, additional analysis and
experimentation is required to distinguish the drivers
from the passengers, and to identify the genes they are
likely to target.
A common approach to identifying driv ers is to study
large collections of cancer samples, on the n otion that
regions containing driver events should be altered at
higher frequencies than regi ons containi ng only passen-
gers [4,6,7,9-14]. For example, we developed an algo-
rithm, GISTIC (Genomic Identification of Significant
Targets in Cancer) [15], that identifies likely driver
SCNAs by evaluating the frequency and amplitude of
observed events. GISTIC has been applied to multiple
cancer types, including glioblastoma [10,15], lung adeno-
carcinoma [16], melanoma [17], colorectal carcinoma
[18], hepatocellular carcinoma [19], ovarian carcinoma
[20], medulloblastoma [21], and lung and esophageal
squamous carcinoma [22], and has helped identify sev-
eral new targets of amplifications (including NKX2-1
[16], CDK8 [18], VEGFA [19], SOX2 [22], and MCL1
and BCL2L1 [4]) and deletions (EHMT1 [21]). Several
* Correspondence:;
Cancer Program, The Broad Institute of MIT and Harvard, 7 Cambridge
Center, Cambridge, MA 02142, USA
Full list of author information is available at the end of the article
Mermel et al. Genome Biology 2011, 12:R41
© 2011 Mermel et al.; l icensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creativ e Commons
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Page 1
additional algorithms for identifying likely driver SCNAs
have also been described [23-25] (reviewed in [26]).
Yet, several critical challen ges have not yet been ade-
quately addressed by any of the existing copy-number
analysis tools. For example, we and others have shown
that the abundance of SCNAs in human cancers varies
according to their size, with chromosome-arm length
SCNAs occurring much mor e frequently than SCNAs of
slightly larger or smaller size [4,27]. Therefore, analysis
methods need to model complex cancer genomes that
contain a mixture of SCNA types occurring at distinct
background rates. Existing copy-number methods have
also used ad hoc heuristics to define the genomic
regions likely to harbor true cancer gene targets. The
inability of these methods to provide a p riori statistic al
confidence has been a major limitation in interpreting
copy-number analyses, an important problem as end-
users typically use these results t o prioritize candidate
genes for time-consuming validation experiments.
Here we describe several methodological improve-
ments to address these challenges, and v alidate the per-
formance of the revised algorithms in both real and
simul ated datasets. We have incorporated these changes
into a revised GISTIC pipeline, termed GISTIC 2.0.
Results and Discussion
Overview of copy-number analysis pipeline
Cancer copy-number analyses can be divided into five
discrete steps (Figure 1): 1) accurately defining the
copy-number profile of each cancer sample; 2)
Array Calibration
Copy Number Estimation
Step 1:
Accurate definition
of the copy number
profile in each sample
Individual .CEL Files
Segmented Copy Number Profiles
Step 2:
of underlying SCNAs
Step 3:
Scoring SCNAs in each
region according to
likelihood of occuring
by chance
Step 4:
Defining independent
genomic regions
undergoing significant
levels of SCNA
Step 5:
Accurate definition
of the copy number
profile in each sample
Deconstruction of segmented profle
into underlying SCNAs
Allows for modelling of background
rate of SCNAs and length-based
separation of arm-level
and focal SCNAs
Elimination of arm-level SCNAs by
use of amplitude threshold
G = frequency x amplitude
p-values computed by random
permutation of markers
across genome
Greedy segment peel-off algorithm
Iteratively subtracts segments
covering each peak and
rescores until no significant peaks
remain on chromosome
Assumes that at most ÔkÕ passenger
events aberrantly define the minimal
common region
G = -log(Probability | Background)
Scores computed on markers or genes
p-values computed by random
permutation of markers or bins
across genome
Arbitrated peel-off algorithm
Formalizes idea that segments can
have multiple targets by allowing
segment scores to be split
among multiple potential peaks
during peel-off
Models expected local variation in
G-score to define boundaries predicted
to contain the true target with
predetermined confidence
GISTIC 1.0 (Beroukhim et al, 2007)
Figure 1 Schematic overview of the copy-number analysis framework. High-level overview of our cancer copy-number analysis framework,
highlighting specific differences between the original GISTIC algorithm [15] and the GISTIC 2.0 pipeline described in this manuscript. The first
step, accurate identification of the copy-number profile in each sample, is common to GISTIC and GISTIC2.0.
Mermel et al. Genome Biology 2011, 12:R41
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identifying the SCNAs that most likely gave rise to these
overall profiles and estimating their background rates of
formation; 3) scoring the SCNAs in each region accord-
ing to their likelihood of occurring by chance; 4) defin-
ing the independent genomic regions undergoing
statistically signif icant levels of SCNA; and 5) identifying
the likely gene targe t(s) of ea ch significan tly altered
region. Figure 1 depicts a schematic overview of this
process, highlighting the specific methodological
improvements we will address in the present
The first step, accurately defining the copy -number
profile of each cancer sample, has been addressed by
multiple previous studies [28-35] and is not discussed in
detail here. We assume that segmented copy-number
profiles have been obtained for all samples and all germ-
line copy-number variations (CNVs) have been removed,
yielding profiles of somatic events. The following sec-
tions describe improvements to steps 2 to 5. We evalu-
ate these improvements on a test set of 178
glioblastoma multiforme (GBM) cancer DNAs hybri-
dized to the Affymetrix Single Nucleotide Polymorphism
(TCGA) project [10] (the TCGA GBM set ), and on
simulated data. Full technical details for each step are
described i n the Supplementary Methods (Additional
file 1).
Deconstruction of segmented copy-number profiles into
underlying SCNAs
Segmented copy number prof iles represent the summed
outcome of all the SCNAs that occurred during cancer
development. Accurate modeling of the background rate
of copy-number alteration requires analysis of the indi-
vidual SCNAs. However, because SCNAs may overlap, it
is impossible to directly infer the underlying events
from the final segmented copy-number profile alone.
Given certain assumptions about SCNA background
rates, however, it is possible to estimate the likelihood
of any given set of candidate SCNAs so as t o select the
most likely one.
We have develope d an algorithm ( Ziggurat Decon-
struction (ZD)) that deconstructs each segmented co py-
number profile into its most likely set of underlying
SCNAs (see Supplementary Methods in Additional file 1
and Supplementary Figure S1 in Additional file 2). ZD is
an iterative optimization a lgorithm that alternatively
esti mates a back ground model for SCNA fo rmation and
then utilizes this model to deter mine the most likely
deconstruction of each copy-number profile. Its output
is a catalog of the individual SCNAs in each cancer
sample, each with an assigned length and amplitude,
that sum to generate the original segmented copy pro-
file. We assume that most of these SCNAs are
passengers, so that their distribution reflects, to a first
approximation, the o peration of the background muta-
tion process (see Supplementary Figure S2 in Additional
file 3).
Length-based separation of focal and arm-level SCNAs
A major ad vantage of the ZD method is its ability to
separate arm-level and focal SCNAs explicitly by l ength.
Prior studies have attempted to exclude arm-level
SCNAs by setting high amplitude thresholds [10,16]
because, in contrast to focal SCNAs, few arm-level
SCNAs reach high amplitude (Fig ure 2a). However, this
approach suffers from at least two undesirable conse-
quences: first, low- to moderate-amplitude focal copy-
number events are eliminated from the analysis, r edu-
cing sensitivity to identify positively selected regions;
and second, the amplitude threshold is left as a free
parame ter, allowing for potential over-fitting of the ana-
lysis to a desired result.
We have previously shown that SCNA frequencies
across cancers of diverse tissue origin are inversely pro-
portional to SCNA lengths, with the striking exception
of SCNAs exactly the length of a chromosome arm or
whole chromosome (which are very frequent) [4]. This
trend is preserved in the TCGA G BM samples (Figure
2b). This reproducible distribution provides a natural
basis for classifying events as arm-level and focal
based purely o n len gth. Such length- based filtering of
events allows for the computational reconstruction of
arm-level and focal representations of the cancer gen-
ome ( Figure 2c) and enables the inclusion of low- to
moderate-amplitude focal copy-number events in the
final analysis.
To determine the benefits of this approach, we ran the
original GISTIC 1.0 algorithm on t he TCGA GBM set
using three different thresholding approaches (Figure 3;
Supplementary Table S1 in Additional file 4): 1) a low
amplitude threshold (log2 ratio of ± 0.1) that only elimi-
nates low-level artifactual segments; 2) a high amplitude
threshold (log2 ratio of 0.848 and -0.737 for amplifica-
tions/deletions) used previously [16] to eliminate arm-
level events; and 3) the low amplitude threshold but
also removing all SCNAs occupying more than 98% of a
chromosome arm, leaving only the focal events.
Filtering out arm-level events through use of either
amplitude or length thresholds greatly increased the
sensitivity of GISTIC for detecting focal amplifications
and deletions (Figure 3; Supplementary Table S 1 in
Additional file 4). While entire chromosomes were
scored as significant using only a low am plitude thresh-
old, including gain of chromosome 7 and loss of chro-
mosome 10 (Figure 3a), a number of recurrent focal
alterations were missed, including amplifications sur-
rounding CDK6, CCND2,andHMGA2.These
Mermel et al. Genome Biology 2011, 12:R41
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alterations were detected usin g either the high ampli-
tude (Figure 3b) or the focal length filters (Figure 3c).
The benefits of length-based filtering result from the
inclusion of low- to moderate-amplitude focal events.
Amplification of PIK3CA and AKT1 and deletion of
WWOX are detec ted using length -based filtering, but
are not significant under the high amplitude filter (com-
pare Figure 3b and 3c). Moreover, the length-based ana-
lysis identified significant SCNAs detected in neither of
the amplitude-based analyses, including amplifications
of MLLT10 and deletions of CDKN1B and NF1.
No known GBM target gene was detected in either of
the amplitude-based analyses that was not also detected
by the length-based analysis. These results suggest that
length-based filtering of arm-level events greatly
improves the sensitivity of GISTIC to identify relevant
regions of focal SCNA.
Probabilistic scoring of SCNAs
We set out to define a scoring framework for SCNAs
that more accurately reflects the background rates of
alteration. Ideally, we aim to score each region of the
genome according to the probability with which the
observed set of SCNAs would occur by chance alone.
Scores using this framework have a clear interpretation:
that the SCNAs in that region are observed entirely by
chance, and the more likely that they underwent positive
The probability of observing a single SCNA of given
length and amplitude can be approximated by the fre-
quency of occurrence of events of similar length and
amplitude across the entire dataset (as in Supplemen-
tary Figure S2 in Additional file 3). However, since
cancer genomes do contain drivers, this procedure is
likely to overestimate the probability of observing
SCNAs under the null model. Specifically, driver
events tend to be shorter in length and of higher
amplitude than passengers and therefore constitute
the majority of events in their length/amplitude
neighborhood (Supplementa ry Figure S3 in Additional
file 5).
Fraction of segments
Length (fraction of chr arm)
0 0.5 1 1.5 2
Arm-level SCNAsFocal SCNAs
Copy Number Change
Focal SCNAs
Arm-level SCNAs
High amp
Low amp
Amplitude of Focal and Arm-level SCNAs Length Distribution of SCNAs
All Data Focal SCNAsArm-level SCNAs
Figure 2 Computational separation of arm-level and focal SCNAs. (a) Boxplot showing the distribution of copy-number changes for
amplified focal (length < 98% of a chromosome arm) and arm-level (length > 98% of a chromosome arm) SCNAs across 178 GBM profiles from
TCGA. The black dotted line denotes a typical low-level amplitude threshold used to eliminate artifactual SCNAs, while the green dotted line
denotes a typical high-level amplitude threshold used in previous version of GISTIC to eliminate arm-level SCNAs. (b) Histogram showing the
frequency of observing SCNAs of a given length across 178 GBM samples. The high frequency of events occupying exactly one chromosome
arm led us to distinguish between focal and arm-level SCNAs. (c) Heatmaps showing the total segmented copy-number profile of the TCGA
GBM set (leftmost panel), and the results of computationally separating these samples into arm-level profiles (middle panel) and focal profiles
(rightmost panel) by summing arm-level and focal SCNAs. In each heatmap, the chromosomes are arranged vertically from top to bottom and
samples are arranged from left to right. Red and blue represent gain and loss, respectively.
Mermel et al. Genome Biology 2011, 12:R41
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To avoid biasing our background model , we set out to
fit the log-probability distribution of SCNAs to a func-
tional form that would be insensitive to the presence of
driver events in the data (Supplementary Methods in
Additional file 1). We made use of a large collection of
3,131 cancer samples run on the Aff ymetrix 250K StyI
SNP Array [4] plus several hundred additional samp les
run on th e Affymetrix SNP6.0 Array ( data not shown).
At the level of resolution provided by these arrays, the
probability of observing a focal SCNA at a given locus
under the background model is roughly independent of
length. As a result, the functional form for the log-prob-
ability distribution is similar to the original GISTIC G-
score definition (G = Frequency × Amplitude), with the
notable excep tion being that the new score is
proportional to the amplitude in copy-number space
rather than log-copy-number space.
Although this functional form was empiri cally derived
from a large collection of sample s run on two different
array-base d platforms, it does lead to increased sensitiv-
ity to differences in dynamic range across platforms as
well as differential saturation characteristics of probes
within the same array platform. To avoid this problem,
we routinely cap the segmented copy -number data at a
level representing the s ignal inte nsity above which most
probes start to saturate (Supplementary Methods in
Additional file 1). This ensures that we are using data
that originate from the linear regime of the probes
response curves and therefore are more comparable
across platforms.
0.053 0.1 0.2 0.4 0.8
0.033 0.1 0.2 0.4 0.8
All Data
Low Amplitude Threshold
All Data
High Amplitude Threshold
Focal Data
Low Amplitude Threshold
0.03 0.1 0.2 0.4 0.8
27 Amplified Regions 41 Amplified Regions 55 Amplified Regions
(b) (c)
15 Deleted Regions 31 Deleted Regions 36 Deleted Regions
Figure 3 Effects of amplitude-based or length-based filtering of arm-level events on GISTIC results. (a-c) GISTI C amplification (top) and
deletion (bottom) plots using all data and a low amplitude threshold (a), using all data and a high amplitude threshold (b), and using the focal
data and a low amplitude threshold (c). The genome is oriented vertically from top to bottom, and GISTIC q-values at each locus are plotted
from left to right on a log scale. The green line represents the significance threshold (q-value = 0.25). For each plot, known or interesting
candidate genes are highlighted in black when identified by all three analyses, in red when identified by the high amplitude or focal length
analyses, in purple when identified by the low amplitude or focal length analyses, and in green when identified only in the focal length analysis.
Mermel et al. Genome Biology 2011, 12:R41
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Page 5
As with GISTIC 1.0, we o btain P-values for each mar-
ker by comparing the score at each locus to a back-
ground score distribution generated by random
permutation of the marker locations in each sample
(Supplementar y Method s in Additional file 1). This pro-
cedure controls for sampl e-specific variations in the rate
of copy-number alteration. We correct the resulting P-
values for multiple-hypothesis testing using the Benja-
mini-Hochberg false discovery rate method [36].
Alternative gene-level scoring for tumor suppressors with
non-overlapping deletions
Some genes are affected by non-overlapping deletions,
either on different alleles in one sample or across multi-
ple samples. For such genes, a marker-based score does
not weight the presence of all deletions affecting that
gene, despite the fact that these events are likely to have
similarly deleterious effects on gene function. We have
developed a modified scoring and permutation proce-
dure, termed GeneGISTIC, that scores genes rather
than markers (Supplementary Methods in Additional file
1). In each sample, we assign each gene the minimal
copy number of any marker contained within that gene,
and then sum across all samples to compute the ge ne
score. Because genes covering more markers are more
permutation procedure is adjusted to account for gene
size;thescoreforagenecoveringn markers is com-
pared against a size-specific null distribution generated
by computing minima overall running windows of size n
in each sample and then randomly permuting these
minimal values across the genome.
To determine the effect of gene-based scoring of dele-
tions, we compared the results of gene-based and mar-
ker-based scoring on the TCGA GBM set (holding all
other parameters equal). As expected, GeneGISTIC
ranks known tumor suppressor genes higher and is
more sensitive for genes subject to n on-overlapping
deletions (Supple mentary Table S2 in Additional file 6).
For example, RB1 was ranked 5th out of 39 regions
using gene-ba sed scorin g (q-value = 2.6e-10) but only
13th out of 3 8 using marker-based scoring (q-value =
0.0013), and CDKN1B was ranked 26th using gene-
based scoring (q-value = 0.08) compared to 38th using
marker-based scoring (q-value = 0.19). NF1 was focally
deleted in 12 of the 178 GBM samples (6.7%), and these
deletions were frequently non-overlapping (Supplemen-
tary Figure S4a in Additional file 7). As a result, NF1
was scored just over or just under the significance
threshold using the marker-based score, depending on
the parameters used. By contrast, NF1 was robustly
identified using gene-based scoring across al l parameter
combinations (Supplementary Table S2 in Additional
file 6 and data not shown).
However, b ecause this scoring method does not score
regions of the genome that are not in annotated genes,
it could underweight or completely miss deletions
occurring in non-genic regions. For example, in our
GBM samples, g ene-based scoring did not identify a
region just outside of PCHD9 on chr13q21.3 that scored
as highly significant (q-value = 4.4e-9) using the stan-
dard marker-based score (Supplementary Figure S4b in
Additional file 7). While many non-genic deletions may
in fact represent technical artifacts or rare germline
events, some may be functionally relevant.
Identification of independent significantly altered regions
Individual SC NAs , and indeed significa ntly amp lified or
deleted regions of the genome, may extend over more
than one oncogene or tumor suppressor gene. Other
significant regions may contain no oncogenes or tumor
suppressor genes, b ut achieve apparent significance due
to their proximity to a target gene. Thus, an additional
step is required after genome-wide scoring to identify
independently significant regions.
GISTIC 1.0 solves t his problem through the use of an
iterative peel-off algorithm, which greedily assigns all
SCNAs to the maximal peak on each chromosome,
removes them fro m the data, and rescores until no
remaining region crosses the significance threshold. This
approach reduces the power to identify secondary peaks
that are close to previously identified significant r egions
(Figure 4a). However, since it is possible for individual
SCNAs to affect multiple driver regions, a less greedy
approach might identify additional peaks without signifi-
cantly increasing the false discovery rate.
We have, therefore, modified the method to allow
SCNAs to contribute to more than one peak (arbitrated
peel-off ). We first greedily assign the entirety of an
SCNAs score to the most significant peak it covers. In
subsequent steps, however, we allow scores of previously
assigned segments to be redistributed before deciding
whether a putative region is significant (Supplementary
Methods in Additional file 1). Like the original algo-
rithm, the process terminates when no region has an
adjusted score that exceeds the significance threshold. A
similar modification of GISTIC has recently been pro-
posed [37].
Arbitrated peel-off is more sensitive t han the original
algorithm (Figure 4a; Supplementary Table S3 in Addi-
tional file 8). We generated 10,000 simulated datasets
each consisting of 300 samples, with each chromosome
containing a primary driver event in 10% of the samples
and a secondary driver event in 5% of the samples. We
analyzed the sensitivity of standard and arbitrated peel-
off to detect the secondary peak as we varied the percen-
tage of secondary driver events that overlapped the pri-
mary driver peak between 0% and 100% (Supplementary
Mermel et al. Genome Biology 2011, 12:R41
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Page 6
Methods in Additional file 1). At 0% overlap, t he two
methods were nearly equally sensitive at identifying the
secondary peak. However, arbitrated peel-off was vastly
more sensitive than standard peel-off as we increased the
rate of overlap between primary and secondary peaks from
5 to 50% (Figure 4b), recovering a n average of 2.4 times
(range 1.2 to 3.8) more secondary peaks. Over 80% of the
novel peaks identified by arbitrated peel-off corresponded
to an actual simulated driver peak, demonstrating that the
increased sensitivity is accompanied by high specificity.
The primary and secondary peaks tend to merge when
the overlap i s above 50%, obscuring any appre ciable dif-
ference between the two methods (Supplementary Fig-
ure S5 in Additional file 9). Indeed, neither method was
capable of ind ependentl y identifying the secondary pe ak
once the percent overlap rose above 80%. Thes e simula-
tions demonstrate both the superior sensitivit y of arbi-
trated peel-off as well as the challenge of identifying
neighboring drivers.
Localizing target genes for each significantly altered
The final step in the GISTIC pipeline is to determine
the region that is most likely to contain the gene or
genes being targeted for each independently significant
region of SCNA (the peak region ). The standard
approach is to focus on the minimal common region
(MCR) of overlap (Figure 5a), the region that is altered in
the greatest number of samples and therefore would be
expected to be the most likely to contain the target genes.
However, one or more passenger SCNAs adjacent to, but
not overlapping, the target gene can result in an MCR that
does not include the true target. This is a frequent occur-
rence, especially when the frequency of the driver event is
low (< 5%; Figure 5b ). An alternative method (utilized by
the GISTIC 1.0) is to apply a heuristic leave-k-out proce-
dure to define the boundaries of each peak region (Figure
5a) [15]. This procedure assumes that up to k passenger
SCNAs (typically, k = 1) may aberrantly define each
boundary of the peak region. While th e leave-k-out pro-
cedure correctly identifies the target gene more often than
the MCR (Figure 5b), it suffers from the potential for over-
fitting introduced by the free parameter k. Moreover, the
accuracy of leave-k-out varies depending on the number
of samples and the frequency of the event under question.
For fixed k, the sensitivity of leave-k-out increases for
increasing driver frequency (Figure 5b) and decreases for
increasing sample size (Figure 5c).
(a) (b)
Arbitrated peel−off
Standard peel−off
% recovery of independent second driver peak
Sensitivity vs. Driver Distance
0 10 20 30 40 50 60
Distance between drivers (Mb)
Sensitivity vs. Driver SCNA Overlap
Fraction overlap between driver events (%)
% recovery of independent second driver peak
Closer Distance Farther Distance
Figure 4 Sensitivity of peel-off to detect secondary driver events. The average fraction of secondary driver events recovered in independent
(not containing the primary driver) peaks by GISTIC using the standard peel-off method (blue line) or arbitrated peel-off (red line) is shown for
two simulated datasets. (a) The data are derived from 1,000 simulated chromosomes across 300 samples with a primary driver event present in
10% of samples and a secondary driver event a fixed distance away that is present in 5% of samples. (b) Data are derived from 10,000 simulated
chromosomes across 300 samples with a primary driver event present in 10% of samples and a secondary driver event present in 5% of samples,
where the fraction of the secondary driver events that overlapped with the primary driver event was varied between 100% (complete
dependence; far left) and 0% (complete independence; far right). Error bars represent the mean ± standard error of the mean (some are too
small to be visible).
Mermel et al. Genome Biology 2011, 12:R41
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We de veloped a no vel a pproach (termed RegBoun-
der) to define th e peak region boundaries in such a way
that target genes would be included at a pre-determined
confidence level, regardless of the event frequency or
number of samp les being studied (Figure 5a; Supple-
mentary Methods in Additional file 1). RegBounder
models the expected random fluctuation in G-scores
within any given window size and uses this distribution
to define a confidence region likely to contain the true
driver at least g% of the time, where g is a desired confi-
dence le vel. Unlike the MCR and leave-k-out proce-
dures, which are highly dependent on one or a few
segment boundaries to define each region, RegBounder
is designed to be relatively robust to random errors
(either due to technical artifacts or passenger segments)
in boundary assignment. When applied to real data,
RegBounder captures known driver genes more effec-
tively than leave-1-out (and MCR) in regions with
Driver Recall as Function of Driver Frequency
(n = 500 samples)
0 1 2 3 4 5 6 7 8 9 10
Driver Frequency (%)
Fraction of drivers identified (%)
RegBounder 50%
RegBounder 75%
RegBounder 95%
Driver Recall as Function of Sample Size
(5% driver frequency)
0 100 200 300 400 500 600 700 800
Number of samples
Fraction of drivers identified (%)
RegBounder 75%
Target Gene
Chromosomal Position
Target Gene
Figure 5 S ensitivity of peak finding algorithms. (a) Schematic diagram demonstrating various peak finding methods . The left panel shows
the GISTIC score profile for a simulated chromosome containing a mix of driver events covering the denoted target gene and passenger events
randomly scattered across the chromosome. The inset at right shows the region around the maximal G-score (gray box in left panel) in higher
detail. The MCR (red dotted lines) is defined as the region of maximal segment overlap, or the region of highest G-score. The leave-k-out
procedure (blue dotted lines, here shown for k = 1) is obtained by repeatedly computing the MCR after leaving out each sample in turn and
taking as the left and right boundaries the minimal and maximal extent of the MCR. RegBounder works by attempting to find a region (dotted
green line) over which the variation between boundary and maximal peak score is within the gth percentile of the local range distribution
(Supplementary Methods in Additional file 1). Here, RegBounder produces a wider region than either the MCR or leave-k-out procedures, but is
the only method whose boundary contains the true driver gene. (b,c) The average fraction of driver events contained within the peak region
(conditional on having found a GISTIC peak within 10 Mb) is plotted as a function of driver-frequency (b) or sample size (c) for the MCR (red),
leave-1-out (blue), and RegBounder algorithms (the latter at various confidence levels: 50%, magenta; 75%, green; 95%, black). In (b), data are
derived from 10,000 simulated chromosomes across 500 samples in which the driver frequency varied from 1 to 10%. In (c), data are derived
from 10,000 simulated chromosomes across a variable number of samples in which the driver frequency was fixed at 5%. Error-bars represent
the mean ± standard error of the mean (some are too small to be visible).
Mermel et al. Genome Biology 2011, 12:R41
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increased local noise (Figure 6a) and yet is capable of
producing narrower boundaries than leav e-1-out in
regions with little noise (Figure 6b).
In simulated dat asets, the performance of RegBounder
was consistent across a wide range of driver SCNA fre-
quencies (Figure 5b) and sample sizes (Figure 5c), and
indeed controlled the probability of containing the dri-
ver. RegBounder captured the true driver gene in an
average of 72%, 85%, and 95% of driver regions of vary-
ing frequency when run with a desired confidence l evel
(g) of 50, 75, and 95%, respectivel y. For no combination
of sample-size, driver frequency, a nd g did t he average
accuracy of RegBounder drop below g.
RegBounder also demonstrated a more optimal trade-
off between peak region sensitivity (the likelihood of
including the target gene) and specificity (the number of
additional genes included) than the MCR or leave-k-
out approaches. The average size of the peak regions
decreases with increasing driver frequency (Figure 7a)
and sample size (Figure 7b) for all three approaches.
However, RegBounder is more sensitive to these vari-
ables than the other methods, so that RegBounder peak
regions (at 75% confidence) can range from an average
of 90 times larger than the l eave-k-out peak regions
(for datasets with few total driver events, in which the
target ge ne locations are truly uncertain) to 37% smaller
than the leav e-k-out procedure (for datasets with many
total driver events). Thus, the increased confidence of
RegBounder can even be achieved while producing nar-
rower regions than the leave-k-out procedure.
RegBounder is also more consistent across datasets
than the MCR and leave-k-out methods. We ran-
domly split the TCGA GBM set into two groups and
compared the peak regions produced by RegBounder
and the MCR and leave-k-out procedures on each.
Considering only those peaks that were identified by
GISTIC in both datasets, only 23% of the MCRs and
31% of the leave-k-out peak regions overlap between
the two datasets, reflectingthelowconfidencewith
which these regions are assigned. By contrast, a major-
ity (53%) of the RegBou nder peak regions (at 75% con-
fidence) overlapped, as expected (0.75
increased overlap came with only a modestly i ncreased
median size of the RegBounder peak regions (370 kb)
compared to the leave-k-out (163 kb) or MCR (115
kb) peak regions.
25 25.5 26 26.5
Chromosome 12 Position (Mb)
1.0 1.5
Chromosome 5 Position (Mb)
RegBounder vs. MCR and Leave-1-Out
on Lung Adenocarcinoma Samples
Figure 6 Comparison of RegBounder to MCR and leave-1-out procedures applied to primary lung adenocarcinomas. The advantages of
RegBounder over previous peak-finding procedures are illustrated for two well-described oncogene peaks identified in GISTIC analysis of 371
lung adenocarcinoma samples characterized on the Affymetrix 250K StyI SNP array (as published in [16]). (a) A well-described amplification peak
is identified on chromosome 12p12.1 with MCR (red dotted lines) near to but not containing the known lung cancer oncogene KRAS. Because
there are more than two apparent passenger events in this region, the leave-1-out peak (blue dotted lines) also does not contain KRAS.
However, RegBounder (green dotted lines) produces a wider peak that captures KRAS. (b) An amplification peak on chromosome 5p15.33
contains hTERT, the catalytic subunit of the human telomerase holoenzyme, within the MCR (red dotted lines). In this case, RegBounder (green
dotted lines) produces a narrower peak region than the corresponding leave-1-out peak (blue dotted lines), demonstrating the ability of
RegBounder to achieve a greater balance between peak region size and accuracy. In both (a) and (b), the y-axis depicts the amplification G-
score and the x-axis denotes position along the corresponding chromosome.
Mermel et al. Genome Biology 2011, 12:R41
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RegBounder regions are, on avera ge, only 19% larger
than the theoretically minimal peak region size for a
wide range of driver frequencies (Figure 7c) and confi-
dence levels (Supplementary Figur e S6 in Additional file
10). These theoretically minimal peak region sizes were
derived from the distribution of distances between the
target gene and the MCR in our simulations (Supple-
mentary Methods in Additional file 1). Our simulations
reveal that RegBounder is capa ble of producing smaller
peak regions than the leave-k-out approach while
simultaneously achieving greater target gene recall
(compare Figures 5b and 7a; RegBounder 75% versus
leave-1-out , for driver frequencies > 5%). Thus,
RegBounder is a robust algorithm for peak region
boundary determination that demonstrates a more
optimal trade-off between statistical confidence and
peak resolution than previous heuristic approaches.
Source code and module availability
The MATLAB source code for the GISTIC2.0 pipeline,
along with a precompiled unix executable, will be avail-
able for download at [38]. In addition, the entire pipe-
line can be accessed through the GenePattern analysis
portal at [39].
In addition to including all the methodological
improvements described in this manuscript, the GIS-
TIC2.0 source code has been designed to make efficient
use of memory in storing segmented copy-number data
(Supplementary Methods in Additional file 1). This
improved memory efficiency should allow users with
RegBounder vs. Theoretically Optimal Peak Region
(n = 500 samples)
Peak Region Size As Function of Driver Frequency
(n = 500 samples)
Driver Frequency (%)
Median Peak region size (markers)
0 1 2 3 4 5 6 7 8 9 10
RegBounder 75%
Peak Region Size As Function of Sample Size
(5% Driver Frequency)
Sample Size
0 100 200 300 400 500 600 700 800
RegBounder 75%
Median Peak region size (markers)
0 1 2 3 4 5 6 7 8 9 10
Theoretical Minimum Peaks (75% confidence)
RegBounder Peaks (75% confidence)
Median Peak region size (markers)
Driver Frequency (%)
Figure 7 Specificity of peak finding algorithms. (a,b) The median size of the peak regions produced by the MCR (red), leave-1-out (blue), and
RegBounder (green, 75% confidence) are shown as a function of driver frequency (a) and sample size (b). In (a), data are derived from 10,000
simulated chromosomes across 500 samples in which the driver frequency varied from 1 to 10%. In (b), data are derived from 10,000 simulated
chromosomes across a variable number of samples in which the driver frequency was fixed at 5%. (c) Comparison of the peak region sizes
obtained by RegBounder (green line) with the theoretically minimal peak region sizes (black line) that could be obtained by any peak finding
algorithm with a similar confidence level (Supplementary Methods in Additional file 1). Error-bars represent the mean ± standard error of the
mean (some are too small to be visible).
Mermel et al. Genome Biology 2011, 12:R41
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limited computational resources to run GISTIC2.0 on
typical size datasets, and will be increasingly important
for all users as t he density of copy-number measuring
platforms continues its rapid rise.
We describe a number of analytical improvements to
the standard copy-number analysis workflow that
increase the sensitivity and specificity with which driver
genes may be localized. We also demonstrate the u tility
of each of these changes using both simulated and real
cancer copy-number datasets. While these changes have
been specifically implemented in GISTIC 2.0, t he chal-
lenges we describe apply broadly to the general task of
identifying significantly aberrant regions of SCNA in
cancer, and we anticipate that the approaches we have
described can be adapted to other copy-number analysis
The p roce dure we outline enab les data-driv en estima-
tion of the background rat es of SCNA and how these
rates vary with features of the SCNA, such as length or
likely to depend on the resolution and characteristics of
the measur ing platfo rm used to generate our datasets
(the Affymetrix 250K StyI and SNP6.0 arrays). As more
cancer samples are characterized using higher-resolution
array and sequen cing platforms, new trends are likely to
emerge. Further improvements would account for such
trends, possibly taking into account additional features
that may determine SCNA background rates, such as
the presence of known fragile sites of the genome or the
surrounding sequence context. Indeed, we and others
have recently shown tha t somatic deletions frequently
occur in genes with large genomic footprints [4,6], sug-
gesting the existence of a contextual bias in the rate of
somatic deletion that is presently unaccounted for in
our background mutation model. Our probabilistic scor-
ing framework allows such trends to be accounted for
once the background model has been specified.
For the significant SCNAs, the background rate esti-
mates also enable the delineation of regions likely to con-
tain the tar get genes at predetermined confidence.
RegBounder, the algorithm we devised to assign these
boundaries, is more robust than either MCR- or leave-k-
out -based methods. RegBounder achieves this higher
sensitivity by producing wider peak r egions when the
number of informative segments at a driver locus is
small, but we find that RegBounder performs well com-
pared to the theoretically optimal performance. However,
RegBounders underlying assumptions may not always be
sati sfied, including the assumption that each peak re gion
tion that copy-number breakpoints are independently
distributed around the driver locus. To the extent that
these assumptions are violated, RegBounder sperfor-
mance may be worse than our simulations suggest.
While the arbitrated peel-off approach described in this
manuscript reflects a more sensitive way of identifying
independently targeted regions of amplification and dele-
tion than our prior approach, it is still an imperfect
attempt to decip her the complexity of cancer copy-num-
ber alterations. One major limitation stems from the fact
that array-based measurements map SCNAs onto a linear
reference genome. However, many SCNAs are preceded
by rearrangement events that ju xtapose g enomic regions
separated by great physical distance in the germline (even
different chromosomes) [40,41]. This level of detailed
structur al information is impossible to infer from prob e-
level copy-number estimates but can be obtained by
sequencing paired-end libraries [13]. Indeed, we anticipate
that copy-number information derived fr om shotgun
sequencing of cancer samples will become more common
as sequencing costs continue to plummet [42]. Tools for
estimating and segmenting copy-number values from
sequencing coverage data already exist [5], and these seg-
mented copy-number profiles can, with only slight modifi-
cation, be run through the GISTIC 2.0 workflow. Fully
exploiting the level of detailed information provided by
these technologies will, however, r equire a significant
extension of the background mutation model to include
the probability of random genomic rearrangements, as
well as the ability to perform significance analysis, segment
peel-off, and peak finding across non-contiguous regions
of the reference genome. The data provided by these
sequencing efforts should lead to new insights into the cel-
lular and molecular processes underlying SCNA genera-
tion in different cancer types, and will allow for the
development of vastly more detailed and accurate models
of the background mutatio n rate of such events during
tumor development.
Materials and methods
Full methods are available in the Supplementary Materi-
als (Additional file 1) [43-46].
Additional material
Additional file 1: Supplementary Methods. Supplementary Methods
contains the full description of the GISTIC2.0 method and details of the
specific analyses presented in this manuscript.
Additional file 2: Supplementary Figure S1: Ziggurat
Deconstruction. (a) A hypothetical segmented chromosome (green line)
is deconstructed with the simplified procedure used by Ziggurat
Deconstruction (ZD) to initialize background SCNA rates. Dotted red and
blue lines denote the length and amplitude of amplified and deleted
SCNAs, respectively, while solid red and blue lines denote the result of
merging the SCNA with the closest adjacent segment. (b) The same
hypothetical segmented chromosome (green line) is deconstructed using
the more flexible procedure of subsequent rounds of ZD. Here, the ZD is
performed with respect to up to two basal levels (dotted magenta lines)
Mermel et al. Genome Biology 2011, 12:R41
Page 11 of 14
Page 11
that are fit to the data, allowing for amplified and deleted SCNAs to be
Additional file 3: Supplementary Figure S2: distribution of SCNA
length and amplitudes. Two-dimensional histogram showing the
frequency (z-axis) of copy number events as a function of length (x-axis)
and amplitude (y-axis). Frequency is plotted on a log-scale to facilitate
visualization of very low frequency copy number events.
Additional file 4: Supplementary Table S1: comparison of amplitude
and length-based filtering of SCNAs. Supplementary Table 1 compares
the GISTIC results obtained using low and high amplitude thresholds
with those obtained using a focal length threshold on 178 GBM samples.
Additional file 5: Supplementary Figure S3: distribution of driver
length and amplitudes. Driver SCNAs are typically of shorter length and
higher amplitude than random passenger SCNAs. (a,b) Here we show
the cumulative frequency distribution of SCNA amplitudes (a) and
lengths (b) for SCNAs covering significantly amplified regions identified
by GISTIC (Driver SCNAs, red line) or by a similar number of randomly
chosen non-driver regions (Random SCNAs, blue line).
Additional file 6: Supplementary Table S2: comparison of
GeneGISTIC and standard GISTIC deletions analysis. Supplementary
Table 2 compares the GISTIC results obtained using the standard GISTIC
deletions analysis with those obtained using GeneGISTIC on 178 GBM
Additional file 7: Supplementary Figure S4: GeneGISTIC versus
standard GISTIC. (a) GeneGISTIC helps identify genes subject to non-
overlapping deletion, such as NF1. The left panel shows the 12 samples
with focal deletions affecting NF1, many of which do not overlap. As a
result, the standard GISTIC marker score (blue line, right panel) has
multiple local maxima over NF1. By contrast, the GeneGISTIC score
counts all of these deletions as contributing to the NF1 score, resulting
in a score for NF1 (red line, right panel) that is significantly greater than
that assigned to any of the individual markers covering NF1. (b)
GeneGISTIC does not score deletions occurring outside of genes. The left
panel shows a region of focal deletion occurring just outside the PCHD9
gene on chromosome 13. These deletions result in a peak in the markers
deletion score (blue line, right panel) that is not detected by GeneGISTIC.
Additional file 8: Supplementary Table S3: new peaks detected by
arbitrated peel-off. Supplementary Table 3 compares the GISTIC results
obtained using the standard peel-off algorithm with those obtained
using arbitrated peel-off on 178 GBM samples.
Additional file 9: Supplementary Figure S5: total recovery of
secondary driver peaks. This figure shows the results from 10,000
simulations of 300 samples in which a primary driver event is present in
10% of samples and a secondary driver event is present in 5% of
samples. In these simulations, we vary the fraction of overlap between
driver events from 100% (total dependence) to 0% (total independence).
Here we present to the total recovery of the secondary driver peak in
GISTIC runs using arbitrated peel-off (left panel) or the standard peel-off
(right panel). The red (left panel) or blue (right panel) lines show the
fraction of secondary driver peaks identified in independent GISTIC peaks
(that is, not containing the primary driver event), as is shown in Figure
4b. The black lines show the fraction of secondary driver peaks identified
in dependent peaks (that is, a peak containing both the primary and
secondary driver events), and the green lines show the total recall of
secondary driver peaks (in any peak). Error-bars representing the mean ±
standard error of the mean are drawn, but may be smaller than the
point used to represent the mean and hence not be visible.
Additional file 10: Supplementary Figure S6: comparison of
RegBounder to theoretically optimal peaks. Comparison between the
peak region sizes obtained by RegBounder (green line) with the
theoretically minimal peak region sizes (black line) that could be
obtained by a similarly confident peak finding algorithm (Supplementary
Methods in Additional file 1) at 50% (left) and 95% (right) confidence.
Error-bars representing the median ± standard error of the mean are
drawn, but may be smaller than the points used to represent the
median and hence not be visible.
CNV: copy number variation; GBM: glioblastoma multiforme; GISTIC: Genomic
Identification of Significant Targets in Cancer; MCR: minimal common region;
SCNA: somatic copy number alteration; SNP: single nucleotide
polymorphism; TCGA: The Cancer Genome Atlas; ZD: Ziggurat
This work was supported by a Genome Characterization Center Grant
(U24CA143867) awarded as part of the NCI/NHGRI funded Cancer Genome
Atlas (TCGA) project. CHM was supported by Medical Scientist Training
Program (MSTP) Award Number T32GM07753 from the National Institute of
General Medical Sciences. RB was supported by NIH K08CA122833, a V
Foundation Scholarship, and the Doris Duke Charitable Foundation. The
content is solely the responsibility of the authors and does not necessarily
represent the official views of the National Institute of General Medical
Sciences or the National Institutes of Health.
Author details
Cancer Program, The Broad Institute of MIT and Harvard, 7 Cambridge
Center, Cambridge, MA 02142, USA.
Department of Medical Oncology, Dana
Farber Cancer Institute, 44 Binney Street, Boston, MA 02115, USA.
Department of Cancer Biology, Dana Farber Cancer Institute, 44 Binney
Street, Boston, MA 02115, USA.
The Center for Cancer Genome Discovery,
Dana Farber Cancer Institute, 44 Binney Street, Boston, MA 02115, USA.
Authors contributions
RB and GG developed and coded the original GISTIC algorithm. CHM, SES,
RB, and GG developed and coded the algorithmic modifications contained
in GISTIC 2.0. CHM, MM, RB, and GG conceived and designed the present
study. CHM, SES, and BH debugged and packaged the GISTIC 2.0 software
release. CHM, MM, RB, and GG wrote the manuscript. All authors read and
approved the final manuscript.
Received: 18 August 2010 Revised: 14 February 201 1
Accepted: 28 April 2011 Published: 28 April 2011
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Cite this article as: Mermel et al.: GISTIC2.0 facilitates sensitive and
confident localization of the targets of focal somatic copy-number
alteration in human cancers. Genome Biology 2011 12:R4 1.
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  • Source
    • "display/GDAC/Download). Using the significant regions of gain or loss identified by GISTIC 2.0 [64], we assigned a discrete copy number alteration status to each gene in each sample. The SIGnaling Network Open Resource (SIGNOR) [32] database, including 3646 proteins with 12, 285 directed relations representing various activating or inhibitory effects, was downloaded and used to constructed a directed gene network. "
    [Show abstract] [Hide abstract] ABSTRACT: Previously reported prognostic signatures for predicting the prognoses of postsurgical hepatocellular carcinoma (HCC) patients are commonly based on predefined risk scores, which are hardly applicable to samples measured by different laboratories. To solve this problem, using gene expression profiles of 170 stage I/II HCC samples, we identified a prognostic signature consisting of 20 gene pairs whose within-sample relative expression orderings (REOs) could robustly predict the disease-free survival and overall survival of HCC patients. This REOs-based prognostic signature was validated in two independent datasets. Functional enrichment analysis showed that the patients with high-risk of recurrence were characterized by the activations of pathways related to cell proliferation and tumor microenvironment, whereas the low-risk patients were characterized by the activations of various metabolism pathways. We further investigated the distinct epigenomic and genomic characteristics of the two prognostic groups using The Cancer Genome Atlas samples with multi-omics data. Epigenetic analysis showed that the transcriptional differences between the two prognostic groups were significantly concordant with DNA methylation alternations. The signaling network analysis identified several key genes (e.g. TP53, MYC) with epigenomic or genomic alternations driving poor prognoses of HCC patients. These results help us understand the multi-omics mechanisms determining the outcomes of HCC patients.
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    • "Recurrently mutated genes in ILC were identified by MutSigCV2 (Lawrence et al., 2013) and included many genes previously implicated in breast cancer (Figure 1B,Table 1) (Cancer Genome Atlas, 2012). Similarly, recurrent copy-number alterations in ILC estimated by GISTIC (Mermel et al., 2011) recapitulated known breast cancer gains and losses, in particular those observed in ER+/luminal tumors (Figure S1A). However, the frequency of these alterations (both mutations and copy-number changes) often differed significantly between IDC and ILC. "
    [Show abstract] [Hide abstract] ABSTRACT: Invasive lobular carcinoma (ILC) is the second most prevalent histologic subtype of invasive breast cancer. Here, we comprehensively profiled 817 breast tumors, including 127 ILC, 490 ductal (IDC), and 88 mixed IDC/ILC. Besides E-cadherin loss, the best known ILC genetic hallmark, we identified mutations targeting PTEN, TBX3, and FOXA1 as ILC enriched features. PTEN loss associated with increased AKT phosphorylation, which was highest in ILC among all breast cancer subtypes. Spatially clustered FOXA1 mutations correlated with increased FOXA1 expression and activity. Conversely, GATA3 mutations and high expression characterized luminal A IDC, suggesting differential modulation of ER activity in ILC and IDC. Proliferation and immune-related signatures determined three ILC transcriptional subtypes associated with survival differences. Mixed IDC/ILC cases were molecularly classified as ILC-like and IDC-like revealing no true hybrid features. This multidimensional molecular atlas sheds new light on the genetic bases of ILC and provides potential clinical options.
    No preview · Article · Oct 2015 · Cell
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    • "Copy number data (gene level) for cancer cell lines was obtained from CCLE (platform: Affymetrix SNP6) [7]. As reported by TCGA and CCLE, the significant focal copy number alterations in individual tumor samples/cancer cell lines were identified from segmented data using GISTIC [15]. Four classes of abnormal segments were considered based on their estimated copy number [16]: "
    [Show abstract] [Hide abstract] ABSTRACT: Breast cancer is one of the most common cancers with high incident rate and high mortality rate worldwide. Although different breast cancer cell lines were widely used in laboratory investigations, accumulated evidences have indicated that genomic differences exist between cancer cell lines and tissue samples in the past decades. The abundant molecular profiles of cancer cell lines and tumor samples deposited in the Cancer Cell Line Encyclopedia and The Cancer Genome Atlas now allow a systematical comparison of the breast cancer cell lines with breast tumors. We depicted the genomic characteristics of breast primary tumors based on the copy number variation and gene expression profiles and the breast cancer cell lines were compared to different subgroups of breast tumors. We identified that some of the breast cancer cell lines show high correlation with the tumor group that agrees with previous knowledge, while a big part of them do not, including the most used MCF7, MDA-MB-231, and T-47D. We presented a computational framework to identify cell lines that mostly resemble a certain tumor group for the breast tumor study. Our investigation presents a useful guide to bridge the gap between cell lines and tumors and helps to select the most suitable cell line models for personalized cancer studies.
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