This document gives an overview of the MANOR package, which is devoted to the normalization of Array Comparative Genomic Hybridization (array-CGH) data (Solinas-Toldo et al. 1997; Pinkel et al. 1998; Snijders et al. 2001; Ishkanian et al. 2004; Hupé et al. 2004). Normalization is a crucial step of microarray analysis which aims at separating biologically relevant signal from experimental artifacts. Typical input data is a file generated by an image analysis software such as GenePix or SPOT (Jain et al. 2002), containing several measurements for each biological variable of interest, i.e. several replicated spots for each clone; this spot-level data is filtered with various statistical criteria (including a spatial bias detection step which is described in (Neuvial et al. 2006)), and aggregated into clean clone-level data.
Using the arrayCGH
framework developed in the package GLAD, which is available under Bioconductor. We propose the formalism of flags
to handle clone and spot filtering: the core of the normalization process consists in applying to an arrayCGH
object a list of flags that successively exclude from the data all irrelevant spots or clones.
We also define quality scores (qscores
) that quantify the quality of an array after normalization: these scores can be used directly to compare the quality of different arrays after the same normalization process, or to compare the efficiency of different normalization processes on a given array or on a given batch of arrays.
This document is organized as follows: after a short description of optional items we add to arrayCGH
objects (section arrayCGH
class, we introduce the classes flag
(section flag
class) and qscore
(section qscore
class) with their attributes and dedicated methods; then we describe two useful graphical representation functions (section Graphical representations), namely genome.plot
and report.plot
; Afterwards we give a short description of the array-CGH datasets we provide (section Data); finally we illustrate the usage of MANOR
by a sample R script (section Sample MANOR sessions).
##
## To cite package 'MANOR' in publications use:
##
## Pierre Neuvial and Philippe Hupé (2020). MANOR: CGH Micro-Array
## NORmalization. R package version 1.62.0.
## http://bioinfo.curie.fr/projects/manor/index.html
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {MANOR: CGH Micro-Array NORmalization},
## author = {Pierre Neuvial and Philippe Hupé},
## year = {2020},
## note = {R package version 1.62.0},
## url = {http://bioinfo.curie.fr/projects/manor/index.html},
## }
##
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
arrayCGH
classFor the purpose of normalization we have added several optional items to the arrayCGH
objects defined in the R package GLAD, including:
profileCGH
objects of GLADcloneValues
and arrayValues
, that can be used as an identifier for the replicates.flag
classWe view the process of filtering microarray data, and especially array-CGH data, as a succession of steps consisting in excluding from the data unreliable spots or clones (according to criteria such as signal to noise ratio or replicate consistency), and correcting signal values from various non-biologically relevant sources of variations (such as spotting effects, spatial effects, or intensity effects).
We introduce the formalism of flags to deal with this filtering issue: in the two following subsections, we describe the attributes and methods devoted to flag
objects.
flag
attributesA flag
object f
is a list whose most important items are a function (f\$FUN
) which has to be applied to an object of class arrayCGH
, and a character value (f\$char
) which identifies flagged spots. Optionally further arguments can be passed to f\$FUN
via f\$args
, and a label can be added via f\$label
. The examples of this subsection use the function to.flag
, which is explained in subsection flag
methods.
As stated above, we make the distinction between flags that exclude spots from further analysis and flags that correct signal values:
If f
is an exclusion flag, f\$FUN
returns a list of spots to exclude and f\$char
is a non NULL
value that quickly identifies the flag. In the following example, we define SNR.flag
, a flag
objects that excludes spots whose signal to noise ratio lower than the threshold snr.thr
.
SNR.FUN <- function(arrayCGH, var.FG, var.BG, snr.thr) {
which(arrayCGH$arrayValues[[var.FG]] < arrayCGH$arrayValues[[var.BG]]*snr.thr)
}
SNR.char <- "B"
SNR.label <- "Low signal to noise ratio"
SNR.flag <- to.flag(SNR.FUN, SNR.char, args=alist(var.FG="REF_F_MEAN", var.BG="REF_B_MEAN", snr.thr=3))
If f
is a correction flag, f\$FUN
returns an object of type arrayCGH
and f\$char
is NULL
. In the following example, global.spatial.flag
computes a spatial trend on the array, and corrects the signal log-ratios from this spatial trend:
global.spatial.FUN <- function(arrayCGH, var)
{
if (!is.null(arrayCGH$arrayValues$Flag))
arrayCGH$arrayValues$LogRatio[which(arrayCGH$arrayValues$Flag!="")] <- NA
## Trend <- arrayTrend(arrayCGH, var, span=0.03, degree=1, iterations=3, family="symmetric")
Trend <- arrayTrend(arrayCGH, var, span=0.03, degree=1, iterations=3)
arrayCGH$arrayValues[[var]] <- Trend$arrayValues[[var]]-Trend$arrayValues$Trend
arrayCGH
}
global.spatial.flag <- to.flag(global.spatial.FUN, args=alist(var="LogRatio"))
We introduce an additional distinction between permanent and temporary flags in order to deal with the case of spots or clone that are known to be biologically relevant, but that have not to be taken into account for the computation of a scaling normalization coefficient. For example in breast cancer, when the reference DNA comes from a male, we expect a gain of the X chromosome and a loss of the Y chromosome in the tumoral sample, and we do not want log-ratio values for X and Y chromosome to bias the estimation of a scaling normalization coefficient.
Any flag
object therefore contains an argument called type
, which defaults to “perm” (permanent) but can be set to “temp” in the case of a temporary flag. In the following example, chromosome.flag
is a temporary flag that identifies clones correcponding to X and Y chromosome:
chromosome.FUN <- function(arrayCGH, var) {
var.rep <- arrayCGH$id.rep
w <- which(!is.na(match(as.character(arrayCGH$cloneValues[[var]]), c("X", "Y"))))
l <- arrayCGH$cloneValues[w, var.rep]
which(!is.na(match(arrayCGH$arrayValues[[var.rep]], as.character(l))))
}
chromosome.char <- "X"
chromosome.label <- "Sexual chromosome"
chromosome.flag <- to.flag(chromosome.FUN, chromosome.char, type="temp.flag", args=alist(var="Chromosome"), label=chromosome.label)
flag
methodsThe function to.flag
is used of the creation of flag
objects, with the specificities described in subsection flag
attributes.
args(to.flag)
## function (FUN, char = NULL, args = NULL, type = "perm.flag",
## label = NULL)
## NULL
Function flag.arrayCGH
simply applies function flag\$FUN
to a flag
object for filtering, and returns:
arrayCGH\$arrayValues\$Flag
filled with the value of flag\$char
for each spot to be excluded from further analysis in the case of an exclusion flag;args(flag.arrayCGH)
## function (flag, arrayCGH)
## NULL
Function flag.summary
computes spot-level information about normalization (including the number of flagged spots and numeric normalization parameters), and displays it in a convenient way. This function can either be applied to an object of type arrayCGH
:
args(flag.summary.arrayCGH)
## function (arrayCGH, flag.list, flag.var = "Flag", nflab = "not flagged",
## ...)
## NULL
or to plain spot-level information, by using the default method:
args(flag.summary.default)
## function (spot.flags, flag.list, nflab = "not flagged", ...)
## NULL
qscore
classAs we point out in the introduction of this document, evaluating the quality of an array-CGH after normalization is of major importance, since it helps answering the following questions: - which is the best normalization process ? - which array is of best quality ? - what is the quality of a given array ?
To this purpose we define quality scores (qscores), which attributes and methods are explianed in the two following subsections.
qcsore
attributesA qscore
object qs
is a list which contains a function (qs\$FUN
), a name (qs\$name
), and optionnally a label (qs\$label
) and arguments to be passed to qs\$FUN
(qs\$args
). In the following example, the quality score pct.spot.qscore
evaluates the percentage of spots that have passed the filtering steps of normalization; it provides an evaluation of the array quality for a given normalization process. The function to.qscore
is explained in subsection qscore
methods.
pct.spot.FUN <- function(arrayCGH, var) {
100*sum(!is.na(arrayCGH$arrayValues[[var]]))/dim(arrayCGH$arrayValues)[1]
}
pct.spot.name <- "SPOT_PCT"
pct.spot.label <- "Proportion of spots after normalization"
pct.spot.qscore <- to.qscore(pct.spot.FUN, name=pct.spot.name, args=alist(var="LogRatioNorm"), label=pct.spot.label)
qscore
methodsThe function to.qscore
is used of the creation of qscore
objects, with the specificities described in subsection [qscore
attributes]
args(to.qscore)
## function (FUN, name = NULL, args = NULL, label = NULL, dec = 3)
## NULL
Function qscore.arrayCGH
simply computes and returns the value of qscore
for arrayCGH
:
args(qscore.arrayCGH)
## function (qscore, arrayCGH)
## NULL
Function qscore.summary.arrayCGH
computes all quality scores of a list (using function qscore.arrayCGH
), and displays the results in a convenient way.
args(qscore.summary.arrayCGH)
## function (arrayCGH, qscore.list)
## NULL
We provide examples of array-CGH data coming from two different platforms. These data illustrate the need for appropriate within-array normalization methods, and especially the need for methods that handle spatial effects. These methods are described in detail in Neuvial et al. (2006).
data(spatial)
For each array we provide raw data (generated by GenePix or SPOT (Jain et al. 2002)), as well as the corresponding arrayCGH
object before and after normalization.
These arrays illustrate the main source of non biological variability of these data sets, namely spatial effects. We classify these effects into two non exclusive types: local bias and global gradients. In the case of local bias, entire areas of the array show lower or higher signal values than the rest of the array, with no biological explanation (array edge
); to our experience, this particular type of artifact roughly affects an array out of two. In the case of global gradients, the array shows an obvious signal gradient from one side of the slide to the other (array gradient
).
edge
Bladder cancer tumors were collected at Henri Mondor Hospital (Cr'eteil, France) (Billerey et al. 2001) and hybridized on arrays CGH composed of 2464 Bacterian Artificial Chromosomes (F. Radvanyi, D. Pinkel et al., unpublished results); each of these BAC is spotted three times on the array, and the three replicates are neighbors on the array. We give the example of an arrayCGH
with local spatial effects: high log-ratios cluster in the upper-right corner of the array.
data(spatial)
## edge: example of array with local spatial effects
GLAD::arrayPlot(edge, "LogRatio", main="Local spatial effects", zlim=c(-1,1), mediancenter=TRUE, bar="h")
gradient
We give the example of two arrays from a breast cancer data set from Institut Curie (O. Delattre, A. Aurias et al., unpublished results). These arrays consist of 3342 clones, organized as a \(4 \times 4\) superblock that is replicated three times%; therefore in this data set replicated spots are not neighbors on the array
. This data set is affected by the two types of spatial effects: local bias areas (as for the previous data set), and spatial gradients from one side of the array to the other. The array gradient
illustrates this second type of spatial effect.
data(spatial)
GLAD::arrayPlot(gradient, "LogRatio", main="Spatial gradient" , zlim=c(-2,2), mediancenter=TRUE, bar="h")
As for any type of data analysis, appropriate graphical representations are of major importance for data understanding. Array-CGH data are typically ratios or log-ratios, that correspond to locations on the array (spots) and to locations on the genome (clones). Therefore in the case of array-CGH data normalization, two complementary types of representations are necessary:
a dotplot of the array, that takes into account the array design. This is a crucial tool in the case of array-CGH data normalization for two reasons: first it provides an easy way to identify spatial artifacts such as row, column, print-tip group effects, as well as spatial bias and spatial gradients on the array; then it performs a post-normalization control, to ensure that the normalization procedure reached its goals, i.e. significantly reduced the observed effects.
a plot of the signal values along the genome, which gives a visual impression of the array quality on the edge of biological relevance; comparing the signal shape before and after normalization provides a qualitative idea of the imrpovement in data quality provided by the normalization method.
The arrayPlot
method provided by the GLAD package and based on maImage
(Dudoit and Yang 2003) addresses the first point; we add two methods to this toolbox:
genome.plot
method displays a plot of any signal value (e.g. log-ratios) along the genome;report.plot
method successively calls arrayPlot
and genome.plot
in order to provide a simultaneous vision of the data using the two relevant metrics (array and genome), with approproate color scales.genome.plot
This method provides a convenient way to plot a given signal along the genome; the signal values can be colored according to their level (which is the default comportment of the function) or to the level of any other variable, in the following way:
data(spatial)
#par(mfrow=c(7,5), mar=par("mar")/2)
genome.plot(edge.norm, chrLim="LimitChr", cex=1)
data(spatial)
edge.norm$cloneValues$ZoneGNL <- as.factor(edge.norm$cloneValues$ZoneGNL)
#par(mfrow=c(7,5), mar=par("mar")/2)
genome.plot(edge.norm, col.var="ZoneGNL", chrLim="LimitChr", cex=1)
report.plot
This method successively calls arrayPlot
and genome.plot
; it checks for color scale consistency between plots, and can automatically set the plot layout:
data(spatial)
report.plot(edge.norm, chrLim="LimitChr", zlim=c(-1,1), cex=1)
In this section we illustrate the use of MANOR on two CGH arrays. Our examples contain several steps, including data preparation, flag definition, array normalization, quality criteria definition, and quality assessment of the array, and highlights of the normalization process.
edge
import
dir.in <- system.file("extdata", package="MANOR")
## import from 'spot' files
spot.names <- c("LogRatio", "RefFore", "RefBack", "DapiFore", "DapiBack", "SpotFlag", "ScaledLogRatio")
clone.names <- c("PosOrder", "Chromosome")
edge <- import(paste(dir.in, "/edge.txt", sep=""), type="spot",
spot.names=spot.names, clone.names=clone.names, add.lines=TRUE)
## [1] "number of lines does not match array design: adding empty lines..."
norm
data(flags)
data(spatial)
## local.spatial.flag$args <- alist(var="ScaledLogRatio", by.var=NULL, nk=5, prop=0.25, thr=0.15, beta=1, family="symmetric")
local.spatial.flag$args <- alist(var="ScaledLogRatio", by.var=NULL, nk=5, prop=0.25, thr=0.15, beta=1, family="gaussian")
flag.list <- list(spatial=local.spatial.flag, spot=spot.corr.flag, ref.snr=ref.snr.flag, dapi.snr=dapi.snr.flag, rep=rep.flag, unique=unique.flag)
edge.norm <- norm(edge, flag.list=flag.list, FUN=median, na.rm=TRUE)
## [1] "spatial"
##
## ************************************************
## *** Spatial Classification with EM algorithm ***
## ************************************************
##
##
## Data : nb points = 7392
## grid size = 88 rows, 84 columns
##
## Neighborhood system :
## max neighb = 4
## Default 1st-order neighbors (horizontal and vertical)
##
##
## NEM parameters :
## beta = 1.00 | nk = 5
##
## Computing initial partition (sort variable 1) ...
##
## criterion NEM = 19782.898 / Ps-Like = 5035.969 / Lmix = 9250.229
## NEM converged after 173 iterations
##
## [1] "mean of unbiased zone : -0.0233232743043007"
## [1] "Spatial bias has been detected"
## zone.number mu effectif effectif.cumul frequency.cumul biased.zone
## 4 5 0.467833333 66 66 0.009189641 1
## 3 4 0.046085967 1582 1648 0.229462545 0
## 5 3 0.005084592 2648 4296 0.598162072 0
## 1 2 -0.032626474 1866 6162 0.857978279 0
## 2 1 -0.080052941 1020 7182 1.000000000 0
## [1] "spot"
## [1] "ref.snr"
## [1] "dapi.snr"
## [1] "rep"
## [1] "unique"
edge.norm <- sort(edge.norm, position.var="PosOrder")
report.plot(edge.norm, chrLim="LimitChr", zlim=c(-1,1), cex=1)
qscore.summary.arrayCGH
##DNA copy number assessment: GLAD
profileCGH <- GLAD::as.profileCGH(edge.norm$cloneValues)
profileCGH <- GLAD::daglad(profileCGH, smoothfunc="lawsglad", lkern="Exponential", model="Gaussian", qlambda=0.999, bandwidth=10, base=FALSE, round=2, lambdabreak=6, lambdaclusterGen=20, param=c(d=6), alpha=0.001, msize=2, method="centroid", nmin=1, nmax=8, amplicon=1, deletion=-5, deltaN=0.10, forceGL=c(-0.15,0.15), nbsigma=3, MinBkpWeight=0.35, verbose=FALSE)
## [1] "Smoothing for each Chromosome"
## [1] "Optimization of the Breakpoints and DNA copy number calling"
## [1] "Check Breakpoints Position"
## [1] "Results Preparation"
edge.norm$cloneValues <- as.data.frame(profileCGH)
edge.norm$cloneValues$ZoneGNL <- as.factor(edge.norm$cloneValues$ZoneGNL)
data(qscores)
## list of relevant quality scores
qscore.list <- list(smoothness=smoothness.qscore,
var.replicate=var.replicate.qscore,
dynamics=dynamics.qscore)
edge.norm$quality <- qscore.summary.arrayCGH(edge.norm, qscore.list)
edge.norm$quality
## name label score
## 1 LOCAL_SMOOTHNESS Local signal variability along the genome 0.021
## 2 VAR_REPLICATE Average variability among replicates 0.011
## 3 SIGNAL_DYNAMICS Dynamics of the DNA copy number variation 0.398
html.report
Function html.report
generates an HTML file with key features of the normalization process: array image and genomic profile before and after normalization, spot-level flag report, and value of the quality criteria.
html.report(edge.norm, dir.out=".", array.name="an array with local bias", chrLim="LimitChr", light=FALSE, pch=20, zlim=c(-2,2), file.name="edge")
The results of the previous command can be viewed in the file edge.html.
gradient
Here we give the example of the normalization of an array with spatial gradient.
import
## import from 'gpr' files
spot.names <- c("Clone", "FLAG", "TEST_B_MEAN", "REF_B_MEAN", "TEST_F_MEAN", "REF_F_MEAN", "ChromosomeArm")
clone.names <- c("Clone", "Chromosome", "Position", "Validation")
ac <- import(paste(dir.in, "/gradient.gpr", sep=""), type="gpr", spot.names=spot.names, clone.names=clone.names, sep="\t", comment.char="@", add.lines=TRUE)
## [1] "number of lines does not match array design: adding empty lines..."
## [1] "calculating array design..."
## compute log-ratio
ac$arrayValues$F1 <- log(ac$arrayValues[["TEST_F_MEAN"]], 2)
ac$arrayValues$F2 <- log(ac$arrayValues[["REF_F_MEAN"]], 2)
ac$arrayValues$B1 <- log(ac$arrayValues[["TEST_B_MEAN"]], 2)
ac$arrayValues$B2 <- log(ac$arrayValues[["REF_B_MEAN"]], 2)
Ratio <- (ac$arrayValues[["TEST_F_MEAN"]]-ac$arrayValues[["TEST_B_MEAN"]])/
(ac$arrayValues[["REF_F_MEAN"]]-ac$arrayValues[["REF_B_MEAN"]])
Ratio[(Ratio<=0)|(abs(Ratio)==Inf)] <- NA
ac$arrayValues$LogRatio <- log(Ratio, 2)
gradient <- ac
norm
data(spatial)
data(flags)
flag.list <- list(local.spatial=local.spatial.flag, spot=spot.flag, SNR=SNR.flag, global.spatial=global.spatial.flag, val.mark=val.mark.flag, position=position.flag, unique=unique.flag, amplicon=amplicon.flag, chromosome=chromosome.flag, replicate=replicate.flag)
gradient.norm <- norm(gradient, flag.list=flag.list, FUN=median, na.rm=TRUE)
## [1] "local.spatial"
##
## ************************************************
## *** Spatial Classification with EM algorithm ***
## ************************************************
##
##
## Data : nb points = 10800
## grid size = 180 rows, 60 columns
##
## Neighborhood system :
## max neighb = 4
## Default 1st-order neighbors (horizontal and vertical)
##
##
## NEM parameters :
## beta = 1.00 | nk = 7
##
## Computing initial partition (sort variable 1) ...
## Warning : pt 0 density = 0
##
## criterion NEM = 12882.131 / Ps-Like = -11189.528 / Lmix = 9832.894
## NEM converged after 1555 iterations
##
## [1] "mean of unbiased zone : 8.4344187599681"
## [1] "There is no spatial bias"
## zone.number mu effectif effectif.cumul frequency.cumul biased.zone
## 1 1 8.434419 10032 10032 1 0
## [1] "spot"
## [1] "SNR"
## [1] "global.spatial"
## [1] "val.mark"
## [1] "position"
## [1] "unique"
## [1] "amplicon"
## [1] "chromosome"
## [1] "replicate"
gradient.norm <- sort(gradient.norm)
genome.plot(gradient.norm, chrLim="LimitChr", cex=1)
qscore.summary.arrayCGH
##DNA copy number assessment: GLAD
profileCGH <- GLAD::as.profileCGH(gradient.norm$cloneValues)
profileCGH <- GLAD::daglad(profileCGH, smoothfunc="lawsglad", lkern="Exponential", model="Gaussian", qlambda=0.999, bandwidth=10, base=FALSE, round=2, lambdabreak=6, lambdaclusterGen=20, param=c(d=6), alpha=0.001, msize=2, method="centroid", nmin=1, nmax=8, amplicon=1, deletion=-5, deltaN=0.10, forceGL=c(-0.15,0.15), nbsigma=3, MinBkpWeight=0.35, verbose=FALSE)
## [1] "Smoothing for each Chromosome"
## [1] "Optimization of the Breakpoints and DNA copy number calling"
## [1] "Check Breakpoints Position"
## [1] "Results Preparation"
gradient.norm$cloneValues <- as.data.frame(profileCGH)
gradient.norm$cloneValues$ZoneGNL <- as.factor(gradient.norm$cloneValues$ZoneGNL)
data(qscores)
## list of relevant quality scores
qscore.list <- list(smoothness=smoothness.qscore, var.replicate=var.replicate.qscore, dynamics=dynamics.qscore)
gradient.norm$quality <- qscore.summary.arrayCGH(gradient.norm, qscore.list)
gradient.norm$quality
## name label score
## 1 LOCAL_SMOOTHNESS Local signal variability along the genome 0.033
## 2 VAR_REPLICATE Average variability among replicates 0.050
## 3 SIGNAL_DYNAMICS Dynamics of the DNA copy number variation 0.294
html.report
Function html.report
generates an HTML file with key features of the normalization process: array image and genomic profile before and after normalization, spot-level flag report, and value of the quality criteria.
html.report(gradient.norm, dir.out=".", array.name="an array with spatial gradient", chrLim="LimitChr", light=FALSE, pch=20, zlim=c(-2,2), file.name="gradient")
The results of the previous command can be viewed in the file gradient.html.
sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.5 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.12-bioc/R/lib/libRlapack.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] MANOR_1.62.0 knitr_1.30
##
## loaded via a namespace (and not attached):
## [1] compiler_4.0.3 magrittr_1.5 bookdown_0.21 htmltools_0.5.0
## [5] tools_4.0.3 GLAD_2.54.0 yaml_2.2.1 stringi_1.5.3
## [9] rmarkdown_2.5 highr_0.8 stringr_1.4.0 digest_0.6.27
## [13] xfun_0.18 rlang_0.4.8 evaluate_0.14
% A silly work-around for the ‘R CMD build’ intermittent issue on Windows: % * creating vignettes …Warning in file(con, “r”) : % cannot open file ‘D:-2.7-bioc6N8fzb3bf51a24’: Permission denied % Error in file(con, “r”) : cannot open the connection % Execution halted
The package MANOR provides sample gpr and spot files, as examples to the import
funciton. However, due to space limitations, only the first 100 lines these file are provided in the current distribution of MANOR. The full files can be downloaded from here:
Billerey, C., D. Chopin, M. H. Aubriot-Lorton, D. Ricol, S. Gil Diez de Medina, B. Van Rhijn, M. P. Bralet, et al. 2001. “Frequent FGFR3 Mutations in Papillary Non-Invasive Bladder (PTa) Tumors.” Am. J. Pathol. 158:955–1959.
Dudoit, S., and Y. H. Yang. 2003. “Bioconductor R Packages for Exploratory Analysis and Normalization of cDNA Microarray Data.” In The Analysis of Gene Expression Data: Methods and Software, edited by G. Parmigiani, E. S. Garrett, R. A. Irizarry, and S. L. Zeger. Springer, New York.
Hupé, P., N. Stransky, J-P. Thiery, F. Radvanyi, and E. Barillot. 2004. “Analysis of Array CGH Data: From Signal Ratios to Gain and Loss of DNA Regions.” Bioinformatics 20:3413–22.
Ishkanian, A. S., C. A. Malloff, S. K. Watson, R. J. DeLeeuw, B. Chi, B. P. Coe, A. Snijders, et al. 2004. “A Tiling Resolution DNA Microarray with Complete Coverage of the Human Genome.” Nat. Genet. 36:299–303.
Jain, A. N., T. A. Tokuyasu, A. M. Snijders, R. Segraves, D. G. Albertson, and D. Pinkel. 2002. “Fully Automatic Quantification of Microarray Image Data.” Genome Res. 12:325–32.
Neuvial, P., P. Hupé, I. Brito, S. Liva, E. Manié, C. Brennetot, F. Radvanyi, A. Aurias, and E. Barillot. 2006. “Spatial Normalization of Array-CGH Data.” BMC Bioinformatics 7 (1):264. https://doi.org/10.1186/1471-2105-7-264.
Pinkel, D., R. Segraves, D. Sudar, S. Clark, I. Poole, D. Kowbel, C. Collins, et al. 1998. “High Resolution Analysis of DNA Copy Number Variation Using Comparative Genomic Hybridization to Microarrays.” Nat. Genet. 20:207–11.
Snijders, A. M., N. Nowak, R. Segraves, S. Blackwood, N. Brown, J. Conroy, G. Hamilton, et al. 2001. “Assembly of Microarrays for Genome-Wide Measurement of DNA Copy Number.” Nat. Genet. 29:263–4.
Solinas-Toldo, S., S. Lampel, S. Stilgenbauer, J. Nickolenko, A. Benner, H. Dohner, T. Cremer, and P. Lichter. 1997. “Matrix-Based Comparative Genomic Hybridization: Biochips to Screen for Genomic Imbalances.” Genes Chromosomes Cancer 20:399–407.