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\begin{document}

\title{\bf Correcting gene specific dye bias}

%%% local shorthands:
\newcommand{\iGSDB}[0]{\textit{iGSDB}}
\newcommand{\slidebias}[0]{\textit{slide bias}}
\newcommand{\etal}[0]{\textit{et~al.}}


\author{Philip Lijnzaad$^1$ and Thanasis Margaritis$^2$}
\maketitle
\begin{center}
1. \email{p.lijnzaad@umcutrecht.nl}\\
2. \email{a.margaritis@umcutrecht.nl}\\
Dept. of Molecular Cancer Research\\
University Medical Center (UMC) \\
Universiteitsweg 100 \\
3584 CG Utrecht \\
The Netherlands
\end{center}

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\tableofcontents


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Overview}

This document gives a brief tutorial on how to use the \Rpackage{dyebias}
package to correct for gene-specific dye bias of two-colour microarray data
using the GASSCO method by \citet{lijnzaad09}. 

A well-known artefact of two-colour microarrays is the intensity-dependent
dye bias, which is usually adequately addressed by using LOESS normalization.
However, gene-specific dye bias is different, and persists after LOESS
normalization. Using dye swaps helps, but is not sufficient, as the bias
firstly wastes statistical power, but more importantly, may leave residual
bias since dye-swaps need not have the same degree of dye bias in both
hybridizations of the dye swapped pair.

Gene-specific dye bias is ubiquitous, and often quite large. The GASSCO
method implemented in the \Rcode{dyebias} package efficiently solves the
problem in a general and robust way.  The principle behind the method --
which can equally well be called a normalization method -- is very simple. We
observed that the total dye bias varies not only with each gene (or, more
precisely, each probe or reporter), but also with each hybridization, in an
apparently linear fashion. The formula is simply

$\beta_{ij} = F_j * \gamma_i $

\noindent where $\beta_{ij}$ is the total dye bias of reporter $i$ in hybridization
$j$; $F_j$ is the estimated \slidebias{} (more precisely: the hybridization
bias), and $\gamma_i$ is the so-called \textit{intrinsic gene specific dye
bias}, or briefly \iGSDB{} (again: \textit{gene} is a
misnomer; \textit{probe} or \textit{reporter} is more precise). 

It turns out that the \iGSDB{} depends on the protocols and somewhat on the
average expression levels, but the largest factor is the reporter
sequence. The slide bias depends largely on the labeling percentage \citep{lijnzaad09}.
Although the \iGSDB{}s can be predicted from the reporter sequence (see
\citet{lijnzaad09}, Supplemental Discussion), it is easier and more precise
to estimate it from the data. All that is needed is either a number of
self-self hybridizations, or a number of experiments that have been done in
dye-swap (also known as dye-flip or fluor-flip). If needed, estimated
\iGSDB{}s can be reused, provided the protocols have not changed.
The genes having the strongest \iGSDB{}s are used to estimate the slide bias.

The steps to perform dye bias correction are, then, 

\begin{enumerate}
  \item{estimate the intrinsinc gene specific dye bias using a number of
      self-self or dye-swapped slides }
  \item{for each slide, estimate the slide bias, and apply the correction}
\end{enumerate}


\noindent The \Rpackage{dyebias} package provides functions to do both, and
also has some plotting routines to judge the correction. The package has been
tested on a wide variety of public data (see \citet{lijnzaad09}), and has
been in active production in our own lab since over a year. We appreciate all
feedback.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Installing}

If you are reading this document and have not yet installed any
software on your computer, visit \\
%%% newline to avoid overful hbox
\url{http://bioconductor.org} and
follow the instructions for installing \Rcode{R} and Bioconductor.  Once
you have installed both \Rcode{R} and Bioconductor, install the
\Rpackage{dyebias} package with

%% dont use a chunk here, easier to postprocess:
\Rcode{                                 
source("http://bioconductor.org/biocLite.R") \\
biocLite("dyebias")
}

\noindent Alternatively, under Windows, select \Rcode{Packages} from the menu
and click on \Rcode{Install package(s) from Bioconductor...}, and select
\Rpackage{dyebias} from the pop--up. Under Linux/Unix you can use the usual
command \texttt{R CMD INSTALL} or set the option \texttt{CRAN} to your
nearest mirror site and use the command \texttt{install.packages} from within
an R session. The latest version of the \Rpackage{dyebias} package can always
be found at \\
%%% newline to avoid overful hbox
\url{http://www.holstegelab.nl/publications/margaritis_lijnzaad}.

Note: if you run \Rcode{R CMD check} on this package, it will complain with
\Rcode{dyebias.apply.correction: no visible global function definition for
  'maR<-'} (nor for \Rcode{'maG<-'}). You can safely ignore this message.

For simple examples of how the \Rpackage{dyebias} package can be used to
correct dyebias, just run the \Rcode{example()}s for any of the functions in
the package. In particular, try \Rcode{example(dyebias.rgplot)},
\Rcode{example(dyebias.boxplot)} and \Rcode{example(dyebias.trendplot)}.
They make use of our own validation data, which is provided by the
\Rpackage{dyebiasexamples} package, which can be installed through
Bioconductor similarly. The current document presents two more
case studies.

\section{Tuteja et al. (2008)}

The first example uses data from \citet{tuteja08}, a genome-wide location
analysis of the transcription factor Foxa2, which is important in liver
development.  The ChIP on chip data comes from five self-spotted mouse cDNA
slides.

\subsection{Reading the data}

The data is deposited in Array Express \citep{arrayexpress07} under accession
\texttt{M-TAB-32}, but for convenience, the data is provided through the
\Rpackage{dyebiasexamples} package. We need the \Rpackage{marray} package
\citep{marray} for the data model, \Rpackage{convert} for converting, and of
course \Rpackage{dyebias} and \Rpackage{dyebiasexamples}:

<<echo=false>>=
options(continue='   ')
@ 

<<>>=
  library(marray)
  library(dyebias)
  library(dyebiasexamples)
  library(convert)

  options(stringsAsFactors = FALSE)
@ 

\noindent The Tuteja data itself is not in the \Rcode{data} directory, since it doesn't
adhere to the \Rcode{R} standards. Instead, it was put in the \Rcode{extradata}
directory. Find it:

<<>>=
  datadir <- system.file("extradata", package="dyebiasexamples")
  datadir
@ 

\noindent The sample file contains descriptions of the hybridizations; read it and 
convert to a proper \Rcode{marrayInfo} object:

<<>>=

  sample.file <-  file.path(datadir, "Tuteja-samples.txt")

  targets <- read.marrayInfo(sample.file)

  summary(targets)

@ 

\noindent It shows that we have five hybridizations, all of them FoxA2-enriched versus
input material. Three of them have the dyes in the ``forward'' direction, two
in the ``reverse'' direction. In other words, the design is not balanced;
more on this below. First prepare the layout information (this was gleaned
from the original submission):

<<>>=

  layout <- read.marrayLayout(fname=NULL, ngr=12, ngc=4, nsr=22, nsc=19)

  n.spots <- maNspots(layout)

  summary(layout)

@ 

\noindent Read the gene information from the first of the data files. The
only thing really needed by the \Rpackage{dyebias} package is the
\Rcode{reporterId} column for the \Rcode{maInfo(maGnames(data))}, but it
doesn't hurt to include \Rcode{control.type} and \Rcode{reporter.group}.
The latter is used to set the \Rcode{maControls}. These are not needed, but
\Rcode{marray} complains otherwise, so we might as well supply the information.

<<>>=

  first.file <- file.path(datadir, maInfo(targets)$filename[1])
  first.file
  gnames <- read.marrayInfo(first.file, info.id=c(7,8,10), labels=10, skip=0)
  names(maInfo(gnames)) <- c("control.type", "reporter.group", "reporterId")

  maInfo(gnames)$reporterId <- as.character(maInfo(gnames)$reporterId)

  #### Following is not really needed (it makes  the 
  ### ``"Controls are generated from an arbitaray columns\n"'' message go way

  controls <- maInfo(gnames)$reporter.group
  controls [ controls == "Experimental"] <-  "gene"
  maControls(layout) <- as.factor(controls)

  summary(gnames)

@ 

\noindent Next, we read the data. In the examples in this document, we assume
that the public data is properly normalized; that is really the starting
point for GASSCO. If the data is not (properly) normalized, results will be
suboptimal (as we will see). In the Tuteja data set both 'raw' and normalized
data are available.  This is good, because the raw data has foreground as
well as background intensities; the latter allow us to better judge the quality
of the spots. We therefore read both, starting with the raw data:

<<>>=

  data.raw <- read.GenePix(fnames = maInfo(targets)$filename,
                           path = datadir,
                           name.Gf = "GenePix:F532 Median",
                           name.Gb ="GenePix:B532 Median",
                           name.Rf = "GenePix:F635 Median",
                           name.Rb = "GenePix:B635 Median",
                           name.W = "GenePix:Flags",
                           layout = layout,
                           gnames = gnames,
                           targets = targets,
                           skip=0, sep = "\t", quote = '"', DEBUG=TRUE)

@ 

\noindent The weights in the file use a different convention, so convert them
to the \Rcode{marray} convention, which is \Rcode{weight == 0} for bad spots,
\Rcode{weight == 1} for good spots. (Bad spots are never used as estimator
genes, and you could also decide not to dye bias-correct them). Also attach
the layout to the \Rcode{data.raw} object, and show what we have:

<<>>=

  maW(data.raw)[ maW(data.raw) == 0] <- 1
  maW(data.raw)[ maW(data.raw) < 0] <- 0

  maLayout(data.raw) <- layout

  summary(data.raw)

@ 

\noindent Let's now read the normalized data. As a short-cut, we will use
\Rcode{data.raw} as a template (using \Rcode{as()} from the
\Rpackage{convert} package), and then only replace the actual values. 

<<>>=

  normalized.data.file <-  file.path(datadir, "E-MTAB-32-processed-data-1641029599.txt")
  data <- read.table(normalized.data.file, sep="\t", as.is=T, header=T, skip=1)
  names(data) <- c("reporterId", "X13685041", "X13685040" , "X13685153" ,"X13685151" ,"X13685042")
  ## get rid of overly long gene names:
  data$reporterId <- sub(pattern="ebi.ac.uk:MIAMExpress:Reporter:A-MEXP-1165\\.(P[0-9]+) .*",
     replacement="\\1", x=data$reporterId, perl=T, fixed=F)
  data$reporterId <- sub(pattern="ebi.ac.uk:MIAMExpress:Reporter:A-MEXP-1165\\.Blank.*",
     replacement="Blank", x=data$reporterId, perl=T, fixed=F)

  data.norm <- as(data.raw,"marrayNorm")

  ## now replace the actual data:
  m <- as.matrix(data[,c(2:6)])
  n <- as.numeric(m)
  dim(n) <- dim(m)

  maM(data.norm) <- n

@ 

\noindent In most cases we have seen, authors have deposited their data such that the dye
swaps have been undone so that the slides all seem  to be in the ``forward'' direction.
(The reason is that you can then more easily compare the treatment
vs. reference behaviour of a set of slides,  regardless of dye orientation.

However, here we are interested only in the dye effect itself, that is, in
the effect of $log_2(Cy5 / Cy3)$, \emph{not} in the difference of
FoxA2-enriched over input material. We therefore have to reswap the undone
dye swaps.  \footnote{Whether the columns have been deposited the right way
  around is often not clear from the description. Sometimes it can be
  inferred from the general behaviour of the data. E.g., in the case of
  knock-down data, the knocked-down gene should be down in one hybridization,
  up in the other; in ChIP data, the ChIP-enriched sample generally should go
  up relative to the input sample and is therefore be visible, in an MA-plot, as a
  cloud of points with a flattish bottom and a bulging top.
}

<<>>=

  maM(data.norm)[,c(3,4)] <- -1 *maM(data.norm)[,c(3,4)]

@ 

\noindent $A$, the average intensity of both channels, is not yet set, so
compute it here:

<<>>=

  maA(data.norm) <- log2(  maRf(data.raw) * maGf(data.raw) ) / 2

@ 

\noindent Note that the code does not really need \Rcode{A}; the correction
is based solely on \Rcode{M}. The \Rcode{A} is not always available; some
labs publish only the \Rcode{M}-values. In such cases, it is fine to
``invent'' an \Rcode{A}, e.g. by sampling from a uniform distribution between
2 and 15 (which is the typical domain of \Rcode{A}). The advantage of such
fake data is that the plotting routines in the \Rpackage{dyebias} package
continue to work.


\subsection{Estimating the \iGSDB{}}

We now have a full-fledged \Rcode{marrayNorm} object that we can use to
estimate the iGSDBs from. 

The design is unbalanced, which is actually uncommon; most designs are (or
should be) balanced. If the design is unbalanced, the
\Rcode{dyebias.estimate.iGSDBs} function uses \Rpackage{limma} \citep{limma}
to obtain estimates for the intrinsic gene specific dye biases. In the
current data set, the \Rcode{reference} is the sample called \Rcode{input}
(see \Rcode{maInfo(maTargets(data.norm))}). The call is therefore:

<<>>=

  iGSDBs.estimated <- dyebias.estimate.iGSDBs(data.norm,
                                              is.balanced=FALSE,
                                              reference="input",
                                              verbose=TRUE) 
   
  summary(iGSDBs.estimated)

@

\noindent This took a little while, mostly be because a full Limma model has to be run
for this unbalanced design. (We ignore its $p$-values, since we have no
use for them). If the design is balanced, the estimate is done by simply
averaging. This gives identical results (and no $p$-values), but is much
faster.

Let's have a quick look at the distribution of the iGSDBs:

%% <<fig=TRUE, png=FALSE>>=
<<fig=TRUE>>=

  hist(iGSDBs.estimated$dyebias, breaks=50)

@ 

\noindent In our own lab, the iGSDBs generally have a distribution that is roughly
symmetrical, with a mean slightly below zero, and a standard deviation of
around 0.2.  The data shown here shows is fairly similar.

\subsection{Applying the dye bias correction}

Before applying the correction, we need to choose which genes
(probes/reporters!) are good enough to base the slide bias estimate on.  We
call them the estimator genes. Generally, we discard reporters that are
likely to have a high biological variability. Generally, reporters not
representing genes, and those corresponding to mitochondrial genes,
transposons, cross-hybridizing and non-unique oligo sequences are therefore
discarded. In the current case, we know nothing about the reporters, so we
only insist that they correspond to genes; that group is called
\Rcode{Experimental}:

<<>>=

  estimator.subset <- (maInfo(maGnames(data.norm))$reporter.group=="Experimental")

  summary(estimator.subset)

@ 

A convenience function is provided to get an index for the spots that are
trustworthy estimator genes. The current data set does have background
signals, so we specify \Rcode{use.background=TRUE}.  (If background signals would
not have been available, we should have specified \Rcode{use.background=FALSE},
which causes the minimum foreground signal to be used as a proxy for the
background signal).

\noindent We now specify which spots we would like to dye
bias-correct. Generally it is best to correct all spots. However, we have
noticed that for signals that are too high or too low, over-correction can
occur. Signals that are too high are due to saturation of the scanner,
whereas those that are too low may be too noisy due to differences in
background signal. We want to be a bit more selective, only correcting genes
where we are certain that we have a trustworthy signal. We therefore insist
that the weight of the spot is 1, and that they lie in the right range. Here,
we choose a signal-to-noise ratio (here defined as foreground over background
signal) $\ge$ 1.5 and an average expression \Rcode{A} $\le$ 15.


<<>>=

  application.subset <- ((maW(data.norm)==1)
                         & dyebias.application.subset(data.raw=data.raw,
                                min.SNR=1.5,
                                maxA=15,
                                use.background=TRUE)
                         )

  summary(as.vector(application.subset))

@ 

\noindent We're now set to apply the correction, simply as:

<<>>=

  correction <- dyebias.apply.correction(data.norm=data.norm,
                                         iGSDBs=iGSDBs.estimated,
                                         estimator.subset=estimator.subset,
                                         application.subset=application.subset,
                                         verbose=TRUE)
@ 

The \Rcode{correction} object contains the complete results. It is a
\Rcode{list} with 4 members: \Rcode{data.corrected}, the corrected data in
\Rcode{marrayNorm} format; \Rcode{estimators}, which contains the estimators
and is used by the plotting routines; \Rcode{summary}, a \Rcode{data.frame}
with statistics concerning the dye bias correction, and lastly (for
convenience) \Rcode{data.uncorrected}, the input data.  For the summary, the
most useful ones are probably \Rcode{avg.correction, var.ratio,
reduction.perc} and \Rcode{p.value}:

<<>>=
  correction$summary[,c("slide", "avg.correction", "var.ratio", "reduction.perc", "p.value")]

@ 

\noindent \Rcode{slide} (or alternatively \Rcode{file}) identifies the slide;
\Rcode{avg.correction} is the slide bias; \Rcode{var.ratio} shows the
reduction in the variance of \Rcode{M}) that was achieved by the correction;
\Rcode{reduction.perc} showing the same, but as a percentage. Lastly,
\Rcode{p.value} indicates the significance of the reduction in variance
($H_0$: variances before and after correction are equal).

It can be seen that slide 3 had the strongest dye bias. Its variance of $M$
is hugely reduced, by 50\%. 

\subsection{Plotting the data}

Let us look at how the correction worked out for one particular slide of this
set, say number 3, the one with the strongest slide bias. We first plot the
uncorrected data, then the corrected data. In both cases, we colour the
strongest 5\% green-biased and red-biased spots accordingly (that is why the
\Rcode{iGSDBs}-argument is required).

There will be an overlap between the estimator genes and those now coloured
red and green. However, the estimator genes only come from the ``middle'' of
the data set (as specified by the default value of the
\Rcode{minmaxA.perc}-argument; see the documentation).


%%% The following code uses Thibaut Jombart's Sweave replacement, which can
%%% produce .png files (see
%%% http://biomserv.univ-lyon1.fr/~jombart/rstuff.html).  This is needed
%%% because the embedded postscript files for scatterplots of 10,000's of
%%% genes are simply too big for acrobat reader.  

%% <<fig=TRUE, png=TRUE, eps=FALSE, pdf=FALSE, width=7, height=4, size=1>>=
<<fig=TRUE>>=

  layout(matrix(1:2, nrow=1,ncol=2))

  dyebias.rgplot(data=data.norm,
                 slide=3,
                 iGSDBs=iGSDBs.estimated,
                 application.subset=application.subset, 
                 main="uncorrected",
                 cex=0.2,
                 cex.lab=0.8,
                 cex.main=0.8,
                 output=NULL)

  dyebias.rgplot(data=correction$data.corrected,
                 slide=3,
                 iGSDBs=iGSDBs.estimated,
                 application.subset=application.subset,
                 main="corrected",
                 cex=0.2,
                 cex.lab=0.8,
                 cex.main=0.8,
                 output=NULL)

@ 

\noindent In the uncorrected slide, there is a clear separation between the
genes with a strong red bias, and those with a strong green bias. After
correction, this separation has disappeared, and the overal spread around the
diagonal is much reduced. As can be seen from from the off-diagonal lines
(representing a two-fold change), some 20 spots appear to have been down by
more than two-fold down just as a result of gene-specific dye bias.


How did the procedure perform for all slides? This is best seen using the
\Rcode{dyebias.boxplot} function. It is called twice, once with the
uncorrected, once with the corrected data. For clarity, we prefer to order
the slides by increasing slide bias (of the uncorrected data), hence the
\Rcode{order} argument:

%% <<fig=TRUE, png=FALSE, height=3, width=6,size=1>>=
<<fig=TRUE>>=

  layout(matrix(1:2, nrow=1,ncol=2))

  order <- dyebias.boxplot(data=data.norm, 
    iGSDBs=iGSDBs.estimated,
    order=NULL,
    ylim=c(-1,1),
    application.subset=application.subset,
    main="uncorrected",
    cex=0.2,
    cex.lab=0.8,
    cex.main=0.8,
    output=NULL
    )

  order <- dyebias.boxplot(data=correction$data.corrected, 
    iGSDBs=iGSDBs.estimated,
    order=order,
    ylim=c(-1,1),
    application.subset=application.subset, 
    main="corrected",
    cex=0.2,
    cex.lab=0.8,
    cex.main=0.8,
    output=NULL
    )

@ 


\noindent If the red and green boxes coincide, this is a sign that the  bias was
removed successfully, and without introducing other biases. This is clearly
the case here. Although in general there is no
correlation between slide bias and residual bias after correction, 
slide number 3 has both the largests slide bias and the largest residual
bias. One could consider throwing this hybridization out. 

In the above, we have restricted the dyebias correction and the plots to
spots that had good quality, by insisting on a weight of 1, good
signal-to-noise and no saturation. If you would plot all spots (by leaving
out the \Rcode{application.subset} argument), you would get a fairly large
residual dye bias.  The reason is that this data set has a high proportion of
spots that we chose not to correct: around 15\% is due to low quality spots,
and around 25\% due to too low or too high intensity.  The solution is to
play with the \Rcode{application.subset} to get more spots corrected; this is
left as an exercise to the reader.


%% ========================================================================

\section{Chen et al. (2007)}

%%% NOTE: this section has been commented out, as it takes too long to build
%%% for Bioconductor. If you're interested, simply get rid of all the 'eval=FALSE'
%%% below. 

The next example is based on genome-wide location data of Orc6, which plays a
role in DNA replication initiation \citep{chen07}.  The data is available
from NCBI's Gene Expression Omnibus \citep{geo07} under accession
\texttt{GSE9318}.  It consists of two sets of Agilent slides: 4 done on
platform \Rcode{GPL3499}, and 9 slides done on platform \Rcode{GPL5991}. Only
the latter set has proper dye swaps, and these will be used to estimate the
intrinsic gene-specific dye bias (iGSDB). These estimates are subsequently
used to correct all 9 \Rcode{GPL5991} slides.

\subsection{Reading the data}

We will try and download the data directly from GEO using the
\Rpackage{GEOquery} \citep{davis07}). The downloading and the subsequent
parsing takes a long while, so we'll first see if we already have the
\Rcode{.RData} file (derived from the \Rcode{.soft} file), if not, prompt for
downloading it to the current directory, and then parse the file and save it
as an \Rcode{R} data dump.  We need the full \Rpackage{.soft}-file, since we
want to have all the data, not just the \Rcode{M}-values.

<<eval=FALSE>>=

  library(GEOquery)
  library(marray)
  library(limma)
  library(dyebias)
  library(dyebiasexamples)

  options(stringsAsFactors = FALSE)


  gse.id <- "GSE9318"
  ## dir <- system.file("data", package = "dyebias")
  dir <- getwd()

  if (! file.exists(dir)) {
    stop(sprintf("could not find directory '%s' (to write GSE9318 data to/from)", dir))
  }

  file.RData <- sprintf("%s/%s.RData", dir,gse.id) 

  if( file.exists(file.RData) ) {
    cat(sprintf("Loading existing data from %s\n", file.RData))
    load(file.RData)
  } else {
    if ( interactive()) { 
      if (readline(prompt=sprintf("Could not find file %s.\nDo you want me to download the data from GEO?\nThis will take a while [y/N]: ", file.RData)) != "y"  ) {
        stop("Exiting")
      }
    }
    cat("Downloading .soft file from GEO ...\n")
    file.soft <- getGEOfile(gse.id, destdir=dir, amount="full")
    cat("done\nParsing .soft file ...\n")
    gse <- getGEO(filename=file.soft)
    cat(sprintf("done\nSaving to %s ... ", file.RData))
    save.image(file.RData)
    cat("done\n")
  } 

@ 

\noindent This data uses the GEOquery classes, and this has to be converted
to \Rcode{marrayNorm} and \Rcode{marrayRaw} objects, since that is what the
\Rpackage{dyebias} package uses. The \Rcode{dyebias.geo2marray}-function in
the \Rpackage{dyebiasexamples} package is provided for that.

The data set consists of slides done on two platforms. The only
hybridizations that were done in dye-swap on the same platform are on
platform \Rcode{GPL5991}. These slides are \Rcode{GSM237352, GSM237353,
  GSM237354} and \Rcode{GSM237355}, and we will use them to estimate the
iGSDBs. We subsequently use this estimate to correct all the slides done the
\Rcode{GPL5991} platform\footnote{The slides done on the other platform
  (\Rcode{GPL3499}) in this data set may or may not benefit from dye bias
  correction using iGSDB estimates from the \Rcode{GPL5991} slides; this is
  left as an exercise to the reader.}.

The reporter label is found under the \Rcode{ProbeName}-column, and probes
(reporters) corresponding to genes look like \Rcode{A\_75\_P01000003}; this is
used for the \Rcode{gene.selector}-function.

Since the normalized data does not contain \Rcode{A}-values, we calculate
(approximate) them from the raw data. The columns etc. are as indicated. You
generally have to be careful with this; use e.g. \\
%%% (newline to avoid overful hbox)
\Rcode{Columns((GSMList(gse))[[1]])} to see what they are, and also plot
them to be sure about the dye orientation.

<<eval=FALSE>>=

  ## following slides are used to obtain iGSDB estimates:
  slide.ids.est <- c( "GSM237352", "GSM237353", "GSM237354", "GSM237355" )

  ## column names:
  cy3.name <- "label_ch1"
  cy5.name <- "label_ch2" 

  ## function to recognize 'genes':
  gene.selector <- function(table){grep("^A_75_", as.character(table[["ProbeName"]]))}

  reporterid.name <- "ProbeName"
  M.name <- "VALUE"              #normalized
  Gf.name <- "Cy3"               #raw
  Gb.name <- "Cy3_Background"
  Rf.name <- "Cy5"               #raw
  Rb.name <- "Cy3_Background"    # yes! (error in the data: Cy5_Background == Cy5 ...)

  ## convert the raw data ...
  data.raw.est <-
    dyebias.geo2marray(gse=gse,
                       slide.ids=slide.ids.est,
                       type="raw",
                       gene.selector=gene.selector,
                       reporterid.name=reporterid.name,
                       cy3.name=cy3.name,
                       cy5.name=cy5.name,
                       Rf.name=Rf.name,
                       Gf.name=Gf.name,
                       Rb.name=Rb.name,
                       Gb.name=Gb.name,
                       )

  ## ... and the normalized data:
  data.norm.est <-
    dyebias.geo2marray(gse=gse,
                       slide.ids=slide.ids.est,
                       type="norm",
                       gene.selector=gene.selector,
                       reporterid.name=reporterid.name,
                       cy3.name=cy3.name,
                       cy5.name=cy5.name,
                       M.name=M.name
                       )

  ## maA was not set; do that here:
  maA(data.norm.est) <- log2(  maRf(data.raw.est) * maGf(data.raw.est) ) / 2

  ## unswap the swapped dye-swaps:
  maM(data.norm.est)[, c(2,4)] <-  - maM(data.norm.est)[, c(2,4)]

@ 

\noindent There is one thing that is not quite right with the current data:
the contents of the \Rcode{Cy3}- and \Rcode{Cy5}-columns are wrong:

<<eval=FALSE>>=

  maInfo(maTargets(data.norm.est))

@ 

\subsection{Estimating the \iGSDB{} }

The current design is balanced, so the dyebias is simply the average of the
raw $M$. However, to show how the ``set of pairwise designs'' estimation
works, we will show what is needed (but not use it). A bit of sleuthing shows
that what is actually needed is the following:

<<eval=FALSE>>=

  info <- maInfo(maTargets(data.norm.est)) 

  info$Cy3 <- c("wt",    "wt IP",  "td",    "td IP" )
  info$Cy5 <- c("wt IP", "wt",     "td IP", "td")

  maInfo(maTargets(data.norm.est)) <- info

  references <- c("wt", "td")

   ### The estimation would then be run as:
   ###
   ###   iGSDBs.estimated <- dyebias.estimate.iGSDBs(data.norm.est, is.balanced=FALSE, 
   ###                                             reference=references, verbose=TRUE)

@ 

\noindent That is, we have one dye-swapped pair of IP vs. input material for
the wild type, and one dye-swapped pair for the temperature-sensitive degron
mutant.  In other words, we have a set of pairwise designs. If
\Rcode{dyebias.estimate.iGSDBs} were to use LIMMA (which is necessary for
unbalanced designs, but not necessary and not used in the current case), then
it has to know what the references are in each case; hence the
\Rcode{references <- c("wt", "td")} assignment. It also has be able to figure
out which ``experimental'' (i.e., non-reference) sample goes with which
reference. Therefore, they all have to start with the name of their
respective reference sample (see the documentation).  Having said that, we
will ignore the \Rcode{references} argument for now, and estimate the iGSDBs
using averaging, simply as:

<<eval=FALSE>>=

  iGSDBs.estimated <- dyebias.estimate.iGSDBs(data.norm.est, is.balanced=TRUE, verbose=TRUE)
  summary(iGSDBs.estimated)

@ 

\subsection{Reading the rest of the data}

We now have an estimate of the intrinsic gene specific dye biases, and we can
use it to correct all the hybridizations done on platform \Rcode{GPL5991}.
However, that is not yet converted to \Rcode{marray} objects, so do that
first, and also make sure \Rcode{A} is set and the dye swaps are swapped back:

<<eval=FALSE>>=

  subset  <- sapply(GSMList(gse), function(x){Meta(x)$platform_id}) == "GPL5991"
  slide.ids.all <- sapply(GSMList(gse), function(x){Meta(x)$geo_accession})[subset]

  data.raw.all <-
    dyebias.geo2marray(gse=gse,
                       slide.ids=slide.ids.all,
                       type="raw",
                       gene.selector=gene.selector,
                       reporterid.name=reporterid.name,
                       cy3.name=cy3.name,
                       cy5.name=cy5.name,
                       Rf.name=Rf.name,
                       Gf.name=Gf.name,
                       Rb.name=Rb.name,
                       Gb.name=Gb.name,
                     )

  data.norm.all <-
    dyebias.geo2marray(gse=gse,
                       slide.ids=slide.ids.all,
                       type="norm",
                       gene.selector=gene.selector,
                       reporterid.name=reporterid.name,
                       cy3.name=cy3.name,
                       cy5.name=cy5.name,
                       M.name=M.name
                       )      

  maA(data.norm.all) <- log2(  maRf(data.raw.all) * maGf(data.raw.all) ) / 2

  swap <- c(1,2,3,5, 7,8,9) 
  maM(data.norm.all)[, swap] <-  - maM(data.norm.all)[, swap]

@

\subsection{Applying the dye bias correction}

As before, we will exclude some spots, based on their intensity, from dye
bias correction. The data set does have its own backgrounds, but we know
little about the suitability of the spots to act as estimators of the slide
bias, so we\'ll set estimator.subset=T. This means that no spot is excluded
from being an estimator, apart from the second condition, which is that they
have an average signal \Rcode{A} falling within the interquartile range (see 
the documentation of \Rcode{dyebias.apply.correction}).

<<eval=FALSE>>=

  application.subset <- ( (maW(data.norm.all) == 1) &
                         dyebias.application.subset(data.raw=data.raw.all,
                                                    min.SNR=1.5,
                                                    maxA=15,
                                                    use.background=TRUE)
                         )

  correction <- dyebias.apply.correction(data.norm=data.norm.all,
                                             iGSDBs=iGSDBs.estimated,
                                             estimator.subset=T,
                                             application.subset=application.subset,
                                             verbose=FALSE)

  correction$summary[,c("slide", "avg.correction", "var.ratio", "reduction.perc", "p.value")]

@ 

\subsection{Plotting the data}

Some people prefer \Rcode{MA}-plots over \Rcode{RG}-plots, so let's 
see how the dyebias correction turned out for slide 6, which had the greatest
bias:

%%% The following code uses Thibaut Jombart's Sweave replacement, which can
%%% produce .png files (see
%%% http://biomserv.univ-lyon1.fr/~jombart/rstuff.html).  This is needed
%%% because the embedded postscript files for scatterplots of 10,000's of
%%% genes are simply too big for acrobat reader.  

%% <<eval=FALSE, fig=TRUE, png=TRUE, eps=FALSE, pdf=FALSE, height=3, width=6, size=1>>=
<<eval=FALSE, fig=FALSE>>=
  layout(matrix(1:2, nrow=1,ncol=2))

  dyebias.maplot(data=data.norm.all,
                 slide=6,
                 iGSDBs=iGSDBs.estimated,
                 application.subset=application.subset,
                 main="uncorrected",
                 cex=0.2,
                 cex.lab=0.8,
                 cex.main=0.8,
                 output=NULL)

  dyebias.maplot(data=correction$data.corrected,
                 slide=6,
                 iGSDBs=iGSDBs.estimated,
                 application.subset=application.subset,
                 main="corrected",
                 cex=0.2,
                 cex.lab=0.8,
                 cex.main=0.8,
                 output=NULL)
@ 

\incompleteVignetteOmission{}

\noindent The difference between the uncorrected and corrected data is quite
big. The strongly red-biased spots had an average two-fold change, which,
after correction, turns out to have been spurious. A number of strongly
green-biased spots appear depleted before correction, but may actually have
been enriched in the immunoprecipitated samples after correction.

What is also visible is that the data is not properly normalized. The left
panel shows a cloud whose bottom has a the downward-sloping trend frequently
found in ChIP-on-chip data. This should not be present in normalized
data\footnote{We did not renormalise this data as the point of this document
  is to demonstrate dye bias correction of existing, normalized data.}.  The dye bias
correction procedure tries to also correct this ChIP-on-chip artifact,
resulting in suboptimal behaviour (see below).

To get a graphical overview of all corrections, \Rcode{dyebias.boxplot} could
be used, but another function is provided that can show to what extent the
data supports our claim that the total dye bias is the product of the slide
bias and the intrinsic bias. We order all slides by the slide bias, and plot
each spot. However, the number of spots is too large to judge whether their
behaviour is linear. The function \Rcode{dyebias.trendplot} therefore bins
all probes by their intrinsic bias, and plots the median of each bin for each
slide:


%%% We can't print the trendplot in the cut-down version, since the data for it
%%% is calculated in a a eval=FALSE block ...
%% <<eval=FALSE, fig=TRUE, png=FALSE, height=3, width=6, size=1>>=
<<eval=FALSE, fig=FALSE, height=3, width=6>>=

  layout(matrix(1:2, nrow=1,ncol=2))

  order <- dyebias.trendplot(data=data.norm.all, 
    iGSDBs=iGSDBs.estimated,
    application.subset=application.subset,
    order=NULL,
    lwd=0.1,
    ylim=c(-0.5,0.5),
    output=NULL,
    main="uncorrected")

  order <- dyebias.trendplot(data=correction$data.corrected, 
    iGSDBs=iGSDBs.estimated,
    application.subset=application.subset, 
    order=order,
    lwd=0.1,
    ylim=c(-0.5,0.5),
    output=NULL,
    main="corrected")

@ 

\incompleteVignetteOmission{}

\noindent The method does a good job, although usually the results are even
better, with all lines hovering around $M=0$ after the correction.  We
attribute this behaviour to the fact that the data is poorly normalized, as
mentioned before. This affects the iGSDB estimates, which in turn impacts the
correction of the rest of the data. The overall variance, however, is clearly
reduced.

From the left panel it is also clear that the total dye bias shows a
consistent trend in each of the bins. This can only happen if the total dye
bias is a monotonic function of the slide bias and the intrinsic
gene-specific dye bias. Our proposal to simply use the product of both
appears to be a good first approximation.

If the monotonicity assumption is warranted, the slopes of each of the
regression lines should increase with increasing iGSDB. This can be tested
using the Mann-Kendall test, which is available from the
\Rcode{dyebias.monotonicity} function.  It plots, for each gene, the slope of
each regression line in the data set.  The function is included to further
support our model of gene specific dye bias, but since the function takes
very long to compute, we strongly discourage its use by end users.


%%% NOTE: this plot takes very long to calculate!

%% <<eval=FALSE, fig=TRUE, png=TRUE, height=3, width=6, size=1>>=
<<eval=FALSE, fig=FALSE>>=

  layout(matrix(1:2, nrow=1,ncol=2))

  order <- dyebias.monotonicityplot(data=data.norm.all, 
    iGSDBs=iGSDBs.estimated,
    order=NULL,
    ylim=c(-0.5,0.5),
    output=NULL,
    main="uncorrected")

  order <- dyebias.monotonicityplot(data=correction$data.corrected, 
    iGSDBs=iGSDBs.estimated,
    order=order,
    ylim=c(-0.5,0.5),
    output=NULL,
    main="corrected")

@ 

\incompleteVignetteOmission{}

\noindent Before dye bias correction with GASSCO, the data shows a clear trend
of increasing apparent $M$, due to dye bias. After correction, this trend has
been strongly reduced, supporting our assumption of monotonicity in this
case.

%% ========================================================================


\section{Closing remarks}

So far, we have not found a data set that does not benefit from GASSCO.  The
code has been in continuous use in our laboratory since early 2008, totalling
hundreds of hybrizations. In our experience, the code and the estimates are
very robust, which we attribute to the use of medians and large samples
wherever appropriate.

The quality of dye bias correction with GASSCO depends on the accuracy of the iGSDB
estimate. This, in turn, depends on having a representative data set of
self-self and/or dye-swapped hybrizations. In our experience, a set of around
12 hybrizations is optimal. However, even as few as four hybrizations can
result in good dye bias correction, as witnessed by the examples given here,
and also by the \Rcode{data.norm} data set used throughout the
\Rcode{example()} code of the \Rcode{dyebias} package.

Make sure the data is properly normalized, and that the dye orientation is
the same as in the original hybridizations (that is, do not swap them back). 

Lastly, we appreciate all feedback.

\vspace{1.5ex}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibliographystyle{abbrvnat}
% \bibliographystyle{plainnat}

\bibliography{dyebias}


\section{sessionInfo}
<<results=tex,echo=false>>=
  toLatex(sessionInfo())
@

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
