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\begin{document}

\title{\bf Bioconductor's marray package: Plotting component}


\author{Yee Hwa Yang$^1$ and Sandrine Dudoit$^2$}

\maketitle
\begin{center}
1. Department of Medicine, University of California, San Francisco,
   {\tt jean@biostat.berkeley.edu}\\
2. Division of Biostatistics, University of California, Berkeley,
   \url{http://www.stat.berkeley.edu/~sandrine}
\end{center}



% library(tools) 
% setwd("C:/MyDoc/Projects/madman/Rpacks/marray/inst/doc")
% Rnwfile<-file.path("C:/MyDoc/Projects/madman/Rpacks/marray/inst/doc","marrayPlots.Rnw")
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% Sweave(Rnwfile,pdf=TRUE,eps=TRUE,stylepath=TRUE,driver=RweaveLatex())

\tableofcontents



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

This document provides a detailed discussion of the plotting functions
in {\tt marray} package, which is a packages for diagnostic plots of
two-color spotted microarray data.  This docuement provides functions
for diagnostic plots of microarray spot statistics, such as boxplots,
scatter--plots, and spatial color images. Examination of diagnostic
plots of intensity data is important in order to identify printing,
hybridization, and scanning artifacts which can lead to biased inference
concerning gene expression.  We encourage users to read the shorter {\it
overview} quick start guide on this package given in the {\tt inst/doc}
directory.  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Getting started}

To load the {\tt marray} package in your R session, type {\tt
library(marray)}.  We demonstrate the functionality of this R packages
using gene expression data from the Swirl zebrafish experiment. These
data are included as part of the package, hence you will also need to
install this package. To load the swirl dataset, use {\tt data(swirl)},
and to view a description of the experiments and data, type {\tt ?
swirl}. \\

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Diagnostic plots}

Before proceeding to normalization or any higher--level analysis, it is
instructive to look at diagnostic plots of spot statistics, such as red
and green foreground and background log--intensities, intensity
log--ratio, area, etc. Such plots are useful for the purpose of
identifying printing, hybridization, and scanning artifacts as
demonstrated below. Three main types of functions were defined to
operate on pre-- and post--normalization microarray objects: functions
for boxplots, scatter--plots, and spatial images. The main arguments to
these functions are microarray objects of classes {\tt marrayRaw}, {\tt
marrayNorm} and arguments specifying which spot statistics to display
(e.g. Cy3 and Cy5 background intensities, intensity log--ratios) and
which subset of spots to include in the plots. Default graphical
parameters are chosen for convenience using the function {\tt
maDefaultPar} (e.g. color palette, axis labels, plot title), but the
user has the option to overwrite these parameters at any point. Note
that by default the plots are done for the first array in a batch. To
produce plots for other arrays, subsetting methods may be used. For
example, to produce diagnostic plots for the second array in the batch
of zebrafish arrays {\tt swirl}, the argument {\tt swirl[,2]} should be
passed to the plot functions. \\


To read in the data for the Swirl experiment and generate the plate
IDs (see {\tt marrayClasses} and {\tt marrayInput} for greater
details)

<<eval=TRUE,echo=TRUE>>= 
library(marray)
data(swirl) 
maPlate(swirl)<-maCompPlate(swirl,n=384) 
@

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Spatial plots of spot statistics -- {\tt image}}

 The function {\tt image} creates {\it images} of shades of gray or
colors that correspond to the values of a statistic for each spot on an
array. Details on the arguments of the function are given in {\tt ?
maImage}. The statistic can be the intensity log--ratio $M$, a spot
quality measure (e.g. spot size or shape), or a test statistic. This
function can be used to explore whether there are any spatial effects in
the data, for example, print--tip or cover--slip effects. In addition to
existing color palette functions, such as {\tt rainbow} and {\tt
heat.colors}, a new function {\tt maPalette} was defined to generate
color palettes from user supplied low, middle, and high color values. To
create white--to--green, white--to--red, and green--to--red palettes for
microarray images


<<eval=TRUE,echo=TRUE>>= 
Gcol<- maPalette(low="white", high="green",k=50) 
Rcol<- maPalette(low="white", high="red", k=50) 
RGcol<-maPalette(low="green", high="red", k=50) 
@


Useful diagnostic plots are images of the Cy3 and Cy5 background
intensities; these images may reveal hybridization artifacts such as
scratches on the slides, drops, cover--slip effects etc. The following
commands produce images of the Cy3 and Cy5 background intensities for
the Swirl 93 array (third array in the batch) using white--to--green
and white--to--red color palettes, respectively.

<<maImageGb,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
tmp<-image(swirl[,3], xvar="maGb", subset=TRUE, col=Gcol,contours=FALSE, bar=FALSE) 
@

<<maImageRb,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
tmp<-image(swirl[,3], xvar="maRb", subset=TRUE, col=Rcol, contours=FALSE, bar=FALSE) 
@

Note that the same images can be obtained using the default arguments
of the function by the shorter commands 

%%<<eval=FALSE,echo=TRUE>>=
\begin{verbatim}
> image(swirl[,3], xvar="maGb") 
> image(swirl[,3], xvar="maRb") 
\end{verbatim}
%%@

If {\tt bar=TRUE}, a calibration color bar is displayed to the right
of the images. The {\tt image} function returns the values and
corresponding colors used to produce the color bar, as well as a six
number summary of the spot statistics. The resulting images are shown
in Figure \ref{fig:maImageb}. It can be noted that the Cy3 and Cy5
background intensities are not uniform across the slide and are higher
in the top right corner, perhaps due to cover slip effects or tilt of
the slide during scanning. Such patterns were not as clearly visible
in the individual Cy3 and Cy5 TIFF images. Similar displays of the Cy3
and Cy5 foreground intensities do not exhibit such strong spatial
patterns. For other arrays, such as the Swirl 81 array, background
images revealed the existence of a scratch with very high background
in print--tip--groups (3,2) and (3,3). \\

The {\tt image} function may also be used to generate an image of
the pre--normalization log--ratios $M$ (or any other statistic of
interest), using a green--to--red color palette. Figure
\ref{fig:maImageMraw} displays such an image for the Swirl 93 array,
highlighting only those spots with the highest and lowest 10\%
pre--normalization log--ratios $M$. Other options include displaying
contours and altering graphical parameters such as axis labels and
plot title.  Figure \ref{fig:maImageMraw} suggests the existence of
spatial dye biases in the intensity log--ratio, with higher values in
grid (3,3) and lower values in grid column 1 of the array.

<<maImageMraw1,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>= 
tmp<-image(swirl[,3], xvar="maM", bar=FALSE, main="Swirl array 93: image of pre--normalization M") 
@

<<maImageMraw2,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>= 
tmp<-image(swirl[,3], xvar="maM", subset=maTop(maM(swirl[,3]), h=0.10,
l=0.10), col=RGcol, contours=FALSE, bar=FALSE,main="Swirl array 93:
image of pre--normalization M for \% 10 tails")  
@

Note that the {\tt image} function (and other functions {\tt
boxplot} and {\tt plot} to be described next) can be used to plot
other statistics than fluorescence intensities. They can be used to
plot layout parameters such as spot coordinates {\tt maSpotRow},
print--tip--group coordinates {\tt maPrintTip}, or plate IDs {\tt
maPlate} (Figure \ref{fig:maImageLayout}).


<<maImageSpotCol,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
tmp<- image(swirl[,3], xvar="maSpotCol", bar=FALSE) 
@

<<maImagePrintTip,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
tmp<- image(swirl[,3], xvar="maPrintTip", bar=FALSE) 
@

<<maImageControls,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
tmp<- image(swirl[,3], xvar="maControls",col=heat.colors(10),bar=FALSE) 
@

<<maImagePlate,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>= 
tmp<- image(swirl[,3], xvar="maPlate",bar=FALSE) 
@


\clearpage

\begin{figure} 
\begin{center} 
\begin{tabular}{cc}
\includegraphics[width=3in,height=3in,angle=0]{maImageGb} &
\includegraphics[width=3in,height=3in,angle=0]{maImageRb} \\
(a) & (b) 
\end{tabular} 
\end{center} 
\caption{Images of background intensities for the Swirl 93 array. Panel (a): Cy3 background
intensities using white--to--green color palette. Panel (b): Cy5
background intensities using white--to--red color palette.}
\protect\label{fig:maImageb} 
\end{figure}


\begin{figure} 
\begin{center} 
\begin{tabular}{cc}
\includegraphics[width=3in,height=3in,angle=0]{maImageMraw1} &
\includegraphics[width=3in,height=3in,angle=0]{maImageMraw2} \\
(a) & (b) 
\end{tabular} 
\end{center} 
\caption{Images of the pre--normalization intensity log--ratios $M$ for the Swirl 93 array,
using a green--to--red color palette. Panel (a): All spots are
displayed. Panel (b): only spots with the highest and lowest 10\%
log--ratios are highlighted.}  
\protect\label{fig:maImageMraw}
\end{figure}

\begin{figure}
\begin{center} 
\begin{tabular}{cc}
\includegraphics[width=2in,height=2in,angle=0]{maImageSpotCol} &
\includegraphics[width=2in,height=2in,angle=0]{maImagePrintTip} \\
(a) & (b)\\
\includegraphics[width=2in,height=2in,angle=0]{maImagePlate} &
\includegraphics[width=2in,height=2in,angle=0]{maImageControls} \\
(c) & (d) 
\end{tabular} 
\end{center} 
\caption{Images of layout parameters for the Swirl 93 array. Panel (a): Spot matrix column
coordinate. Panel (b): Print--tip--group. Panel (c): Plate
index. Panel (d): Control status.}   
\protect\label{fig:maImageLayout}
\end{figure}

\clearpage


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Boxplots of spot statistics -- {\tt boxplot}}

 Boxplots of spot statistics by plate, print--tip--group, or slide can
also be useful to identify spot or hybridization artifacts. {\it
Boxplots}, also called {\it box--and--whisker plots}, were first
proposed by Tukey in 1977 as simple graphical summaries of the
distribution of a variable. The summary consists of the median, the
upper and lower quartiles, the range, and, possibly, individual extreme
values. The central box in the plot represents the {\it inter--quartile
range (IQR)}, which is defined as the difference between the 75th
percentile and 25th percentile, i.e., the upper and lower quartiles. The
line in the middle of the box represents the median; a measure of
central location of the data.  Extreme values, greater than 1.5 IQR
above the 75th percentile and less than 1.5 IQR below the 25th
percentile, are typically plotted individually.

The function {\tt boxplot} produces boxplots of microarray spot
statistics for the classes {\tt marrayRaw}, {\tt marrayNorm}.  The
function {\tt boxplot} has three main arguments:
\begin{description} 
\item {{\tt x}:} Microarray object of class {\tt marrayRaw} or {\tt marrayNorm}.
\item {{\tt xvar}:} Name of accessor method for the spot statistic used to
stratify the data, typically a slot name for the microarray layout
object such as {\tt maPlate} or a method such as {\tt maPrintTip}. If
{\tt xvar} is {\tt NULL}, the data are not stratified.  
\item {{\tt yvar}:} Name of accessor method for the spot statistic of
interest, typically a slot name for the microarray object {\tt m}, such
as {\tt maM}.
\end{description}


Figure \ref{fig:maBoxplot1} panel (a) displays boxplots of
pre--normalization log--ratios $M$ for each of the 16 print--tip--groups
for the Swirl 93 array.  This plot was generated by the following
commands
<<maBoxplot1pre,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
boxplot(swirl[,3], xvar="maPrintTip", yvar="maM", main="Swirl array 93: pre--normalization") 
@

The boxplots clearly reveal the need for normalization, since most
log--ratios are negative in spite of the fact that only a small
proportion of genes are expected to be differentially expressed in the
mutant and wild--type zebrafish. As is often the case, this
corresponds to higher signal in the Cy3 channel than in the Cy5
channel even in the absence of differential expression. In addition,
the boxplots show the existence of spatial dye biases in the
log--ratios. In particular, print--tip--group (3,3) clearly stands out
from the remaining ones, as suggested also in the image of Figure
\ref{fig:maImageMraw}. The function {\tt maBoxplot} may also be used
to produce boxplots of spot statistics for all arrays in a batch. Such
plots are useful when assessing the need for between array
normalization, for example, to deal with scale differences among
different arrays. The following command produces a boxplot of the
pre--normalization intensity log--ratios $M$ for each array in the
batch {\tt swirl}.  Figure \ref{fig:maBoxplot2} panel (a) suggest that
different normalizations may be required for different arrays,
including possibly scale normalization.


<<maBoxplot2pre,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
boxplot(swirl, yvar="maM", main="Swirl arrays: pre--normalization") 
@

The function {\tt maNorm} from the {\tt marrayNorm} package can be used
for different types of within-array location normalization.  The
following command normalizes all four arrays in the Swirl experiment
simultaneously. Please refer to the vignette on normalization for more
information.  The following command performs within print-tip group
loesss normalization.

<<eval=TRUE>>= 
swirl.norm <- maNorm(swirl, norm="p")
@

The following commands can be used to produce post--normalization
boxplots of the log--ratios. The plots are shown in panel (b) of
Figures \ref{fig:maBoxplot1} and \ref{fig:maBoxplot2}.

<<maBoxplot1post,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
boxplot(swirl.norm[,3], xvar="maPrintTip", yvar="maM",
	main="Swirl array 93: post--normalization") 
@

<<maBoxplot2post,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
boxplot(swirl.norm, yvar="maM", col="green", main="Swirl arrays: post--normalization") 
@


\clearpage

\begin{figure} 
\begin{center} 
\begin{tabular}{cc}
\includegraphics[width=3in,height=3in,angle=0]{maBoxplot1pre} &
\includegraphics[width=3in,height=3in,angle=0]{maBoxplot1post} \\
(a) & (b) 
\end{tabular} 
\end{center} 
\caption{Boxplots by print--tip--group of the pre-- and post--normalization intensity log--ratios $M$ for the Swirl 93 array. }
\protect\label{fig:maBoxplot1} 
\end{figure}

\begin{figure} 
\begin{center} 
\begin{tabular}{cc}
\includegraphics[width=3in,height=3in,angle=0]{maBoxplot2pre} &
\includegraphics[width=3in,height=3in,angle=0]{maBoxplot2post} \\
 (a) & (b) 
\end{tabular} 
\end{center} 
\caption{Boxplots of the pre--and
post--normalization intensity log--ratios $M$ for the four arrays in
the Swirl experiment. } 
\protect\label{fig:maBoxplot2} 
\end{figure}


\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Scatter--plots of spot statistics -- {\tt maPlot} or {\tt plot}}

The function {\tt plot} produces {\it scatter--plots} of microarray spot
statistics for the classes {\tt marrayRaw} and {\tt marrayNorm}. It also
allows the user to highlight and annotate subsets of points on the plot,
and display fitted curves from robust local regression or other
smoothing procedures (see details in {\tt ? maPlot}). The function {\tt
maPlot} has seven main arguments:

\begin{description} 
\item {{\tt x}:} Microarray object of class {\tt marrayRaw} or  {\tt
  marrayNorm}.  
\item {{\tt xvar}:} Name of accessor function for the abscissa spot
statistic, typically a slot name for the microarray object {\tt m},
such as {\tt maA}.
  \item {{\tt yvar}:} Name of accessor function for the
ordinate spot statistic, typically a slot name for the microarray
object {\tt m}, such as {\tt maM}.  
\item {{\tt zvar}:} Name of accessor
method for the spot statistic used to stratify the data, typically a
slot name for the microarray layout object such as {\tt maPlate} or a
method such as {\tt maPrintTip}. If 
{\tt zvar} is {\tt NULL}, the data are not stratified.  

\item {{\tt lines.func}:} Function for computing and plotting smoothed
fits of {\tt yvar} as a function of {\tt xvar}, separately within values
of {\tt zvar}, e.g. {\tt maLoessLines}.  If {\tt lines.func} is {\tt
NULL}, no fitting is performed.  \item {\tt {\tt text.func}:} Function
for highlighting a subset of points, e.g., {\tt maText}. If {\tt
text.func} is {\tt NULL}, no points are highlighted.

\item {{\tt legend.func}:} Function for adding a legend to the plot,
e.g. {\tt maLegendLines}. If {\tt legend.func} is {\tt NULL}, there is
no legend.  
\end{description}

As usual, optional graphical parameters may be supplied and these will
overwrite the default parameters set in the plot functions.  A number
of functions for computing and plotting the fits are provided,
 such as {\tt maLowessLines} and {\tt maLoessLines} for
robust local regression using the R functions {\tt lowess} and {\tt
loess}, respectively (type {\tt ? loess} or {\tt ? lowess} for a brief
description of R functions for robust local regression). Functions are
also provided for highlighting points (e.g. {\tt text}) and adding a
legend to the plot (e.g. {\tt maLegendLines}).\\

{\bf $MA$--plots.} Single--slide expression data are typically
displayed by plotting the log--intensity $\log_2 R$ in the red channel
vs. the log--intensity $\log_2 G$ in the green channel. Such plots
tend to give an unrealistic sense of concordance between the red and
green intensities and can mask interesting features of the data. We
thus recommend plotting the intensity log--ratio $M=\log_2 R/G$
vs. the mean log--intensity $A = \log_2 \sqrt{RG}$. An $MA$--plot
amounts to a $45^o$ counterclockwise rotation of the $(\log_2 G,\log_2
R)$-- coordinate system, followed by scaling of the coordinates. It is
thus another representation of the $(R,G)$ data in terms of the
log--ratios $M$ which directly measure differences between the red and
green channels and are the quantities of interest to most
investigators. We have found $MA$--plots to be more revealing than
their $\log_2 R$ vs.  $\log_2 G$ counterparts in terms of identifying
spot artifacts and for normalization purposes
\citep{Dudoitetal02,Norm,NormNAR}. \\

Figure \ref{fig:maPlot1} panel (a) displays the pre--normalization
$MA$--plots for the Swirl 93 array, with the sixteen lowess fits for
each of the print--tip--groups (using a smoother span $f=0.3$ for the
{\tt lowess} function). The figure was generated with the following
commands

<<maPlot1pre,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
defs<-maDefaultPar(swirl[,3],x="maA",y="maM",z="maPrintTip")

# Function for plotting the legend
legend.func<-do.call("maLegendLines",defs$def.legend)

# Function for performing and plotting lowess fits
lines.func<-do.call("maLowessLines",c(list(TRUE,f=0.3),defs$def.lines))

plot(swirl[,3], xvar="maA", yvar="maM", zvar="maPrintTip",
		      lines.func,
		      text.func=maText(),
		      legend.func,
		      main="Swirl array 93: pre--normalization MA--plot") 
@

<<maPlot1post,fig=TRUE,prefix=FALSE,echo=TRUE,include=FALSE>>=
plot(swirl.norm[,3], xvar="maA", yvar="maM", zvar="maPrintTip",
		      lines.func,
		      text.func=maText(),
		      legend.func,
		      main="Swirl array 93: post--normalization MA--plot") 
@

The same plots can be obtain using the default arguments of the
function by the commands 

\begin{verbatim}
> plot(swirl[,3])
> plot(swirl.norm[,3], legend.func=NULL) 
\begin{verbatim}

To highlight, say, the spots with the highest and lowest 5\%
log--ratios using purple points, or using red symbol {\tt a} use the
following commands 

\begin{verbatim}
> points(swirl.norm[,3], subset=maTop(maM(swirl.norm[,3]),h=0.05,l=0.05),
pch=19, col="purple")
> text(swirl.norm[,3], subset=maTop(maM(swirl.norm[,3]),h=0.05,l=0.05),
labels="a", col="red")
\begin{verbatim}

\begin{figure}
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=3in,height=3in,angle=0]{maPlot1pre} &
\includegraphics[width=3in,height=3in,angle=0]{maPlot1post} \\ 
(a) & (b)
\end{tabular}
\end{center}
\caption{Pre-- and post--normalization $MA$--plot for the Swirl 93
  array, with the lowess fits for individual
  print--tip--groups. Different colors are used to represent lowess
  curves for print--tips from different rows, and different line types
  are used to represent lowess curves for print--tips from different
  columns. } 
\protect\label{fig:maPlot1}
\end{figure}


Figure \ref{fig:maPlot1} illustrates the non--linear dependence of the
log--ratio $M$ on the overall spot intensity $A$ and thus suggests that
an intensity or $A$--dependent normalization method is preferable to a
global one (e.g. median normalization). Also, the lowess fits vary among
print--tip--groups, again revealing the existence of spatial dye
biases. Figure \ref{fig:maPlot1} panel (b) displays the $MA$--plot after
within--print--tip--group loess location normalization.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Wrapper functions for basic sets of diagnostic plots -- {\tt maQualityPlots}}
The following command in another package {\tt arrayQuality} will
generate qualitative diagnostic plots for each arrays in the {\tt
marrayRaw} object and by default, saved it as different png files in the
working directory.  More details of this can be found in the package
{\tt arrayQuality}.


\begin{verbatim}
library(arrayQuality)
maQualityPlots(swirl)
\end{verbatim}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\bf Note: Sweave.} This document was generated using the \Rfunction{Sweave}
function from the R \Rpackage{tools} package. The source file is in the
\Rfunction{/inst/doc} directory of the package \Rpackage{marray}.

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

\bibliography{marrayPacks}

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