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\begin{document}

\title{Introduction to the xps Package: Comparison to Affymetrix Power Tools (APT)}
\date{June, 2009}
\author{Christian Stratowa}
\maketitle

\tableofcontents

\section{Introduction}

The aim of this document is to compare the results obtained with package \xps\ to the results
obtained with Affymetrix Power Tools (APT version apt-1.10.2). For this purpose the Exon Array Data 
Set "Tissue Mixture" will be used, which can be downloaded from the Affymetrix web-site for 
expression arrays "Human Genome U133 Plus 2.0", "Human Gene 1.0 ST" and "Human Exon 1.0 ST", 
respectively. First, APT and \xps\ will be compared for each array type seperately, then the 
results obtained with the different arrays will be compared to each other for both APT and \xps.
To speed up analysis only two human tissues will be used, namely breast and prostate.

For analyzing expression arrays, including gene and exon arrays, APT contains the command-line 
program \Robject{apt-probeset-summarize}, which supports background correction (RMA, MAS5), 
normalization (linear scaling, quantile, sketch), and summarization (RMA, MAS5, PLIER) methods. \\

{\bf Note:} In order to keep this document short, only example code will be presented here, 
the full source code is available in files "script4xps2apt.R" and "script4bestmatch.R" located 
in directory "xps/examples". 


\section{Comparison of results for the Human Genome U133 Plus 2.0 Array}

\subsection{Comparison of different implementations of RMA summarization}

When doing RMA summarization with \Robject{apt-probeset-summarize}, sketch-quantile normalization
(using only a subset of data) is applied by default in order to decrease memory consumption.
Furthermore, the Affymetrix GUI application "Expression Console" can only use sketch-quantile 
normalization. For this reason let us first compare RMA using sketch-quantile vs quantile 
normalization.

The following command will compute RMA using sketch-quantile normalization:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=-1.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true -d HG-U133_Plus_2.cdf *.CEL}
\end{verbatim}

Note that all CEL-files and the corresponding CDF-file must be located in the current directory.

The output can be directly imported into R:

%<<eval=FALSE, keep.source=TRUE>>=
<<eval=FALSE>>=
apt.rma.sk <- read.delim("rma-bg.quant-norm.pm-only.med-polish.summary.txt", row.names=1, comment.char="", skip=52)
@

To compute RMA using full quantile normalization the following command is used:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=0.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true -d HG-U133_Plus_2.cdf *.CEL
\end{verbatim}

Again, the output can be directly imported into R:

<<eval=FALSE>>=
apt.rma <- read.delim("rma-bg.quant-norm.pm-only.med-polish.summary.txt", row.names=1, comment.char="", skip=52)
@

Please note that in both cases the name of the output file is the same. \\

To compare the results, we will use "MvA-plots" in almost all cases. Thus we can plot:

<<eval=FALSE>>=
plot(log2(apt.rma[,1] * apt.rma.sk[,1])/2, log2(apt.rma.sk[,1]/apt.rma[,1]), main="APT: RMA vs RMA-sketch", xlab="A = Log2(SketchRMA*RMA)", ylab="M = Log2(SketchRMA/RMA)",log="",ylim=c(-0.1,0.1))
@

Since we use only the triplicate CEL-files for breast and prostate, respectively, column one of 
the \Rfunction{data.frame}s \Robject{apt.rma.sk} and \Robject{apt.rma} show the normalized 
expression values of tissue "breast\_A". \\

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{U133P2_APT_RMA_RMAsketch_MvA.png}
  \caption{APT RMA using quantile vs quantile-sketch.}
  \label{sketch}
\end{center}
\end{figure}

The resulting Figure \ref{sketch} shows that using sketch-quantile normalization gives a slightly
different result, especially at low expression values. Thus, for all following comparisons we
will use the full quantile normalization. \\

{\bf Note:} One advantage of package \xps\ compared to APT is, that you can do RMA with full
quantile normalization on computers with only 1GB RAM, even for exon arrays. \\

\pagebreak

Now let us compare APT and \xps. For this purpose we compute RMA as described in vignette 
"xps.pdf", and extract \Rfunction{data.frame} \Robject{xps.rma} from \Rclass{data.rma}:

<<eval=FALSE>>=
data.rma <- rma(data.u133p2, "MixU133P2RMA", background="pmonly", normalize=TRUE)
xps.rma  <- validData(data.rma)
@

Now we can compare the results obtained with APT and \xps\ for tissue "breast\_A" using 
an "MvA-plot":

<<eval=FALSE>>=
plot(log2(apt.rma[,1] * xps.rma[,1])/2, log2(xps.rma[,1]/apt.rma[,1]), main="RMA: XPS vs APT", xlab="A = Log2(XPS*APT)", ylab="M = Log2(XPS/APT)",log="",ylim=c(-0.1,0.1))
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{U133P2_XPS_APT_RMA_MvA.png}
  \caption{RMA computed with apt and xps, respectively.}
  \label{rma133xpsapt}
\end{center}
\end{figure}

As shown in Figure \ref{rma133xpsapt}, the results obtained with APT and \xps\ are identical. \\

\pagebreak

For the sake of completeness, let us compare both results to the results obtained with
package \Rpackage{affy}. For this purpose we compute:

<<eval=FALSE>>=
affy.rma <- justRMA()
affy.rma <- 2^exprs(affy.rma)
@

and plot:

<<eval=FALSE>>=
tmp <- cbind(xps.rma[,1],affy.rma[,1],apt.rma[,1])
colnames(tmp) <- c("xps.rma","affy.rma","apt.rma")
pairs(log2(tmp), labels=colnames(tmp))
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{U133P2_XPS_AFFY_APT_RMA.png}
  \caption{RMA computed with xps, affy and apt, respectively.}
  \label{rma133pairs}
\end{center}
\end{figure}

As shown in Figure \ref{rma133pairs}, the results are identical in all three cases. 
For example, the differences between \xps\ and APT or \Rpackage{affy} are less than 4e-6. \\

\pagebreak


\subsection{Comparison of different implementations of MAS 5.0 summarization}

The command-line to compute MAS5 summarization using APT is:

\begin{verbatim}
apt-probeset-summarize -a mas5-bg,pm-mm,mas5-signal -d HG-U133_Plus_2.cdf *.CEL
\end{verbatim}

The output is imported into R and must be scaled to \Rcode{sc=500} since APT does not allow 
for signal level normalization across the chip (as mentioned in APT FAQ):

<<eval=FALSE>>=
apt.mas5 <- read.delim("mas5-bg.pm-mm.mas5-signal.summary.txt", row.names=1, comment.char="", skip=52)
apt.mas5 <- apply(apt.mas5, 2, function(x){x*(500/mean(x, trim=0.02))})
@

Now we compute MAS5 with \xps\ as described in vignette "xps.pdf":

<<eval=FALSE>>=
data.mas5 <- mas5(data.u133p2,"MixU133P2MAS5All", normalize=TRUE, sc=500, update=TRUE)
xps.mas5 <- validData(data.mas5)
@

Finally, we compute MAS5 using package \Rpackage{affy}:

<<eval=FALSE>>=
affy <- ReadAffy()
affy.mas5 <- mas5(affy, normalize=TRUE, sc=500)
affy.mas5 <- exprs(affy.mas5)
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=90mm]{U133P2_XPS_APT_EC_AFFY_MAS5_MvA_3x2.png}
%  \includegraphics[scale=1]{U133P2_XPS_APT_EC_AFFY_MAS5_MvA_3x2.png}
  \caption{MAS5 computed with xps, affy, apt and EC, respectively.}
  \label{u133mas5}
\end{center}
\end{figure}

Using "MvA-plots" to compare the MAS5 expression levels for sample "Breast\_A" we obtain
the results shown in Figure \ref{u133mas5}. 

The upper row shows how the implementation of the MAS5 algorithm in packages \xps\ and
\Rpackage{affy} compare to APT. Both packages show clear differences to APT, especially
at low expression levels. However, as APT FAQ mentions, "a new implementation of the MAS5 
methods was necessary to get this method to work in the APT architecture". Thus, the middle
row shows how  packages \xps\ and \Rpackage{affy} compare to the MAS5 results obtained with
the Affymetrix "Expression Console", which has implemented MAS5 identical to GCOS. There are 
still differences seen in the expression levels, with the \xps\ implementation of MAS5 being
slightly more close to the GCOS implementation of MAS5. Finally, the lower row shows the
differences between APT and GCOS, and between \xps\ and \Rpackage{affy}, respectively.

\pagebreak


\subsection{Comparison of different implementations of MAS 5.0 detection calls}

Now let us compute MAS5 detection calls. The command-line for APT is:

\begin{verbatim}
apt-probeset-summarize -a pm-mm,mas5-detect.calls=1.pairs=1 -d HG-U133_Plus_2.cdf -x 10 *.CEL
\end{verbatim}

Using package \xps\, MAS5 detection calls are computed as follows:

<<eval=FALSE>>=
call.mas5 <- mas5.call(data.u133p2,"MixU133P2Call")
xps.pval  <- validData(call.mas5)
@

while package \Rpackage{affy} uses the following commands:

<<eval=FALSE>>=
affy <- ReadAffy()
affy.dc5  <- mas5calls(affy)
affy.pval <- assayData(affy.dc5)[["se.exprs"]]
@

Figure \ref{u133mas5pvalpairs} compares the detection p-values obtained with packages 
\xps\ and \Rpackage{affy}, as well as Expression Console and APT.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=100mm]{U133P2_XPS_AFFY_EC_APT_MAS5_pval.png}
  \caption{Comparison of p-values obtained with xps, affy, Expression Console and APT.}
  \label{u133mas5pvalpairs}
\end{center}
\end{figure}

While Expression Console and APT result in identical p-values, both \xps\ and \Rpackage{affy}
differ from APT. However, as shown in Figure \ref{u133mas5pval}, the detection call p-values 
obtained with  \xps\ and \Rpackage{affy} are identical. 

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{U133P2_Diff_XPS_AFFY_MAS5_pval.png}
  \caption{Difference between p-values obtained with xps and affy.}
  \label{u133mas5pval}
\end{center}
\end{figure}

\pagebreak


\section{Comparison of results for the Human Gene 1.0 ST Array}

\subsection{Comparison of the RMA summarization implementations}

While the results for expression arrays obtained with \xps\ and APT, respectively, can be
directly compared, since the probesets used are identical, comparison of \xps\ and APT with
gene/exon arrays requires the definition of common probesets first. \\

Let us first compute RMA using package \xps:

<<eval=FALSE>>=
data.rma.tc <- rma(data.genome,"MixHuGeneRMAcore_tc", background="antigenomic",
                   normalize=TRUE, option="transcript", exonlevel="core")
xps.rma.tc  <- validData(data.rma.tc)
@

Now we can create a file specifying the probesets to summarize for APT:

<<eval=FALSE>>=
tmp <- as.data.frame(rownames(xps.rma.tc))
colnames(tmp) <- "probeset_id"
write.table(tmp, "transcriptList.txt", quote=FALSE, row.names=FALSE)
@

This transcriptList contains now the probesets used by \xps\ and can be added  as option 
when computing RMA using APT:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=0.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true \
    -p HuGene-1_0-st-v1.r3.pgf -c HuGene-1_0-st-v1.r3.clf \
    -s transcriptList.txt *.CEL
\end{verbatim}

Figure \ref{generma} shows the resulting "MvA-plot" for tissue "breast\_A".

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuGene_XPS_APT_RMA_MvA_tc_r4.png}
  \caption{RMA computed with xps and apt, respectively.}
  \label{generma}
\end{center}
\end{figure}

\pagebreak

As Figure \ref{generma} shows, there is clearly a difference of few percent in the expression 
levels obtained when using \xps\ or APT, respectively, including a non-linearity at low expression 
levels. \\

In order to understand this difference let us first compare the "median-polish" summarization 
step (w/o background correction and quantile normalization). 

In package \xps\ this is done as follows:

<<eval=FALSE>>=
expr.mp.tc <- express(data.genome, "MixHuGeneMedPolcore_tc", summarize.method="medianpolish",
              summarize.select="pmonly", summarize.option="transcript", summarize.logbase="log2",
              summarize.params=c(10, 0.01, 1.0), exonlevel="core")
xps.mp.tc <- validData(expr.mp.tc)
@

while APT uses the following command:

\begin{verbatim}
apt-probeset-summarize -a pm-only,med-polish.expon=true \
   -p HuGene-1_0-st-v1.r3.pgf -c HuGene-1_0-st-v1.r3.clf \
   -s transcriptList.txt *.CEL
\end{verbatim}

The resulting Figure \ref{genemp} shows that the results obtained with \xps\ and APT are 
identical (the difference being less than 4e-6, see scale of y-axis).

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuGene_XPS_APT_MedPol_MvA_tc_r4.png}
  \caption{Median-polish only, computed with xps and apt, respectively.}
  \label{genemp}
\end{center}
\end{figure}

\pagebreak

Since the results of median-polish are identical for \xps\ and APT, the differences seen in 
Figure \ref{generma} are due to background correction and/or quantile normalization, respectively. 
Package \xps\ uses only those probes to compute background and quantile normalization, which are 
also used for summarization, as defined by parameter \Rcode{exonlevel}. The reason for this is 
that RMA estimates the background from the PM probe intensities only, as described in 
\citep{iriz:etal:2003}. Analogously, quantile normalization \citep{bols:etal:2003} is applied
only to the probes which are used for summarization.

It seems that APT uses (almost) all probes on the array for background correction and quantile 
normalization. Since package \xps\ has an (unsupported) option to use (almost) all probes (which 
include internal control probes and background probes), there is a possibility to use all probes 
by setting parameter \Rcode{exonlevel} individually for background correction, quantile 
normalization and median-polish summarization, respectively. This is done as follows:

<<eval=FALSE>>=
data.rma.tc.bq99 <- rma(data.genome, "HuGeneMixRMAbgqu99mp9", background="antigenomic",
                         normalize=TRUE, exonlevel=c(992316,992316,9216))
xps.rma.tc.bq99 <- validData(data.rma.tc.bq99)
@

Here, we have set \Rcode{exonlevel="core+affx+unmapped+exon+intron+antigenomic"} for background 
correction and quantile normalization, respectively, and \Rcode{exonlevel="core"} for median-polish 
summarization (see \Rcode{?exonLevel}). Comparing the results of this setting to APT, we obtain 
the following "MvA-plot" for tissue "breast\_A", see Figure \ref{genermabq99}.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuGene_XPS_APT_RMA_bg99qu99_MvA_tc_r4.png}
  \caption{RMA, computed with xps and apt, respectively.}
  \label{genermabq99}
\end{center}
\end{figure}

\pagebreak

As Figure \ref{genermabq99} shows, the expression levels obtained when using \xps\ or APT, 
respectively, are now identical, indicating that APT does indeed use all probes on the array 
for background correction and quantile normalization (exluding only the probes hybridizing 
to the control oligo). \\


\subsection{Comparison of the DABG call implementations}

Now let us compute the detected above background (DABG) calls. The command-line for APT is:

\begin{verbatim}
apt-probeset-summarize -a dabg \
   -p HuGene-1_0-st-v1.r3.pgf -c HuGene-1_0-st-v1.r3.clf \
   -b HuGene-1_0-st-v1.r3.bgp -s probesetList.txt  -x 8 *.CEL
\end{verbatim}

Using package \xps\, DABG calls are computed as follows:

<<eval=FALSE>>=
call.dabg.tc <- dabg.call(data.genome, "HuGeneMixDABGcore_tc", 
                          option="transcript", exonlevel="core")
xps.pval.tc <- validData(call.dabg.tc)
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuGeneDiff_XPS_APT_DABG_pval_tc_r4.png}
  \caption{Comparison of p-values obtained with xps and APT.}
  \label{genedabgpval}
\end{center}
\end{figure}

Figure \ref{genedabgpval} shows the difference in the detection p-values obtained with \xps\ 
and APT, respectively. The detection p-values are identical (the minor apparent difference 
only due to different numbers of digits exported). \\


\pagebreak

\subsection{Comparison of results when using HuGene as exon array}

With release r4 of the library files Affymetrix has converted the HuGene-1\_0-st-v1 array into 
an exon array. While the probes for "HuGene-1\_0-st-v1.r3.pgf" were grouped according to the 
\Rcode{transcript\_cluster\_id}s, the probes for "HuGene-1\_0-st-v1.r4.pgf" are grouped according 
to the \Rcode{probeset\_id}s of the new probeset annotation file.

Thus in order to compare \xps\ and APT at the transcript level it is now necessary to create 
the transcript probesets for APT using function \Rcode{metaProbesets()}:

<<eval=FALSE>>=
writeLines(rownames(xps.rma.tc), "core.txt")
metaProbesets(scheme.genome, "core.txt", "coreList.mps", "core")
@

Now we need to use this 'coreList.mps' file to compute RMA and DABG, respectively, at the 
transcript level using APT, e.g. we compute RMA as follows:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=0.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true \
    -p HuGene-1_0-st-v1.r4.pgf -c HuGene-1_0-st-v1.r4.clf \
    -m coreList.mps *.CEL
\end{verbatim}

The results for RMA and DABG are identical to the results obtained with release r3 of the 
library files shown above. \\

In addition to the transcript level release r4 allows now to compute both RMA and DABG on the 
probeset level as well, analogously to the exon arrays. For this purpose we compute first RMA 
at the probeset level using package \xps:

<<eval=FALSE>>=
data.rma.ps <- rma(data.genome, "MixHuGeneRMAcore_ps", background="antigenomic",
                   normalize=TRUE, option="probeset", exonlevel="core")
xps.rma.ps  <- validData(data.rma.ps)
@

Then we create a file specifying the probesets to summarize for APT:

<<eval=FALSE>>=
tmp <- as.data.frame(rownames(xps.rma.ps))
colnames(tmp) <- "probeset_id"
write.table(tmp, "probesetList.txt", quote=FALSE, row.names=FALSE)
@

Finally we use this probesetList to compute RMA using APT:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=0.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true \
    -p HuGene-1_0-st-v1.r4.pgf -c HuGene-1_0-st-v1.r4.clf \
    -s probesetList.txt *.CEL
\end{verbatim}

The resulting figure \ref{probesetrma} shows once again a difference of few percent in the 
expression levels obtained when using \xps\ or APT.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuGene_XPS_APT_RMA_MvA_ps_r4.png}
  \caption{RMA for probesets computed with xps and apt, respectively.}
  \label{probesetrma}
\end{center}
\end{figure}

However, when using the same probes for background correction and quantile normalization as APT:

<<eval=FALSE>>=
data.rma.ps.bq99 <- rma(data.genome,"HuGeneMixRMAbgqu99mp9_ps", background="antigenomic",
                        normalize=TRUE, option="probeset", exonlevel=c(992316,992316,9216))
xps.rma.ps.bq99 <- validData(data.rma.ps.bq99)
@

the results are once again identical to the results obtained with APT, as shown in Figure 
\ref{probeset99rma}.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuGene_XPS_APT_RMA_bg99qu99_MvA_ps_r4.png}
  \caption{RMA for probesets computed with xps and apt, respectively.}
  \label{probeset99rma}
\end{center}
\end{figure}

\pagebreak


\section{Comparison of results for the Human Exon 1.0 ST Array}

\subsection{Comparison of RMA summarization at the probeset level}

As already mentioned, comparison of \xps\ and APT with exon arrays requires the definition 
of common probesets first. \\

Thus we compute first RMA at the probeset level using package \xps:

<<eval=FALSE>>=
data.rma.ps <- rma(data.exon, "MixHuExonRMAcore_ps", background="antigenomic",
                   normalize=TRUE, option="probeset", exonlevel="core")
xps.rma.ps  <- validData(data.rma.ps)
@

Then we can create a file specifying the probesets to summarize for APT:

<<eval=FALSE>>=
tmp <- as.data.frame(rownames(xps.rma.ps))
colnames(tmp) <- "probeset_id"
write.table(tmp, "corePSList.txt", quote=FALSE, row.names=FALSE)
@

Finally we use this probesetList to compute RMA using APT:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=0.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true \
    -p HuEx-1_0-st-v2.r2.pgf -c HuEx-1_0-st-v2.r2.clf \
    -b HuEx-1_0-st-v2.r2.antigenomic.bgp -s corePSList.txt *.CEL
\end{verbatim}

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_XPS_APT_RMA_MvA_ps.png}
  \caption{RMA computed with xps and apt, respectively.}
  \label{exonrmaps}
\end{center}
\end{figure}

\pagebreak

As the resulting "MvA-plot" for tissue "breast\_A", shown in Figure \ref{exonrmaps}, reveals, 
there is quite some difference for the probeset levels computed with \xps\ or APT, respectively.
Thus let us compare the "median-polish" summarization step only, as done before for the gene 
array. \\

In package \xps\ this is done as follows:

<<eval=FALSE>>=
expr.mp.ps <- express(data.exon, "HuExonMedPolcorePS", summarize.method="medianpolish",
              summarize.select="pmonly", summarize.option="probeset", summarize.logbase="log2",
              summarize.params=c(10, 0.01, 1.0), exonlevel="core")
xps.mp.ps <- validData(expr.mp.ps)
@

while APT uses the following command:

\begin{verbatim}
apt-probeset-summarize -a pm-only,med-polish.expon=true \
   -p HuEx-1_0-st-v2.r2.pgf -c HuEx-1_0-st-v2.r2.clf \
   -s corePSList.txt *.CEL
\end{verbatim}

The resulting Figure \ref{exonmpps} shows that the results obtained with \xps\ and APT are 
identical (the difference being less than 6e-6, see scale of y-axis).

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_XPS_APT_MedPol_MvA_ps.png}
  \caption{Median-polish only, computed with xps and apt, respectively.}
  \label{exonmpps}
\end{center}
\end{figure}

\pagebreak

As for gene arrays, the differences seen in Figure \ref{exonrmaps} are due to background correction 
and quantile normalization, respectively. This time we set parameter \Rcode{exonlevel} 
individually to \Rcode{exonlevel= "all+genomic+antigenomic+intron+exon+unmapped"} for background 
correction and quantile normalization, respectively, and \Rcode{exonlevel="core"} for 
median-polish summarization:

<<eval=FALSE>>=
data.rma.ps.bq103 <- rma(data.exon, "HuExonMixRMAbgqu103mp9_ps", background="antigenomic",
                     normalize=TRUE, option="probeset", exonlevel=c(1032124,1032124,9216))
xps.rma.ps.bq103 <- validData(data.rma.ps.bq103)
@

Comparing the results of this setting to APT, we obtain the following "MvA-plot" for tissue 
"breast\_A" shown in Figure \ref{exonrmabq103ps}.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_XPS_APT_RMA_bg103qu103_MvA_ps.png}
  \caption{RMA, computed with xps and apt, respectively.}
  \label{exonrmabq103ps}
\end{center}
\end{figure}

\pagebreak

As Figure \ref{exonrmabq103ps} shows, the differences in the expression levels obtained when using 
\xps\ or APT, respectively, are dramatically reduced. At high expression levels there is no 
difference, while the difference at low expression levels is reduced to at most 20\%. 
However, in contrast to the HuGene array the difference is still visible. Thus in this case it 
is not clear to me which probes Affymetrix is using for background correction and quantile 
normalization. \\


\subsection{Comparison of RMA summarization at the transcript level}

Comparing \xps\ and APT with exon arrays at the gene level requires the definition 
of common probesets for each transcript, i.e. a file containing meta probeset definitions. \\

First we compute RMA at the transcript level using package \xps:

<<eval=FALSE>>=
data.rma.tc <- rma(data.exon, "MixHuExonRMAcore_tc", background="antigenomic",
                   normalize=TRUE, option="transcript", exonlevel="core")
xps.rma.tc  <- validData(data.rma.tc)
@

Then we can create a meta probeset file using function \Rcode{metaProbesets()}:

<<eval=FALSE>>=
writeLines(rownames(xps.rma.tc), "core.txt")
metaProbesets(scheme.exon, "core.txt", "coreList.mps", "core")
@

Now we use this 'coreList.mps' file to compute RMA using APT:

\begin{verbatim}
apt-probeset-summarize -a rma-bg,quant-norm.sketch=0.usepm=true.bioc=true, \
    pm-only,med-polish.expon=true \
    -p HuEx-1_0-st-v2.r2.pgf -c HuEx-1_0-st-v2.r2.clf \
    -m coreList.mps *.CEL
\end{verbatim}

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_XPS_APT_RMA_MvA_tc.png}
  \caption{RMA computed with xps and apt, respectively.}
  \label{exonrma}
\end{center}
\end{figure}

\pagebreak

As expected, the resulting "MvA-plot" for tissue "breast\_A", shown in Figure \ref{exonrma}, is 
similar to Figure \ref{exonrmaps}. Again, we compare the "median-polish" summarization step only. \\

In package \xps\ this is done as follows:

<<eval=FALSE>>=
expr.mp.tc <- express(data.exon, "HuExonMedPolcore", summarize.method="medianpolish",
              summarize.select="pmonly", summarize.option="transcript", summarize.logbase="log2",
              summarize.params=c(10, 0.01, 1.0), exonlevel="core")
xps.mp.tc <- validData(expr.mp.tc)
@

while APT uses the following command:

\begin{verbatim}
apt-probeset-summarize -a pm-only,med-polish.expon=true \
   -p HuEx-1_0-st-v2.r2.pgf -c HuEx-1_0-st-v2.r2.clf \
   -m coreList.mps *.CEL
\end{verbatim}

As for the probesets, the resulting Figure \ref{exonmp} shows that the results obtained with 
\xps\ and APT are identical (the difference being less than 6e-6, see scale of y-axis).

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_XPS_APT_MedPol_MvA_tc.png}
  \caption{Median-polish only, computed with xps and apt, respectively.}
  \label{exonmp}
\end{center}
\end{figure}

\pagebreak

When we set parameter \Rcode{exonlevel} individually to 
\Rcode{exonlevel="all+genomic+antigenomic+intron+exon+unmapped"} for background correction and 
quantile normalization, respectively, and \Rcode{exonlevel="core"} for median-polish summarization:

<<eval=FALSE>>=
data.rma.tc.bq103 <- rma(data.exon, "HuExonMixRMAbgqu103mp9_tc", background="antigenomic",
                     normalize=TRUE, option="transcript", exonlevel=c(1032124,1032124,9216))
xps.rma.tc.bq103 <- validData(data.rma.tc.bq103)
@

and compare the results to APT, we obtain the "MvA-plot" for tissue "breast\_A" shown in 
Figure \ref{exonrmabq103}.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_XPS_APT_RMA_bg103qu103_MvA_tc.png}
  \caption{RMA, computed with xps and apt, respectively.}
  \label{exonrmabq103}
\end{center}
\end{figure}

\pagebreak

As Figure \ref{exonrmabq103} shows, the differences in the expression levels obtained when using 
\xps\ or APT, respectively, are also dramatically reduced. At high expression levels there is 
almost no difference, while the difference at low expression levels is reduced to less than 20\%. \\


\subsection{Comparison of the DABG call implementations}

Now let us compare the detected above background (DABG) calls at the probeset level. 

The command-line for APT is:

\begin{verbatim}
apt-probeset-summarize -a dabg \
   -p HuEx-1_0-st-v2.r2.pgf -c HuEx-1_0-st-v2.r2.clf \
   -b HuEx-1_0-st-v2.r2.antigenomic.bgp -s corePSList.txt  -x 12 *.CEL
\end{verbatim}

while package \xps\ computes DABG calls as follows:

<<eval=FALSE>>=
call.dabg.ps <- dabg.call(data.exon, "HuExonDABGcorePS", option="probeset", exonlevel="core")
xps.pval.ps <- validData(call.dabg.ps)
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{HuExon_Diff_XPS_APT_DABG_pval_ps.png}
  \caption{Comparison of p-values obtained with xps and APT.}
  \label{exondabgpvalps}
\end{center}
\end{figure}

Figure \ref{exondabgpvalps} shows the difference in the detection p-values obtained with \xps\ 
and APT, respectively. The detection p-values are identical (the minor apparent difference 
only due to different numbers of digits exported). \\

\pagebreak

{\bf Note:} Another advantage of package \xps\ compared to APT is, that you can compute DABG 
calls not only at the probeset level but also at the transcript level. This is simply done 
as follows:

<<eval=FALSE>>=
call.dabg.tc <- dabg.call(data.exon, "HuExonDABGcoreTC", option="transcript", exonlevel="core")
xps.pval.tc <- pvalData(call.dabg.tc)
@


\section{Comparison of Affymetrix gene expression arrays}

In this section we want to compare the gene expression levels obtained with arrays HG-U133\_Plus\_2, 
HuGene-1\_0-st-v1 and HuEx-1\_0-st-v2, respectively, for tissues breast and prostate.
For this purpose we need to select first a subset of transcripts common to all three arrays.
Then we want to find differentially expressed transcripts and compare the results for the  
normalized expression levels obtained with \xps\ or APT, respectively. 


\subsection{Comparison of RMA summarization for common transcript probesets}

In order to create a subset of transcripts common to all three arrays, we import as a first 
step the "Array Comparison Spreadsheets", which can be downloaded from the Affymetrix web-site: 

<<eval=FALSE>>=
hx2hg <- read.delim("HuExVsHuGene_BestMatch.txt", row.names=3)
up2hx <- read.delim("U133PlusVsHuEx_BestMatch.txt", row.names=3)
up2hg <- read.delim("U133PlusVsHuGene_BestMatch.txt", row.names=3)
@

Since we want to compare the RMA normalized expression levels \Robject{xps.urma} (HG-U133\_Plus\_2), 
\Robject{xps.grma} (HuGene-1\_0-st-v1) and \Robject{xps.xrma} (HuEx-1\_0-st-v2), with \Robject{xps.grma} 
and \Robject{xps.xrma} using only the "core" transcript probesets, we obtain the common 
subset \Robject{core}, containing unique exon and genome transcripts identical to U133P2 
as follows:

<<eval=FALSE>>=
hx2hg <- uniqueframe(hx2hg)
up2hx <- uniqueframe(up2hx)
up2hg <- uniqueframe(up2hg)
u2x   <- intersectframes(up2hx, up2hg)
u2g   <- intersectframes(up2hg, up2hx)
tmp   <- intersectrows(u2gx, xps.grma, 1, NULL)
core  <- intersectrows(tmp,  xps.xrma, 2, NULL)
@

The resulting subset \Robject{core} consists of 11033 transcripts common to all arrays.

{\bf Note:} The full source code and the functions \Rfunction{uniqueframe}, \Rfunction{intersectframes} 
and \Rfunction{intersectrows} are described in file "script4bestmatch.R" located in directory 
"examples". \\

Now we obtain the following subsets of normalized expression data:

<<eval=FALSE>>=
xpsu <- intersectrows(xps.urma, core, NULL, NULL)
xpsg <- intersectrows(xps.grma, core, NULL, 1, -1)
xpsx <- intersectrows(xps.xrma, core, NULL, 2, -1)
aptg <- intersectrows(apt.grma, core, NULL, 1, -1)
aptx <- intersectrows(apt.xrma, core, NULL, 2, -1)
@

where \Robject{aptg} and \Robject{aptx} are the corresponding data for APT (w/o \Robject{aptu} 
since it is identical to \Robject{xpsu}). 

\begin{figure}[h]
\begin{center}
  \includegraphics[width=90mm]{XPS_U133P2_Gene_Exon_mean_dot.png}
  \caption{Scatter plot of mean expression summaries for breast.}
  \label{breastpairs}
\end{center}
\end{figure}

A scatter plot of the averaged gene-level summaries for breast tissue is shown in Figure 
\ref{breastpairs} for the data obtained with package \xps. The corresponding figure for the data 
obtained with APT is almost identical. Furthermore, Figure \ref{breastpairs} is very similar to
the supplementary figure (page 10) published by Robinson \& Speed in \citep{robin:speed:2007}, 
however, using the averaged gene-level summaries for one particular mixture, and Ensembl 
gene-centric probesets.


\subsection{Differentially expressed transcripts in breast vs prostate}

Now we consider the task of finding differentially expressed genes between the breast and 
prostate samples. Following Robinson \& Speed \citep{robin:speed:2007} we will use the moderated 
t-statistics from package \Rpackage{limma} to compute raw p-values, which are then adjusted by 
a Benjamini--Hochberg correction (the default setting). \\

For this purpose we create the design matrix:

<<eval=FALSE>>=
tissue <- c(rep("Breast", 3), rep("Prostate", 3))
design <- model.matrix(~factor(tissue)) 
colnames(design) <- c("Breast","BreastvsProstate") 
@

which we use to compute the moderated t-statistics for each platform, e.g. for data \Robject{xpsu}:

<<eval=FALSE>>=
tmp <- as.matrix(log2(xpsu))
fit <- lmFit(tmp, design) 
fit <- eBayes(fit) 
xpsu.lm <- topTable(fit, coef=2, n=length(rownames(tmp)), adjust="BH")
@

Now we can first compare the fold-change values for the different platforms.

\begin{figure}[h]
\begin{center}
  \includegraphics[width=90mm]{XPS_U133P2_HuGene_HuExon_logFC.png}
  \caption{Scatter plot of fold-change values.}
  \label{fcpairs}
\end{center}
\end{figure}

Figure \ref{fcpairs} shows a scatter plot of the fold-change values for the data obtained with 
package \xps. The corresponding figure for the data obtained with APT is (almost) identical.

\pagebreak

Regarding the computed p-values, let us first compare the p-values for the HuGene-1\_0-st-v1 
data \Robject{xpsg} and \Robject{aptg} , obtained with \xps\ or APT, respectively. \\

\begin{figure}[h]
\begin{center}
  \includegraphics[width=90mm]{XPS_APT_HuGene_PValue.png}
  \caption{Scatter plot of p-values obtained with xpsg, aptg, and bq99g.}
  \label{pvalgene}
\end{center}
\end{figure}

The upper rows of Figure \ref{pvalgene} compare the p-values obtained with \Robject{xpsg} and 
\Robject{aptg}, respectively, whereby the right scatter-plot compares the lowest p-values 
only, i.e. the most relevant p-values. The lower rows of Figure \ref{pvalgene} compare the 
p-values obtained with \Robject{bq99g} and \Robject{aptg}, respectively, where \Robject{bq99g} is 
identical to \Robject{aptg}, as shown in Figure \ref{genermabq99}. 

Comparing the upper and lower scatter-plots reveals that the differences between \xps\ and APT, 
seen in Figure \ref{generma}, may not have a large effect when computing moderated t-statistics. 
The same is true when comparing the adjusted p-values. However, the differences between 
\Robject{xpsg} and \Robject{aptg} are only a few percent, as seen in Figure \ref{generma}, 
thus it is not unexpected that the (adjusted) p-values are very similar. \\

In contrast, the differences between the expression levels obtained with array HuEx-1\_0-st-v2, 
i.e. \Robject{xpsx} and \Robject{aptx}, respectively, are quite pronounced, as demonstrated 
earlier (see Figure \ref{exonrma}). Thus it can be expected that these differences are also 
reflected in differences in p-values, when computing the moderated t-statistics for \Robject{xpsx} 
or \Robject{aptx}, respectively. As shown in Figure \ref{pvalexon}, this is indeed the case. 

\begin{figure}[h]
\begin{center}
  \includegraphics[width=90mm]{XPS_APT_HuExon_AdjPValue.png}
  \caption{Scatter plot of adjusted p-values obtained with xpsx, aptx, and bq103x.}
  \label{pvalexon}
\end{center}
\end{figure}

\pagebreak

In this case, the upper rows of Figure \ref{pvalexon} compare the BH-adjusted p-values obtained 
with \Robject{xpsx} and  \Robject{aptx}, respectively, whereby the right scatter-plot compares 
once again the lowest p-values only, i.e. the most relevant p-values.

This time, the (adjusted) p-values computed for \Robject{xpsx} and \Robject{aptx}, respectively, 
show clearly are larger variance. Of special interest is the upper right part of the figure, 
which compares only the the most relevant p-values. It is evident, that the relevant adjusted 
p-values computed for \Robject{xpsx} are smaller than the corresponding p-values computed for 
\Robject{aptx} (as the slope of an imaginary fitted line would show). This indicates that the 
expression levels \Robject{xpsx} obtained with package \xps\ result in a better separation between 
tissues breast and prostate for the most relevant genes than the expression levels \Robject{aptx} 
obtained with APT. 

As described earlier, we have also adjusted background correction and quantile normalization to 
resemble the APT expression levels (see Figure \ref{exonrmabq103}), resulting in subset 
\Robject{bq103x}. Comparing the adjusted p-values obtained with these expression levels 
(\Robject{bq103x}), with the p-values obtained with subset \Robject{aptx} results in the scatter 
plot shown in the lower part of Figure \ref{pvalexon}. This part of the figure looks similar to 
Figure \ref{pvalgene}, and shows that the adjusted p-values for \Robject{bq103x} and \Robject{aptx} 
are very similar, although there is still a difference of about 20\% at low expression levels 
(Figure \ref{exonrmabq103}). However, in both cases the relvant p-values are larger than the 
p-values obtained with subset \Robject{xpsx}. In my opinion, this is a clear indication that 
only those probes should be used for background correction and quantile normalization, which 
are also used for median-polish summarization. 


\section{Summary}

Comparison of packages \xps\ and \Rpackage{affy} with APT for expression arrays shows that the 
different implementations of the RMA algorithm result in identical expression levels, as shown 
in Figure \ref{rma133pairs}. (The negligible difference of less than 5e-6 is due to the fact 
that package \xps\ does all computations with double-precision (64bit), but saves the results 
as floats (32bit)). \\

Interestingly, all three implementations of the MAS5 algorithm (\Rpackage{xps}, \Rpackage{affy}, 
APT) differ from the original GCOS implementation, with \xps\ probably being slightly more close 
to GCOS than \Rpackage{affy} (Figure \ref{u133mas5}), but I may be biased. \\

The implementations of MAS5 detection calls are identical for \xps\ and \Rpackage{affy}, but differ 
slightly from the APT implementation which is identical to the GCOS implementation (Figure 
\ref{u133mas5pvalpairs}). \\

For the gene and exon arrays I have only compared \xps\ and APT, which both use the new 
CLF-files and PGF-files as library files, and are able to use the separate probeset groups 'core', 
'extended' and/or 'full', which are defined in the Affymetrix annotation files. \\

Although the \xps\ and APT implementations of the RMA algorithm give identical results for 
expression arrays, the results for both gene arrays and exon arrays seem to differ, as shown in 
Figures \ref{generma} and \ref{exonrma}, respectively. As we have demonstrated earlier, this 
difference is caused by using different probes for background correction and quantile normalization, 
respectively, since using identical probes (HuGene) or applying only median-polish summarization 
gives identical results (Figures \ref{genermabq99}, \ref{genemp} and \ref{exonmp}). 

While package \xps\ uses by default the identical "PM" probes for all three steps of the RMA 
algorithm, e.g. for \Rcode{exonlevel="core"} only probes belonging to the 'core' probesets 
defined in the Affymetrix annotation files are used, APT uses (almost) all probes on the 
respective array. Thus \xps\ follows the implementation of RMA for expression arrays, while 
APT differes in the probes usage at the different steps. 

In order to determine whether this difference in the probes usage may have an influence on 
subsequent expression analysis steps, I have applied moderated t-statistics from package 
\Rpackage{limma} to find differentially expressed genes between tissues breast and prostate.
Computing raw and adjusted p-values for the gene array data results in almost identical 
p-vlaues, indicating that the small difference seen in Figure \ref{generma} does not affect 
further processing. In contrast, computing raw and adjusted p-values for the exon array data 
reveals that the \xps\ default usage of identical probes for RMA normalization results in 
lower (better) p-values in the relevant range to select genes of interest. \\

The implementation of the DABG call algorithm in \xps\ is identical to APT, however for exon 
arrays, \xps\ allows to apply DABG at both the probeset level as well as the transcript level. \\

In summary, package \xps\ offers the following advantages compared to APT:

\begin{itemize}
\item full quantile normalization can be done on computers with 1GB RAM only.
\item for RMA the same probes are used by default for background correction, quantile 
 normalization and median-polish summarization for all three types of arrays.
\item in addition, for gene and exon arrays it is possible to select probes to be used for 
 background correction, quantile normalization and median-polish summarization, respectively,
 independently.
\item MAS5 detection calls can be applied to all three tpyes of arrays.
\item DABG calls can be applied to all three tpyes of arrays.
\item for exon arrays DABG can be applied at the probeset level and the transcript level,
 respectively.
\end{itemize}



\pagebreak

\appendix

\section{Appendices}

\subsection{Some notes on PLIER}

As an alternative to RMA, Affymetrix has developed a new algorithm, called PLIER:
"The PLIER (Probe Logarithmic Error Intensity Estimate) method produces an improved signal 
by accounting for experimentally observed patterns in feature behavior and handling error 
at the appropriately at low and high signal values." (according to the APT manual) \\

Using the HG-U133\_Plus\_2 data set, the command-line for APT is:

\begin{verbatim}
apt-probeset-summarize -a plier-mm -d HG-U133_Plus_2.cdf *.CEL
\end{verbatim}

Now we import the results into R for visualization:

<<eval=FALSE>>=
apt.plier <- read.delim("plier-mm.summary.txt", row.names=1, comment.char="", skip=52)
@

There are many methods to visualize the quality of the normalization step, often based on 
advanced statistical methods. However, often a simple visualization, e.g. a simple scatter-plot 
is already very helpful. 
Thus let us create a scatter-plot of the normalized data for the replicated breast tissue:

<<eval=FALSE>>=
plot(apt.plier[,1], apt.plier[,2], main="APT: PLIER", xlab="Breast_A", ylab="Breast_B",log="xy")
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=80mm]{U133P2_APT_PLIER_Scatter.png}
  \caption{Scatter-plot.}
  \label{u133plier}
\end{center}
\end{figure}

For comparison purposes, we create also "MvA-plots" for "Breast\_A" vs "Breast\_B" using either 
PLIER or RMA for normalization:

<<eval=FALSE>>=
plot(log2(apt.plier[,1] * apt.plier[,2])/2, log2(apt.plier[,1]/apt.plier[,2]), main="APT: PLIER", xlab="A = Log2(BrA*BrB)", ylab="M = Log2(BrA/BrB)",log="")
plot(log2(apt.rma[,1] * apt.rma[,2])/2, log2(apt.rma[,1]/apt.rma[,2]), main="APT: RMA", xlab="A = Log2(BrA*BrB)", ylab="M = Log2(BrA/BrB)",log="",ylim=c(-10,10))
@

\begin{figure}[h]
\begin{center}
  \includegraphics[width=70mm]{U133P2_APT_PLIER_MvA.png}
  \includegraphics[width=70mm]{U133P2_APT_RMA_MvA.png}
  \caption{MvA-plot using PLIER (left) or RMA (right).}
  \label{u133plierrma}
\end{center}
\end{figure}

%\pagebreak

As Figure \ref{u133plierrma} shows, the differences between PLIER and RMA are dramatically. \\

%\pagebreak

Please note that the following is only my personal subjective opinion:

As both Figure \ref{u133plier} and Figure \ref{u133plierrma} reveal, PLIER produces severe 
artifacts, even for replicate data, which are supposed to have very similar expression values. 
Probably other people will not agree with me, however for this reason I never use PLIER, and 
this is one of the reasons why I have decided not to implement PLIER in package \xps. 


%\pagebreak

\bibliographystyle{plainnat}
\bibliography{xps}

\end{document}
