%\VignetteIndexEntry{msmsTests: controlling batch effects by blocking}
%\VignetteDepends{msmsTests}
%\VignetteKeywords{multivariate, hplot}
%\VignettePackage{msmsTests}

\documentclass[12pt,a4paper,oneside]{article}
\usepackage{fullpage}
\usepackage{float}
\usepackage[section]{placeins}
\usepackage{enumerate}

\begin{document}
\SweaveOpts{keep.source=TRUE,concordance=TRUE}

\title{msmsTests package\\
       Blocks design to compensate batch effects}
\author{Josep Gregori, Alex Sanchez, and Josep Villanueva\\
   Vall Hebron Institute of Oncology \&\\
   Statistics Dept. Barcelona University\\
  \texttt{josep.gregori@gmail.com}}

\maketitle

\tableofcontents

\section{Introduction}

This vignette exemplifies the use of the packages msmsEDA and msmsTests
in discovering and correcting batch effects in label-free LC-MS/MS data
based on spectral counts. Label-free experiments are specially sensitive
to these effects as each condition has to be measured separately and may be
influenced by uncontrolled factors in a different extend.

\section{Dataset}

This dataset \cite{gregori2013} is the result of spiking experiments, 
showing real LC-MS/MS data. Samples of 500 micrograms of a standard 
yeast lysate are spiked with 200 and 600fm of a complex mix of 
48 equimolar human proteins (UPS1, Sigma-Aldrich).
The dataset comes with the package msmsEDA \cite{msmsEDA},
and was used to evidence batch effects by exploratory data analysis 
tools \cite{josep2012}.
The dataset consists in an instance of the \emph{MSnSet} class, defined in the 
MSnbase package \cite{Gatto2012}, a S4 class \cite{chambers} \cite{genolini}. 
This \emph{MSnSet} object contains
a spectral counts (SpC) matrix in the \emph{assayData}
slot, and factors treatment and batch in the \emph{phenoData} slot.
(See also the expressionSet vignette by vignette("ExpressionSetIntroduction",package="Biobase") \cite{gentleman})
<<echo=FALSE>>=
options(continue=" ")
@

<<SetupChunk, echo = TRUE>>=
library(msmsTests)
data(msms.dataset)
msms.dataset
msms.counts <- exprs(msms.dataset)
dim(msms.counts)
table(pData(msms.dataset)$treat,pData(msms.dataset)$batch)
@

Although the mix is equimolar the signal strength of each protein is markedly
different, allowing to cover a wide range of SpC values, what makes it 
specially worth in this sort of experiments:

<<DistChunk, echo = TRUE>>=
idx <- grep("HUMAN",featureNames(msms.dataset)) 
mSpC <- t( apply(msms.counts[idx,],1,function(x) 
                   tapply(x,pData(msms.dataset)$treat,mean)) )
apply(mSpC,2,summary)
@

\section{Batch effects}

Real life LC-MS/MS experiments use to be complicated enough 
to be able to get all required technical or biological replicates 
in a single batch run. Commonly a dataset collects results from
multiple batches. The batches may be influenced by factors 
which escape our control capacity, and typically these datasets
show the so known '\emph{batch effects}' when the runs where
obtained in different dates. The confounding
caused by these effects is easily evidenced by multidimensional
tools like Principal Components Analysis (PCA) or Hierarchical
Clustering (HC), when the samples cluster by batches instead
of by treatment \cite{josep2012} \cite{luo2010} .  

<<PCAChunk, echo=TRUE, tidy=FALSE>>=
snms <- substr(as.character(pData(msms.dataset)$treat),1,2)
snms <- paste(snms,as.integer(pData(msms.dataset)$batch),sep=".")
smpl.pca <- counts.pca(msms.dataset,snms=snms)$pca
@

\begin{figure}[H]
\centering
<<fig=TRUE, echo=FALSE, width=6.5, height=4>>=
par(mar=c(4,4,0.5,2)+0.1)
facs <- data.frame(batch=pData(msms.dataset)$batch)
counts.pca(msms.dataset,facs=facs,snms=snms)
@
\caption{Principal Components Analysis}\label{pca}
\end{figure}


\section{Results on a single batch}

The next code shows the results obtained from the data of a single
batch with four replicates in each condition. The statistic test
used for differential expression is the quasi-likelihood GLM
\cite{agresti2002} \cite{li2010}, and
the p-values are adjusted with FDR control by the Benjamini-Hochberg
\cite{BH} method. The quality of the results is given by a truth table.

<<SubsetChunk, echo = TRUE>>=
###  Subset and pre-process dataset
fl <- pData(msms.dataset)$batch=="2502"
e <- msms.dataset[,fl]
e <- pp.msms.data(e)
### Null and alternative model
null.f <- "y~1"
alt.f <- "y~treat"
### Normalizing condition
counts <- exprs(e)
div <- apply(counts,2,sum)
### Quasi-likelihood GLM
ql.res <- msms.glm.qlll(e,alt.f,null.f,div=div)
### Adjust p-values with FDR control.
adjp <- p.adjust(ql.res$p.value,method="BH")
###  Truth table
nh <- length(grep("HUMAN",featureNames(e)))
ny <- length(grep("HUMAN",featureNames(e),invert=TRUE))
tp <- length(grep("HUMAN",rownames(ql.res)[adjp<=0.05]))
fp <- sum(adjp<=0.05)-tp
(tt.ql1 <- data.frame(TP=tp,FP=fp,TN=ny-fp,FN=nh-tp))
@

These results may be polished by a post-test filter, so
that only relevant features are accepted as differentially expressed,
and the false positives are further restricted \cite{gregori2013}.

<<SubsetFChunk, echo = TRUE>>=
###  Post-test filter
ql.tbl <- test.results(ql.res,e,pData(e)$treat,"U600","U200",div,
                    alpha=0.05,minSpC=2,minLFC=1,method="BH")$tres
ql.nms <- rownames(ql.tbl)[ql.tbl$DEP]
###  Truth table
ridx <- grep("HUMAN",ql.nms)
tp <- length(ridx)
fp <- length(ql.nms)-length(ridx)
(tt.ql11 <- data.frame(TP=tp,FP=fp,TN=ny-fp,FN=nh-tp))
@

\section{Results on the global dataset}

With a higher number of replicates the tests become more sensitive, and
a higher number of differentially expressed features may be identified.
The next code explores the full dataset, composed of two batches and
seven replicates of each condition. Again the quality of the results 
is given by a truth table.

<<GlobalChunk, echo = TRUE>>=
###  Pre-process dataset
gble <- pp.msms.data(msms.dataset)
### Null and alternative model
null.f <- "y~1"
alt.f <- "y~treat"
### Normalizing condition
div <- apply(exprs(gble),2,sum)
### Quasi-likelihood GLM
ql.res <- msms.glm.qlll(gble,alt.f,null.f,div=div)
### Adjust p-values with FDR control.
adjp <- p.adjust(ql.res$p.value,method="BH")
###  Truth table
nh <- length(grep("HUMAN",featureNames(gble)))
ny <- length(grep("HUMAN",featureNames(gble),invert=TRUE))
tp <- length(grep("HUMAN",rownames(ql.res)[adjp<=0.05]))
fp <- sum(adjp<=0.05)-tp
(tt.ql2 <- data.frame(TP=tp,FP=fp,TN=ny-fp,FN=nh-tp))
@

Applying a post-test filter, as before, the results become:

<<GlobalFChunk, echo = TRUE>>=
###  Post-test filter
ql.tbl <- test.results(ql.res,gble,pData(gble)$treat,"U600","U200",div,
                    alpha=0.05,minSpC=2,minLFC=1,method="BH")$tres
ql.nms <- rownames(ql.tbl)[ql.tbl$DEP]
###  Truth table
ridx <- grep("HUMAN",ql.nms)
tp <- length(ridx)
fp <- length(ql.nms)-length(ridx)
(tt.ql22 <- data.frame(TP=tp,FP=fp,TN=ny-fp,FN=nh-tp))
@

\section{Results on the global dataset with a blocking factor}

When the batches are balanced in the treatment conditions the
presence of confounding factors translates into bigger variance
and lower sensitivity. We may account for this extra variability 
by introducing the batches into the model, as a blocking factor.
The next code explores the corresponding results.

<<BlockChunk, echo = TRUE>>=
### Null and alternative model
null.f <- "y~batch"
alt.f <- "y~treat+batch"
### Quasi-likelihood GLM
ql.res <- msms.glm.qlll(gble,alt.f,null.f,div=div)
### Adjust p-values with FDR control.
adjp <- p.adjust(ql.res$p.value,method="BH")
###  Truth table
nh <- length(grep("HUMAN",featureNames(gble)))
ny <- length(grep("HUMAN",featureNames(gble),invert=TRUE))
tp <- length(grep("HUMAN",rownames(ql.res)[adjp<=0.05]))
fp <- sum(adjp<=0.05)-tp
(tt.ql3 <- data.frame(TP=tp,FP=fp,TN=ny-fp,FN=nh-tp))
@

The correction improved the number of true positives, but significantly
increased the number of false positives. This may be polished by the
post-test filter to remove the non relevant features:

<<BlockFChunk, echo = TRUE>>=
###  Post-test filter
ql.tbl <- test.results(ql.res,gble,pData(gble)$treat,"U600","U200",div,
                    alpha=0.05,minSpC=2,minLFC=1,method="BH")$tres
ql.nms <- rownames(ql.tbl)[ql.tbl$DEP]
###  Truth table
ridx <- grep("HUMAN",ql.nms)
tp <- length(ridx)
fp <- length(ql.nms)-length(ridx)
(tt.ql33 <- data.frame(TP=tp,FP=fp,TN=ny-fp,FN=nh-tp))
@

\section{Comparison of results}

The following table collects the results obtained so far, where we see
how increasing the number of replicates we improve the sensitivity,
how the use of a post-test filter helps in restricting the number of
false positives, and how blocking helps to remove the extra variability
introduced by batch effects.

<<CompChunk, echo = FALSE, results=tex>>=
gbl.tt <- rbind(tt.ql1,tt.ql11,tt.ql2,tt.ql22,tt.ql3,tt.ql33)
rownames(gbl.tt) <- c("subset","subset filtered",
                      "global","global filtered",
                      "blocking","blocking filtered")		  
library(xtable)
print(xtable(gbl.tt,align=c("r","r","r","r","r"),
             caption=c("Truth tables"),
             display=c("s","d","d","d","d")),
      type="latex",hline.after=c(-1,0,2,4,6),include.rownames=TRUE)
@

\begin{figure}[H]
\centering
<<fig=TRUE, echo=FALSE, width=3, height=3.5>>=
par(mar=c(5, 3, 2, 2) + 0.1)
par(cex.axis=0.8,cex.lab=0.8)
rownames(gbl.tt) <- c("subset","subset\nfiltered",
                      "global","global\nfiltered",
                      "blocking","blocking\nfiltered")		  
barplot(t(data.matrix(gbl.tt[,1:2])),beside=TRUE,las=2,space=c(0,0.25),
        legend.text=c("TP","FP"),args.legend=list(x="topleft",cex=0.8,bty="n"))
@
\caption{Comparison of results}\label{barplot}
\end{figure}

\newpage

\begin{thebibliography}{11}
\bibitem{gregori2013}  
Gregori J., Villareal L., Sanchez A., Baselga J., 
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http://dx.doi.org/10.1016/j.jprot.2013.05.030
\bibitem{msmsEDA}
Gregori J., Sanchez A. and Villanueva J. (2013). \emph{msmsEDA: 
Exploratory Data Analysis of LC-MS/MS data by spectral counts}.
R package version 1.0.
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sensitivity of significance tests in spectral counting-based comparative 
discovery proteomics}, Journal of Proteomics, 2012, 75, 3938-3951
\bibitem{Gatto2012} Laurent Gatto and Kathryn S. Lilley, MSnbase - an R/Bioconductor package for isobaric tagged mass spectrometry data visualization, processing and quantitation, Bioinformatics 28(2), 288-289 (2012).
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\bibitem{luo2010}
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\bibitem{agresti2002}
Agresti A., \emph{Categorical Data Analysis},
Wiley-Interscience, Hoboken NJ, 2002
\bibitem{li2010}
Li, M.; Gray, W.; Zhang, H.; Chung, C. H.; Billheimer, D.; Yarbrough, W.
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\end{thebibliography}

\end{document}
 

