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\title{Getting started with \Rpackage{flowStats}}
\author{F. Hahne, N. Gopalakrishnan}

\begin{document}
\maketitle

\begin{abstract}
\Rpackage{flowStats} is a collection of algorithms for the statistical
analysis of flow cytometry data. So far, the focus is on automated
gating and normalization.
\end{abstract}


\section{Introduction}
Since \Rpackage{flowStats} is more a collection of algorithms, writing
a coherent Vignette is somewhat difficult. Instead, we will present a
hypothetical data analysis process that also makes heavy use of the
functionality provided by \Rpackage{flowCore}, mainly the work flow
infrastructure.

We start by loading the \Robject{GvHD} data set from the
\Rpackage{flowCore} package.
<<loadGvHD>>=
library(flowStats)
data(ITN)
@ 
%
The data was acquired from blood samples by 3 groups of patients, each
group containing 5 samples. Each \Rclass{flowFrame} includes, in
addition to FSC and SSC, 5 fluoresence parameters: CD3, CD4, CD8, CD69
and HLADR.

First we need to tranform all the fluorescense channels. This is a
good point to start using a \Rclass{workFlow} object to keep track of
our progress.
<<transform>>=
wf <- workFlow(ITN)
tl <- transformList(colnames(ITN)[3:7], asinh, transformationId="asinh")
add(wf, tl)
@ 
%
In a initial analysis step we first want to indentify and subset all
T-cells. This can be archived by gating in the CD3 and SSC dimensions,
however there are several other sub-populations, and we need to
either specify our selection further, or segment the individual
sub-populations. One solution for the latter aproach is to use the
mixture modelling infrastructure provided by the \Rclass{flowClust}
package. However, since we are only interested in one single
sub-population, the T-cell, it is much faster and easier to use the
\Rfunction{lymphGate} function in the \Rpackage{flowStats}
package. The idea here is to first do a rough preselection in the
two-dimensional projection of the data based on expert knowledge or
prior experience and subsequently to fit a \Rclass{norm2Filter} to
this subset. The function also allows to derive the pre-selection
through back-gating: we know that CD4 positive cells are a subset of
T-cells, so by estimating CD4 positive cells first we can get a rough
idea on where to find the T-cells in the CD3 SSC projection.

<<lymphGate>>=
lg <- lymphGate(Data(wf[["asinh"]]), channels=c("SSC", "CD3"),
                preselection="CD4", filterId="TCells", eval=FALSE,
                scale=2.5)
add(wf, lg$n2gate, parent="asinh")
<<lymphGatePlot, fig=TRUE>>=
library(flowViz)
print(xyplot(SSC ~ CD3| PatientID, wf[["TCells+"]],
      par.settings=list(gate=list(col="red", 
         fill="red", alpha=0.3))))
@ 

In the next step we want to separate T-helper and NK cells using the
CD4 and CD8 stains. A convenient way of doing this is to apply a
\Rclass{quadGate}, assuming that both CD4 and CD8 are binary markers
(cells are either positive or negative for CD4 and CD8). Often
investigators use negative samples to derive a split point between the
postive and negative populations, and apply this constant gate on all
their samples. This will only work if there are no unforseen shifts in
the fluorescence itensities between samples which are purely caused by
technical variation rather than biological phenotype. Let's take a
look at this variation for the T-cell subset and all 4 remaining
fluorescense channels:

<<variation, fig=TRUE>>=
pars <- colnames(Data(wf[["base view"]]))[c(3,4,5,7)]
print(densityplot(PatientID~., Data(wf[["TCells+"]]), channels=pars, groups=GroupID,
                  scales=list(y=list(draw=F)), filter=lapply(pars, curv1Filter),
                  layout=c(4,1)))
@ 

Indeed the data, especially for CD4 and CD8, don't align well. At
this point we could decide to compute the \Rclass{quadGates} for each
sample separately. Alternatively, we can try to normalize the data and
then compute a common gate. The \Rfunction{warpSet} function can be
used to normalize data according to a set of landmarks, which
essentially are the peaks or high-density areas in the density
estimates shown before. The ideas here are simple:

\begin{itemize}
\item High density areas represent particular sub-types of cells. 
\item Markers are binary. Cells are either positive or negative for
  a particular marker.
\item Peaks should aline if the above statements are true.
\end{itemize}

The algorithm in \Rfunction{warpSet} performs the following steps:
\begin{enumerate}
\item Identify landmarks for each parameter using a \Rfunction{curv1Filter}
\item Estimate the most likely total number (k) of landmarks
\item Perform k-means clustering to classify landmarks
\item Estimate warping functions for each sample and parameter that
  best align the landmarks, given the underlying data. This step uses
  functionality from the \Rpackage{fda} package.
\item Transform the data using the warping functions.
\end{enumerate}

The algorithm should be robust to missing peaks in some of the
samples, however the classification in step 3 becomes harder since it
is not clear which cell population it represents.   

<<norm>>=
norm <- normalization(normFun=function(x, parameters, ...)
                      warpSet(x, parameters, ...),
                      parameters=pars,
                      arguments=list(grouping="GroupID", monwrd=TRUE),
                      normalizationId="Warping")
add(wf, norm, parent="TCells+")
<<normPlot, fig=TRUE>>=
print(densityplot(PatientID~., Data(wf[["Warping"]]), channels=pars, groups=GroupID,
                  scales=list(y=list(draw=F)), filter=lapply(pars, curv1Filter),
                  layout=c(4,1)))
@

After normalization the data look much cleaner and we should be able
to use a single static gate for all \Rclass{flowFrames} in order to
separate CD4 and CD8 positive cells. Typically one would use a
\Rclass{quadGate}, and the \Rfunction{quadrantGate} function in
\Rpackage{flowStats} can be used to automatically estimate such a
gate. 

<<quadGate>>=
qgate <- quadrantGate(Data(wf[["Warping"]]), stains=c("CD4", "CD8"),
                      filterId="CD4CD8", sd=3)
add(wf, qgate, parent="Warping")
@ 
<<quadGatePlot, fig=TRUE>>=
print(xyplot(CD8 ~ CD4 | PatientID, wf[["CD4+CD8+"]],
             par.settings=list(gate=list(fill="transparent", col="red"))))
@ 

In a final step we might be interested in finding the proportion of
activated T-helper cells by means of the CD69 stain. The
\Rfunction{rangeGate} function is helpful in separating positive and
negative peaks in 1D.

<<rangeGate>>=
CD69rg <- rangeGate(Data(wf[["Warping"]]), stain="CD69",
                    alpha=0.75, filterId="CD4+CD8-CD69", sd=2.5)
add(wf, CD69rg, parent="CD4+CD8-")
@
<<rangeGatePlot, fig=TRUE>>=
print(densityplot(PatientID ~ CD69, Data(wf[["CD4+CD8-"]]), main = "CD4+",
            groups=GroupID, refline=CD69rg@min))
@ 

\section{Probability Binning}
A probability binning algorithm for quantitating multivariate distribution 
differences was described by Roederer et al. The algorithm identifies the flow 
parameter in a flowFrame with the largest variance and divides the events in the 
flowFrame into two subgroups based on the median of the parameter. This process 
continues until the number of events in each subgroup is less than a user 
specified threshold.

For comparison across multiple samples, probability binning algorithm can be applied
to a control dataset to obtain the position of bins and the same bins can be 
applied to the experimental dataset. The number of events in the control and sample
bins can then be compared using the Pearsons chi-square test or the probability 
binning metric defined by Roederer et al.

Although probability binning can be applied simultaneously to all parameters in 
a flowFrame with bins in n dimensional hyperspace, we proceed with a two dimenstional
example from our previous discussion involving CD4 and CD8 populations. This helps
to simplify the demonstration of the method and interpretation of results. 

From the workflow object containing the warped data, we extract our data frame of 
interest. We try to compare the panels using probability binning to identify patients 
with CD4, CD8 populations different from a control flowFrame that we create using the
data from all the patients.

<<createData>>=
dat <- Data(wf[["Warping"]])

@

The dat is visualized below
<<rawData, fig=TRUE>>=
print( xyplot(CD8 ~ CD4 , dat, main= "Experimental data set"))
@

The control dataset is created by combining all the flowFrames in the flowSet. 
The flowFrame is then subsetted after applying a sampleFilter so that the control
flowSet created has approximately the same number of events as the other flowSets
in our example.

<<createControlData>>=
datComb <- as(dat,"flowFrame")
subCount <- nrow(exprs(datComb))/length(dat)
	sf <- sampleFilter(filterId="mySampleFilter", size=subCount)
	fres <- filter(datComb, sf)
	ctrlData <- Subset(datComb, fres)
	ctrlData <- ctrlData[,-ncol(ctrlData)] ##remove the  column name "original"
	
@

The probability binning algorithm can then applied to the control data. The 
terminating condition for the algorithm is set so that the number of events 
in each bin is approximately 5 percent of the total number of events in the 
control data.
<<BinControlData>>=
minRow=subCount*0.05
refBins<-proBin(ctrlData,minRow,channels=c("CD4","CD8"))
	
@

The binned control Data can be visualized using the \Rfunction{plotBins} function.
Areas in the scatter  plot with a large number of data points have a higher
density of bins. Each bin also has approximately same number of events.


<<controlBinsPlot, fig=TRUE>>=
plotBins(refBins,ctrlData,channels=c("CD4","CD8"),title="Control Data")

@

The same bin positions from the control data set are then applied to each flowFrame
in our sample Data set.

<<binSampleData>>=
sampBins <- fsApply(dat,function(x){
		   binByRef(refBins,x)
		   })
@

For each patient, the number events in the control and sample bins can be compared
using the \Rfunction{calcPearsonChi} or using Roederers probability binning 
metric.

<<pearsonStat>>=
pearsonStat <- lapply(sampBins,function(x){
		      calcPearsonChi(refBins,x)
                     })
@

<<Roderers PBin metric>>=
sCount <- fsApply(dat,nrow)
pBStat <-lapply(seq_along(sampBins),function(x){
		calcPBChiSquare(refBins,sampBins[[x]],subCount,sCount[x])
		})
@


For each sample, the results can be visualized using the \Rfunction{plotBins} function.
The residuals from Roeders probability binning metric or the Pearsons chi square
test can be used to shade bins to highlight bins in each sample that differ 
the most from the control sample.

<<plotBinsresiduals, fig=TRUE>>=
par(mfrow=c(4,4),mar=c(1.5,1.5,1.5,1.5))

plotBins(refBins,ctrlData,channels=c("CD4","CD8"),title="Control Data")
patNames <-sampleNames(dat)
tm<-lapply(seq_len(length(dat)),function(x){
		plotBins(refBins,dat[[x]],channels=c("CD4","CD8"),
			title=patNames[x],
			residuals=pearsonStat[[x]]$residuals[2,],
			shadeFactor=0.7)
		
		}
      )
@

The patient with CD4/CD8 populations most different from that of the 
control group can be identified from the magnitue of Pearson-chi square
statistic(or Probability binning statistic). 


<<chiSqstatisticvalues,echo=FALSE>>=
library(xtable)
chi_Square_Statistic <- unlist(lapply(pearsonStat,function(x){
		x$statistic
		}))

pBin_Statistic <-unlist(lapply(pBStat,function(x){
                x$pbStat
						                        })) 
	
frame <- data.frame(chi_Square_Statistic, pBin_Statistic)
rownames(frame) <- patNames
 	
@

<<echo=FALSE,results=tex>>=
print(xtable(frame))
@

\clearpage


<<echo=FALSE,results=tex>>=
toLatex(sessionInfo())
@
 

\end{document}

