Weighted curvefit normalization between a pair of channels
Description
Weighted curvefit normalization between a pair of channels.
This method will estimate a smooth function of the dependency between the logratios and the logintensity of the two channels and then correct the logratios (only) in order to remove the dependency. This is method is also known as intensitydependent or lowess normalization.
The curvefit methods are by nature limited to pairedchannel data. There exist at least one method trying to overcome this limitation, namely the cycliclowess [1], which applies the paired curvefit method iteratively over all pairs of channels/arrays. Cycliclowess is not implented here.
We recommend that affine normalization [2] is used instead of curvefit normalization.
Usage
1 2 3 4 5 6 7 8 9 10 11 12  ## S3 method for class 'matrix'
normalizeCurveFit(X, weights=NULL, typeOfWeights=c("datapoint"),
method=c("loess", "lowess", "spline", "robustSpline"), bandwidth=NULL,
satSignal=2^16  1, ...)
## S3 method for class 'matrix'
normalizeLoess(X, ...)
## S3 method for class 'matrix'
normalizeLowess(X, ...)
## S3 method for class 'matrix'
normalizeSpline(X, ...)
## S3 method for class 'matrix'
normalizeRobustSpline(X, ...)

Arguments
X 
An Nx2 
weights 
If 
typeOfWeights 
A 
method 

bandwidth 
A 
satSignal 
Signals equal to or above this threshold will not be used in the fitting. 
... 
Not used. 
Details
A smooth function c(A) is fitted throught data in (A,M), where M=log_2(y_2/y_1) and A=1/2*log_2(y_2*y_1). Data is normalized by M < M  c(A).
Loess is by far the slowest method of the four, then lowess, and then robust spline, which iteratively calls the spline method.
Value
A Nx2 matrix
of the normalized two channels.
The fitted model is returned as attribute modelFit
.
Negative, nonpositive, and saturated values
Nonpositive values are set to notanumber (NaN
).
Data points that are saturated in one or more channels are not used
to estimate the normalization function, but they are normalized.
Missing values
The estimation of the normalization function will only be made
based on complete nonsaturated observations, i.e. observations that
contains no NA
values nor saturated values as defined by satSignal
.
Weighted normalization
Each data point, that is, each row in X
, which is a
vector of length 2, can be assigned a weight in [0,1] specifying how much
it should affect the fitting of the normalization function.
Weights are given by argument weights
, which should be a numeric
vector
of length N. Regardless of weights, all data points are
normalized based on the fitted normalization function.
Note that the lowess and the spline method only support zeroone {0,1} weights. For such methods, all weights that are less than a half are set to zero.
Details on loess
For loess
, the arguments family="symmetric"
,
degree=1
, span=3/4
,
control=loess.control(trace.hat="approximate"
,
iterations=5
, surface="direct")
are used.
Author(s)
Henrik Bengtsson
References
[1] M. Åstrand,
Contrast Normalization of Oligonucleotide Arrays,
Journal Computational Biology, 2003, 10, 95102.
[2] Henrik Bengtsson and Ola Hössjer, Methodological Study of Affine Transformations of Gene Expression Data, Methodological study of affine transformations of gene expression data with proposed robust nonparametric multidimensional normalization method, BMC Bioinformatics, 2006, 7:100.
See Also
normalizeAffine
().
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104  pathname < system.file("dataex", "PMTRGData.dat", package="aroma.light")
rg < read.table(pathname, header=TRUE, sep="\t")
nbrOfScans < max(rg$slide)
rg < as.list(rg)
for (field in c("R", "G"))
rg[[field]] < matrix(as.double(rg[[field]]), ncol=nbrOfScans)
rg$slide < rg$spot < NULL
rg < as.matrix(as.data.frame(rg))
colnames(rg) < rep(c("R", "G"), each=nbrOfScans)
layout(matrix(c(1,2,0,3,4,0,5,6,7), ncol=3, byrow=TRUE))
rgC < rg
for (channel in c("R", "G")) {
sidx < which(colnames(rg) == channel)
channelColor < switch(channel, R="red", G="green");
#                                
# The raw data
#                                
plotMvsAPairs(rg[,sidx])
title(main=paste("Observed", channel))
box(col=channelColor)
#                                
# The calibrated data
#                                
rgC[,sidx] < calibrateMultiscan(rg[,sidx], average=NULL)
plotMvsAPairs(rgC[,sidx])
title(main=paste("Calibrated", channel))
box(col=channelColor)
} # for (channel ...)
#                                
# The average calibrated data
#
# Note how the red signals are weaker than the green. The reason
# for this can be that the scale factor in the green channel is
# greater than in the red channel, but it can also be that there
# is a remaining relative difference in bias between the green
# and the red channel, a bias that precedes the scanning.
#                                
rgCA < rg
for (channel in c("R", "G")) {
sidx < which(colnames(rg) == channel)
rgCA[,sidx] < calibrateMultiscan(rg[,sidx])
}
rgCAavg < matrix(NA_real_, nrow=nrow(rgCA), ncol=2)
colnames(rgCAavg) < c("R", "G");
for (channel in c("R", "G")) {
sidx < which(colnames(rg) == channel)
rgCAavg[,channel] < apply(rgCA[,sidx], MARGIN=1, FUN=median, na.rm=TRUE);
}
# Add some "fake" outliers
outliers < 1:600
rgCAavg[outliers,"G"] < 50000;
plotMvsA(rgCAavg)
title(main="Average calibrated (AC)")
#                                
# Normalize data
#                                
# Weightdown outliers when normalizing
weights < rep(1, nrow(rgCAavg));
weights[outliers] < 0.001;
# Affine normalization of channels
rgCANa < normalizeAffine(rgCAavg, weights=weights)
# It is always ok to rescale the affine normalized data if its
# done on (R,G); not on (A,M)! However, this is only needed for
# esthetic purposes.
rgCANa < rgCANa *2^1.4
plotMvsA(rgCANa)
title(main="Normalized AC")
# Curvefit (lowess) normalization
rgCANlw < normalizeLowess(rgCAavg, weights=weights)
plotMvsA(rgCANlw, col="orange", add=TRUE)
# Curvefit (loess) normalization
rgCANl < normalizeLoess(rgCAavg, weights=weights)
plotMvsA(rgCANl, col="red", add=TRUE)
# Curvefit (robust spline) normalization
rgCANrs < normalizeRobustSpline(rgCAavg, weights=weights)
plotMvsA(rgCANrs, col="blue", add=TRUE)
legend(x=0,y=16, legend=c("affine", "lowess", "loess", "r. spline"), pch=19,
col=c("black", "orange", "red", "blue"), ncol=2, x.intersp=0.3, bty="n")
plotMvsMPairs(cbind(rgCANa, rgCANlw), col="orange", xlab=expression(M[affine]))
title(main="Normalized AC")
plotMvsMPairs(cbind(rgCANa, rgCANl), col="red", add=TRUE)
plotMvsMPairs(cbind(rgCANa, rgCANrs), col="blue", add=TRUE)
abline(a=0, b=1, lty=2)
legend(x=6,y=6, legend=c("lowess", "loess", "r. spline"), pch=19,
col=c("orange", "red", "blue"), ncol=2, x.intersp=0.3, bty="n")
