Weighted curve-fit normalization between a pair of channels

Description

Weighted curve-fit normalization between a pair of channels.

This method will estimate a smooth function of the dependency between the log-ratios and the log-intensity of the two channels and then correct the log-ratios (only) in order to remove the dependency. This is method is also known as intensity-dependent or lowess normalization.

The curve-fit methods are by nature limited to paired-channel data. There exist at least one method trying to overcome this limitation, namely the cyclic-lowess [1], which applies the paired curve-fit method iteratively over all pairs of channels/arrays. Cyclic-lowess is not implented here.

We recommend that affine normalization [2] is used instead of curve-fit normalization.

Usage

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## 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 matrix where the columns represent the two channels to be normalized.

weights

If NULL, non-weighted normalization is done. If data-point weights are used, this should be a vector of length N of data point weights used when estimating the normalization function.

typeOfWeights

A character string specifying the type of weights given in argument weights.

method

character string specifying which method to use when fitting the intensity-dependent function. Supported methods: "loess" (better than lowess), "lowess" (classic; supports only zero-one weights), "spline" (more robust than lowess at lower and upper intensities; supports only zero-one weights), "robustSpline" (better than spline).

bandwidth

A double value specifying the bandwidth of the estimator used.

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, non-positive, and saturated values

Non-positive values are set to not-a-number (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 non-saturated 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 zero-one {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, 95-102.
[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 non-parametric multi-dimensional normalization method, BMC Bioinformatics, 2006, 7:100.

See Also

normalizeAffine().

Examples

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 pathname <- system.file("data-ex", "PMT-RGData.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
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# Weight-down 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")

# Curve-fit (lowess) normalization
rgCANlw <- normalizeLowess(rgCAavg, weights=weights)
plotMvsA(rgCANlw, col="orange", add=TRUE)

# Curve-fit (loess) normalization
rgCANl <- normalizeLoess(rgCAavg, weights=weights)
plotMvsA(rgCANl, col="red", add=TRUE)

# Curve-fit (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")

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