R/901.CalibrationAndNormalization.R

In HenrikBengtsson/aroma.light-BioC_release: Light-Weight Methods for Normalization and Visualization of Microarray Data using Only Basic R Data Types

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# @RdocDocumentation "1. Calibration and Normalization"
#
# \encoding{latin1}
#
# \description{
#   In this section we give \emph{our} recommendation on how spotted
#   two-color (or multi-color) microarray data is best calibrated and
#   normalized.
# }
#
# \section{Classical background subtraction}{
#   We do \emph{not} recommend background subtraction in classical
#   means where background is estimated by various image analysis
#   methods.  This means that we will only consider foreground signals
#   in the analysis.
#
#   We estimate "background" by other means. In what is explain below,
#   only a global background, that is, a global bias, is estimated
#   and removed.
# }
#
# \section{Multiscan calibration}{
#   In Bengtsson et al (2004) we give evidence that microarray scanners
#   can introduce a significant bias in data. This bias, which is
#   about 15-25 out of 65535, \emph{will} introduce intensity dependency
#   in the log-ratios, as explained in Bengtsson &
#   \enc{Hössjer}{Hossjer} (2006).
#
#   In Bengtsson et al (2004) we find that this bias is stable across
#   arrays (and a couple of months), but further research is needed
#   in order to tell if this is true over a longer time period.
#
#   To calibrate signals for scanner biases, scan the same array at
#   multiple PMT-settings at three or more (K >= 3) different
#   PMT settings (preferably in decreasing order).
#   While doing this, \emph{do not adjust the laser power settings}.
#   Also, do the multiscan \emph{without} washing, cleaning or by other
#   means changing the array between subsequent scans.
#   Although not necessary, it is preferred that the array
#   remains in the scanner between subsequent scans. This will simplify
#   the image analysis since spot identification can be made once
#   if images aligns perfectly.
#
#   After image analysis, read all K scans for the same array into the
#   two matrices, one for the red and one for the green channel, where
#   the K columns corresponds to scans and the N rows to the spots.
#   It is enough to use foreground signals.
#
#   In order to multiscan calibrate the data, for each channel
#   separately call \code{Xc <- calibrateMultiscan(X)} where \code{X}
#   is the NxK matrix of signals for one channel across all scans.  The
#   calibrated signals are returned in the Nx1 matrix \code{Xc}.
#
#   Multiscan calibration may sometimes be skipped, especially if affine
#   normalization is applied immediately after, but we do recommend that
#   every lab check at least once if their scanner introduce bias.
#   If the offsets in a scanner is already estimated from earlier
#   multiscan analyses, or known by other means, they can readily be
#   subtracted from the signals of each channel.  If arrays are still
#   multiscanned, it is possible to force the calibration method to
#   fit the model with zero intercept (assuming the scanner offsets
#   have been subtracted) by adding argument \code{center=FALSE}.
# }
#
# \section{Affine normalization}{
#   In Bengtsson & \enc{Hössjer}{Hossjer} (2006), we carry out a detailed
#   study on how biases in each channel introduce so called
#   intensity-dependent log-ratios among other systematic artifacts.
#   Data with (additive) bias in each channel is said to be \emph{affinely}
#   transformed. Data without such bias, is said to be \emph{linearly}
#   (proportionally) transform. Ideally, observed signals (data) is a
#   linear (proportional) function of true gene expression levels.
#
#   We do \emph{not} assume proportional observations. The scanner bias
#   is real evidence that assuming linearity is not correct.
#   Affine normalization corrects for affine transformation in data.
#   Without control spots it is not possible to estimate the bias in each
#   of the channels but only the relative bias such that after
#   normalization the effective bias are the same in all channels.
#   This is why we call it normalization and not calibration.
#
#   In its simplest form, affine normalization is done by
#   \code{Xn <- normalizeAffine(X)} where \code{X} is a Nx2 matrix with
#   the first column holds the foreground signals from the red channel and
#   the second holds the signals from the green channel.  If three- or
#   four-channel data is used these are added the same way.  The normalized
#   data is returned as a Nx2 matrix \code{Xn}.
#
#   To normalize all arrays and all channels at once, one may put all
#   data into one big NxK matrix where the K columns hold the all channels
#   from the first array, then all channels from the second array and so
#   on.  Then \code{Xn <- normalizeAffine(X)} will return the across-array
#   and across-channel normalized data in the NxK matrix \code{Xn} where
#   the colunms are stored in the same order as in matrix \code{X}.
#
#   Equal effective bias in all channels is much better. First of all,
#   any intensity-dependent bias in the log-ratios is removed \emph{for
#   all non-differentially expressed genes}. There is still an
#   intensity-dependent bias in the log-ratios for differentially expressed
#   genes, but this is now symmetric around log-ratio zero.
#
#   Affine normalization will (by default and recommended) normalize
#   \emph{all} arrays together and at once. This will guarantee that
#   all arrays are "on the same scale". Thus, it \emph{not} recommended
#   to apply a classical between-array scale normalization afterward.
#   Moreover, the average log-ratio will be zero after an affine
#   normalization.
#
#   Note that an affine normalization will only remove curvature in the
#   log-ratios at lower intensities.
#   If a strong intensity-dependent bias at high intensities remains,
#   this is most likely due to saturation effects, such as too high PMT
#   settings or quenching.
#
#   Note that for a perfect affine normalization you \emph{should}
#   expect much higher noise levels in the \emph{log-ratios} at lower
#   intensities than at higher. It should also be approximately
#   symmetric around zero log-ratio.
#   In other words, \emph{a strong fanning effect is a good sign}.
#
#   Due to different noise levels in red and green channels, different
#   PMT settings in different channels, plus the fact that the
#   minimum signal is zero, "odd shapes" may be seen in the log-ratio
#   vs log-intensity graphs at lower intensities. Typically, these
#   show themselves as non-symmetric in positive and negative log-ratios.
#   Note that you should not see this at higher intensities.
#
#   If there is a strong intensity-dependent effect left after the
#   affine normalization, we recommend, for now, that a subsequent
#   curve-fit or quantile normalization is done.
#   Which one, we do not know.
#
#   Why negative signals?
#   By default, 5\% of the normalized signals will have a non-positive
#   signal in one or both channels. \emph{This is on purpose}, although
#   the exact number 5\% is chosen by experience. The reason for
#   introducing negative signals is that they are indeed expected.
#   For instance, when measure a zero gene expression level, there is
#   a chance that the observed value is (should be) negative due to
#   measurement noise. (For this reason it is possible that the scanner
#   manufacturers have introduced scanner bias on purpose to avoid
#   negative signals, which then all would be truncated to zero.)
#   To adjust the ratio (or number) of negative signals allowed, use
#   for example \code{normalizeAffine(X, constraint=0.01)} for 1\%
#   negative signals. If set to zero (or \code{"max"}) only as much
#   bias is removed such that no negative signals exist afterward.
#   Note that this is also true if there were negative signals on
#   beforehand.
#
#   Why not lowess normalization?
#   Curve-fit normalization methods such as lowess normalization are
#   basically designed based on linearity assumptions and will for this
#   reason not correct for channel biases. Curve-fit normalization
#   methods can by definition only be applied to one pair of channels
#   at the time and do therefore require a subsequent between-array
#   scale normalization, which is by the way very ad hoc.
#
#   Why not quantile normalization?
#   Affine normalization can be though of a special case of quantile
#   normalization that is more robust than the latter.
#   See Bengtsson & \enc{Hössjer}{Hossjer} (2006) for details.
#   Quantile normalization is probably better to apply than curve-fit
#   normalization methods, but less robust than affine normalization,
#   especially at extreme (low and high) intensities.
#   For this reason, we do recommend to use affine normalization first,
#   and if this is not satisfactory, quantile normalization may be applied.
# }
#
# \section{Linear (proportional) normalization}{
#   If the channel offsets are zero, already corrected for, or estimated
#   by other means, it is possible to normalize the data robustly by
#   fitting the above affine model without intercept, that is, fitting
#   a truly linear model.  This is done adding argument \code{center=FALSE}
#   when calling \code{normalizeAffine()}.
# }
#
# @author "HB"
#*/#########################################################################





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# HISTORY:
# 2011-02-05
# o DOCUMENTATION: Added paragraphs on how to do affine normalization
#   when channel offsets are known/zero.  Same for multiscan calibration
#   when scanner offsets are known/zero.
# 2006-06-29
# o Added to aroma.light instead.
# 2005-02-02
# o Created.
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