smoother: Wrapper for Several Smoothers of Amplification Data
In chipPCR: Toolkit of Helper Functions to Pre-Process Amplification Data

Description Usage Arguments Details Author(s) References Examples

Smoother is a wrapper for several smoothing functions including LOWESS, Moving Average, Friedman's SuperSmoother, Cubic Spline and Savitzky-Golay smoothing filter, Friedman's SuperSmoother, and Whittaker smoother for amplification curve data.

## S4 method for signature 'numeric,numeric'
smoother(x, y, trans = FALSE, 
		    bg.outliers = FALSE, method = "savgol", 
		    CPP = TRUE, paralell = NULL)
## S4 method for signature 'matrix,missing'
smoother(x, y, trans = FALSE, 
		    bg.outliers = FALSE, method = "savgol", 
		    CPP = TRUE, paralell = NULL)
## S4 method for signature 'data.frame,missing'
smoother(x, y, trans = FALSE, 
		    bg.outliers = FALSE, method = "savgol", 
		    CPP = TRUE, paralell = NULL)

`x`	`x` is a vector containing values for smoothing or data frame/matrix with values for smoothing.
`y`	`y` values for smoothing. Used only if `x` is also a vector.
`trans`	perform a linear transformation based on the trend of the background range.
`bg.outliers`	logical parameter which indicates of outliers should be removed from background range.
`method`	a list where each element is character vector representing a smoothing method or a named list of additional arguments to a smoothing algorithm. See Examples section. The Savitzky-Golay smoothing filter is the default smoother. Use "lowess" for LOWESS smoother (locally-weighted polynomial regression, "mova" for moving average, "savgol" for Savitzky-Golay smoothing filter, "smooth" for cubic spline smooth, "spline" for standard cubic spline smooth, "supsmu" for Friedman's SuperSmoother, "whit1" for weighted Whittaker smoothing with a first order finite difference penalty, "whit2" for weighted Whittaker smoothing with a second order finite difference penalty or "all" for all implemented smoothing algorithms. Both upper and lower case names are accepted.
`CPP`	logical parameter which indicates if CPP (curve pre-processor) should be used.
`paralell`	should contain a cluster object, created by package `parallel` or `snow` package. If `NULL`, no parallelization is used.

Amplification curve data of experimental thermo-cyclers may deliver results which are hard to interpret due to noise and scatter. For data presentation it is often useful to smooth or filter the data prior to presentation. Smoothing and filtering are different approaches with a similar outcome to preprocess an input signal in order to make it available for an analysis step. Filtering uses methods of signal processing. They take a data input and apply a function to form an output. There are linear and non-linear filters. The most common example of a linear filter is the the moving average. A moving average filter replaces sequentially data points with the average of the neighbor data points. The average is calculated from a defined span ("window") of odd count (e.g., 3, 5). The average herein may also refer to the median, the geometric or exponential mean. Smoothing in contrast uses statistical approaches. Such approaches use for example local regression models (e.g., least squares estimate) or cubic splines. Splines apply non-parametric regression by local cubic polynomials between knot points. Other examples for smoothers include Savitzky-Golay smoothing filter, Friedman's SuperSmoother, and Whittaker smoother. Several methods were integrated in the chipPCR package. A careful evaluation of this preprocessing step is of high importance (Spiess et al. 2014).

smoother is a wrapper for smoother functions and filters commonly used to process amplification curve data. The smoother function was enhanced by functionality of the fixNA and CPP functions. The parameter "lowess" for LOWESS smoother (locally-weighted polynomial regression) can be tuned by the parameters f and iter (see lowess for details). The parameter "mova" for moving average can be tuned by the parameter movaww. movaww is the window size used for the moving average (see filter for details). The parameter "savgol" for Savitzky-Golay smoothing filter can be tuned by the parameter p and n (see sgolayfilt for details). The parameter "smooth" for cubic spline smooth can be tuned by the parameter df.fact. A df.fact value of 1 will leave the raw data almost unaffected while a value 0.5 will smooth the curve considerably. For further details refer to the smooth.spline function. The parameter "spline" for standard cubic spline smooth has currently no additional parameter. The parameter "supsmu" for Friedman's SuperSmoother can be tuned by the parameter span. For further details refer to the supsmu function. The parameter "lambda" is used in Weighted Whittaker smoothing.

Stefan Roediger, Michal Burdukiewicz

Roediger S, Boehm A, Schimke I. Surface Melting Curve Analysis with R. The R Journal 2013;5:37–53.

Spiess, A.-N., Deutschmann, C., Burdukiewicz, M., Himmelreich, R., Klat, K., Schierack, P., Roediger, S., 2014. Impact of Smoothing on Parameter Estimation in Quantitative DNA Amplification Experiments. Clinical Chemistry clinchem.2014.230656. doi:10.1373/clinchem.2014.230656

# Results of different smoothers. A in-silico amplification was performed
# using the AmpSim function and different smoothers were applied. Optimally
# all smoothers should give the same result (which is not the case)).
# refMFI means referenced Mean Fluorescence Intensity 
# (Roediger et al. 2013)
tmp <- AmpSim(cyc = 1:35, bl = 0)

plot(tmp, main = "In-silico real-time PCR\n Effect of Smoother", 
     xlab = "Cycles", ylab ="refMFI", ylim = c(0,1), pch = 20, 
     type = "b", lwd = 2)

legend(25, 0.8, c("Raw data", "savgol", "lowess", "mova 3", "mova 5", 
		  "smooth", "spline", "supsmu"), pch = 20, lwd = 2, 
		  col = c(1:8))

#else
tmp.smooths <- smoother(tmp, method = list("savgol",
                                           "lowess",
                                           mova = list(movaww = 3),
                                           mova = list(movaww = 5),
                                           "smooth",
                                           "spline",
                                           "supsmu"))
for (i in 1:ncol(tmp.smooths))
  lines(tmp[, 1], tmp.smooths[, i], type = "b", pch = 20, lwd = 2, col = i 
+ 1)

default.par <- par(no.readonly = TRUE)
par(fig = c(0.15,0.6,0.45,0.99), new = TRUE)
plot(tmp, main = "", xlab = "Cycles", ylab ="refMFI", 
     pch = 20, xlim = c(14,20), ylim = c(0,0.45))

for (i in 1:ncol(tmp.smooths))
  lines(tmp[, 1], tmp.smooths[, i], type = "b", pch = 20, lwd = 2, col = i 
+ 1)


# Plot the difference of the smoothed / filtered data
# to the raw data against the cycles
# The largest error is in the transition phases between
# start and end of the detectable amplification process.
par(fig = c(0,1,0,0.65))
plot(NA, NA, type = "b", col = 2, pch = 20, xlim = c(1,35), 
      ylim = c(-0.1,0.1), xlab = "Cycle", 
      ylab = "delta refMFI (raw - smoothed)", 
     main = "Smoothed / Filtered data")

legend(1.5, 0.1, ncol = 2, c("savgol", "lowess", "mova 3", "mova 5", 
	"smooth", "spline", "supsmu"), pch = 20, lwd = 2, 
	col = c(2:8))

for (i in 1:ncol(tmp.smooths))
  lines(tmp[, 1], tmp[, 2] - tmp.smooths[, i], type = "b", pch = 20, lwd = 
2, col = i + 1)

par(fig = c(0,1,0.55,1), new = TRUE)

plot(tmp, type = "b", col = 1, pch = 20, xlab = "", ylab = "RFU", 
      main = "Raw data")

#different ways of using smoother
#1. single method
single.smooth <- smoother(tmp, method = list("mova"))
#single smooth, additional argument specified
single.smooth.add <- smoother(tmp, method = list(mova = list(movaww = 3)))
#3. more than one smoothing method, no additional arguments specified
double.smooth <- smoother(tmp, method = list("savgol", "mova"))
#4. more than one smoothing method, additional arguments specified
double.smooth.add <- smoother(tmp, method = list("savgol", mova = 
list(movaww = 3)))
#5. all smoothing methods, no additional arguments specified
all.smooth <- smoother(tmp, method = list("all"))
par(default.par)