cycle (version 1.26.0)

fdrfourier: Calculation of the false discovery rates (FDR) for periodic expression

Description

The function calculates the empirical FDR based on derived Fourier scores derived by fourierscore for the observed expression and the comparison with scores derived for different background model generated by backgroundData.

Usage

fdrfourier(eset,T,times,background.model="rr",N=100,progress=FALSE)

Arguments

eset

object of the class “ExpressionSet”

T

cycle period

times

time of measurements

background.model

model for generation of background data: “rr”- permutation within rows, “gauss”- Gaussian background, “ar1”- AR1 models

N

number of generated data sets for the background distribution

progress

if set to TRUE, a progress of calculations is reported

Value

fdr), and Fourier scores for ExpressionSet object (F) and the background data (F.b).

Details

To assess the significance of the Fourier score obtained for the original gene expression time series, the probability has to be calculated of how often such a score would be observed by chance based on the chosen background distribution. The statistical significance is given by the calculated false discovery rate. It is defined here as the expected proportion of false positives among all genes detected as periodically expressed. Mathematical details can be found in the given reference.

References

Matthias E. Futschik and Hanspeter Herzel (2008) Are we overestimating the number of cell-cycling genes? The impact of background models on time series analysis, Bioinformatics, 24(8):1063-1069

Examples

if (interactive()){

set.seed(1)
data(yeast) # loading the reduced CDC28 yeast set (from the Mfuzz package)

# Data preprocessing 
yeast <- filter.NA(yeast) # filters genes with more than 25% of the expression values missing 
yeast  <- fill.NA(yeast) # for illustration only; rather use knn method for 
yeast <- standardise(yeast)
# 
T.yeast <- 85   # cell cycle period (t=85min)
times.yeast <-  pData(yeast)$time  # time of measurements
#
yeast.test <- yeast[1:600,] # To speed up the example
#

NN <- 50 # number of generated background models
         # Here, a small number was chosen for demonstration purpose.
	 # For the actual analysis, rather set N = 1000 
 
# Calculation of FDRs
# i) based on random permutation as background model
fdr.rr <- fdrfourier(eset=yeast.test,T=T.yeast,
                    times=times.yeast,background.model="rr",N=NN,progress=TRUE)
# ii) based on Gaussian distribution 
fdr.g <- fdrfourier(eset=yeast.test,T=T.yeast,
                   times=times.yeast,background.model="gauss",N=NN,progress=TRUE)
# iii) based on AR(1) models as background
fdr.ar1 <- fdrfourier(eset=yeast.test,T=T.yeast,
                     times=times.yeast,background.model="ar1",N=NN,progress=TRUE)


# Number of significant genes based on diff. background models
sum(fdr.rr$fdr < 0.1) 
sum(fdr.g$fdr < 0.1)
sum(fdr.ar1$fdr < 0.1)

# Plot top scoring gene
plot(times.yeast,exprs(yeast.test)[order(fdr.ar1$fdr)[1],],type="o",
     xlab="Time",ylab="Expression",
     main=paste(featureNames(yeast.test)[order(fdr.ar1$fdr)[1]],"-- FDR:",
       fdr.ar1$fdr[order(fdr.ar1$fdr)[1]]))

# List significant genes
fdr.ar1$fdr[which(fdr.ar1$fdr < 0.1)]
}