# Searching for differentially expressed genes/probes using an approach based on the Perron-Frobenius theorem Implementation of a method based on fold change and the Perron theorem for detecting differentially expressed genes in a dataset. This function should be used with two biological conditions dataset (microarray or RNA-seq, ...). Using pairwise combinations of samples from the two biological conditions, fold changes (FC) are calculated. For each combination, the FC obtained are sorted in increasing order and corresponding rank values are associated with genes. Then, a statistic is assigned to the robust average ordered rank values for each gene/probe. ```r pfco(xdata, cont, test, log2.opt = 0, trim.opt = 0.25) ``` ## Arguments - `xdata`: A matrix or a table containing two biological conditions dataset to process for detecting differentially expressed genes. The rownames of xdata are used for the output idnames. - `cont`: A vector containing the label names of the control samples: `cont` = c("cont01", "cont02", ...). - `test`: A vector containing the label names of the test samples: `test` = c("test01", "test02", "test03", ...). - `log2.opt`: A scalar equals to 0 or 1. The value 0 (default) means that data in the matrix "xdata" are expressed in a log2 scale: `log2.opt` = 0 - `trim.opt`: A scalar between 0 and 0.5. The value 0.25 (default) means that 25% of the lower and the upper rank values of each gene are not used for computing its statistics "ri", i.e. the interquartile range rank values are averaged: `trim.opt` = 0.25 ## Details Label names appearing in the parameter "samp" should match with some label names in the columns of the data matrix "xdata". It is not necessary to use all label names appearing in the columns of the dataset matrix. ## Returns This function returns a data frame containing 9 components - **idnames**: A vector containing the list of IDs or symbols associated with genes - **ri**: The average of rank values associated with genes. These values are rank values statistics leading to f-values and p-values. - **FC**: The fold changes for genes in the dataset. These fold changes are calculated as a ratio of averages from the test and the control samples. Non log scale values are used in the calculation. - **FC2**: The robust fold changes for genes. These fold changes are calculated as a trimmed mean of the fold changes or ratios obtained from the dataset samples. Non log scale values are used in the calculation. - **f.value**: The f-values are probabilities associated with genes using the "mean" and the "standard deviation" ("sd") of the statistics "ri". The "mean" and "sd" are used as a normal distribution parameters. - **p.value**: The p-values associated with genes. These values are obtained using a one sample Student t-test on the fold change rank values. - **comp**: Singular values. - **comp.w**: Singular values weights. - **comp.wcum**: Cumulative sum of the singular values weights. ## Author(s) Doulaye Dembele doulaye@igbmc.fr ## References Dembele D, Analysis of high biological data using their rank values, Stat Methods Med Res, accepted for publication, 2018 ## Examples ```r data(fdata); rownames(fdata) <- fdata[,1]; cont <- c("cont01", "cont07", "cont03", "cont04", "cont08"); test <- c("test01", "test02", "test08", "test09", "test05"); log2.opt <- 0; trim.opt <- 0.25; # perform pfco() af <- pfco(fdata, cont, test, log2.opt, trim.opt); # now select top 20 down and/or up regulated genes top20 <- fcrosTopN(af, 20); alpha1 <- top20$alpha[1]; alpha2 <- top20$alpha[2]; id.down <- matrix(0, 1); id.up <- matrix(0, 1); n <- length(af$FC); f.value <- af$f.value; idown <- 1; iup <- 1; for (i in 1:n) { if (f.value[i] <= alpha1) { id.down[idown] <- i; idown <- idown + 1; } if (f.value[i] >= alpha2) { id.up[iup] <- i; iup <- iup + 1; } } data.down <- fdata[id.down[1:(idown-1)], ]; ndown <- nrow(data.down); data.up <- fdata[id.up[1:(iup-1)], ]; nup <- nrow(data.up); # now plot down regulated genes t <- 1:20; op = par(mfrow = c(2,1)); plot(t, data.down[1,2:21], type = "l", col = "blue", xlim = c(1,20), ylim = c(0,18), main = "Top down-regulated genes"); for (i in 2:ndown) { lines(t,data.down[i,2:21], type = "l", col = "blue") } # now plot down and up regulated genes plot(t, data.up[1,2:21], type = "l", col = "red", xlim = c(1,20), ylim = c(0,18), main = "Top up-regulated genes"); for (i in 2:nup) { lines(t, data.up[i,2:21], type = "l", col = "red") } par(op) ```

pfco.rd function