# Estimate LPC False Discovery Rates. An estimated false discovery rate for each gene is computed, based on the LPC scores. Estimated false discovery rates based on T scores (Cox, regression coefficient, or two-sample t-statistic) are also given. ```r EstimateLPCFDR(x, y, type, nreps=100,soft.thresh=NULL, censoring.status=NULL) ``` ## Arguments - `x`: The matrix of gene expression values; pxn where n is the number of observations and p is the number of genes. - `y`: A vector of length n, with an outcome for each observation. For two-class outcome, y's elements are 1 or 2. For quantitative outcome, y's elements are real-valued. For survival data, y indicates the survival time. For multiclass, y is coded as 1,2,3,... - `type`: One of "regression" (for a quantitative outcome), "two class", "multiclass", or "survival". - `nreps`: The number of training/test set splits used to estimate LPC's false discovery rates. Default is 100. - `soft.thresh`: The value of the soft threshold to be used in the L1 regression of the scores onto the eigenarrays. This can be the value of the soft-threshold chosen adaptively by LPC function when it is run on the data; if not entered by the user, then that adaptive value is computed. - `censoring.status`: For survival outcome only, a vector of length n which takes on values 0 or 1 depending on whether the observation is complete or censored. ## Details Details of false discovery rate estimation for LPC can be found in the paper: http://www-stat.stanford.edu/~dwitten \ As explained in the paper, FDR of LPC is estimated by computing the FDR of simpler scores (Cox for survival outcome, standardized regression coefficients for regression outcome, and two-sample t-statistic for two-class outcome) and then estimating the difference between the FDR of LPC and the FDR of these simpler scores. ## Returns - **fdrlpc**: A vector of length p (equal to the number of genes), with the LPC false discovery rate for each gene. - **fdrt**: A vector of length p (equal to the number of genes), with the T false discovery rate for each gene. - **fdrdiff**: The FDR of T minus the FDR of LPC. This is approximately equal to fdrt-fdrlpc, with the caveat that the FDR of LPC (computed via this difference) must be between 0 and 1. - **pi0**: The fraction of genes that are believed to be null. - **soft.thresh**: The value of the soft threshold used in the L1 constraint for LPC. - **call**: The function call made. ## References Witten, D.M. and Tibshirani, R. (2008) Testing significance of features by lassoed principal components. Annals of Applied Statistics. http://www-stat.stanford.edu/~dwitten ## Author(s) Daniela M. Witten and Robert Tibshirani ## Examples ```r ### Uncomment to run.... #set.seed(2) #n <- 40 # 40 samples #p <- 1000 # 1000 genes #x <- matrix(rnorm(n*p), nrow=p) # make 40x1000 gene expression matrix #y <- rnorm(n) # quantitative outcome ## make first 50 genes differentially-expressed #x[1:25,y<(-.5)] <- x[1:25,y<(-.5)]+ 1.5 #x[26:50,y<0] <- x[26:50,y<0] - 1.5 ## compute LPC and T scores for each gene #lpc.obj <- LPC(x,y, type="regression") ## Look at plot of Predictive Advantage #pred.adv <- #PredictiveAdvantage(x,y,type="regression",soft.thresh=lpc.obj$soft.thresh) ## Estimate FDRs for LPC and T scores #fdr.lpc.out <- #EstimateLPCFDR(x,y,type="regression",soft.thresh=lpc.obj$soft.thresh,nreps=50) ## Estimate FDRs for T scores only. This is quicker than computing FDRs ## for LPC scores, and should be used when only T FDRs are needed. If we ## started with the same random seed, then EstimateTFDR and EstimateLPCFDR ## would give same T FDRs. #fdr.t.out <- EstimateTFDR(x,y, type="regression") ## print out results of main function #lpc.obj ## print out info about T FDRs #fdr.t.out ## print out info about LPC FDRs #fdr.lpc.out ## Compare FDRs for T and LPC on 6% of genes. In this example, LPC has ## lower FDR. #PlotFDRs(fdr.lpc.out,frac=.06) ## Print out names of 20 genes with highest LPC scores, along with their ## LPC and T scores. #PrintGeneList(lpc.obj,numGenes=20) ## Print out names of 20 genes with highest LPC scores, along with their ## LPC and T scores and their FDRs for LPC and T. #PrintGeneList(lpc.obj,numGenes=20,lpcfdr.out=fdr.lpc.out) # Now, repeating everything that we did before, but using a # **survival** outcome # NOT RUNNING DUE TO TIME CONSTRAINTS -- UNCOMMENT TO RUN #set.seed(2) #n <- 40 # 40 samples #p <- 1000 # 1000 genes #x <- matrix(rnorm(n*p), nrow=p) # make 40x1000 gene expression matrix #y <- rnorm(n) + 10 # survival times; must be positive ## censoring outcome: 0 or 1 #cens <- rep(1,40) # Assume all observations are complete ## make first 50 genes differentially-expressed #x[1:25,y<9.5] <- x[1:25,y<9.5]+ 1.5 #x[26:50,y<10] <- x[26:50,y<10] - 1.5 #lpc.obj <- LPC(x,y, type="survival", censoring.status=cens) ## Look at plot of Predictive Advantage #pred.adv <- PredictiveAdvantage(x,y,type="survival",soft.thresh=lpc.obj$soft.thresh, #censoring.status=cens) ## Estimate FDRs for LPC scores and T scores #fdr.lpc.out <- EstimateLPCFDR(x,y,type="survival", #soft.thresh=lpc.obj$soft.thresh,nreps=20,censoring.status=cens) ## Estimate FDRs for T scores only. This is quicker than computing FDRs ## for LPC scores, and should be used when only T FDRs are needed. If we ## started with the same random seed, then EstimateTFDR and EstimateLPCFDR ## would give same T FDRs. #fdr.t.out <- EstimateTFDR(x,y, type="survival", censoring.status=cens) ## print out results of main function #lpc.obj ## print out info about T FDRs #fdr.t.out ## print out info about LPC FDRs #fdr.lpc.out ## Compare FDRs for T and LPC scores on 10% of genes. #PlotFDRs(fdr.lpc.out,frac=.1) ## Print out names of 20 genes with highest LPC scores, along with their ## LPC and T scores. #PrintGeneList(lpc.obj,numGenes=20) ## Print out names of 20 genes with highest LPC scores, along with their ## LPC and T scores and their FDRs for LPC and T. #PrintGeneList(lpc.obj,numGenes=20,lpcfdr.out=fdr.lpc.out) ```

EstimateLPCFDR function