EstimatorsFDR: Estimators of Local False Discovery Rate (LFDR)
In CorrectedFDR: Correcting False Discovery Rates

Description Usage Arguments Details Value Author(s) References Examples

EstimatorsFDR is an R function that computes the Nonlocal False Discovery Rate (NFDR) and the estimators of local false discovery rate: Corrected False discovery Rate (CFDR) and Re-ranked False Discovery rate (RFDR).

1	EstimatorsFDR(pvalue)

pvalue

Input numeric vector of pvalues.

The input is a list of pvalues. The pvalues can be obtained for example by performing Student's t-test between two datasets. The two groups can be data from healthy and disease states. Let i=1, 2, ..., N, where i represents the ith feature (SNP or gene, for example). Then, for each i, the hypothesis indicator A_i can have two possible values.
A_i=0, if the ith null hypothesis is true, or
A_i=1, if the ith null hypothesis is not true,
where the null hypothesis is defined by: the ith feature is unaffected by a treatment, unassociated with a disease, etc. The values for each estimator (NFDR, CFDR, RFDR) indicate the probability that the null hypothesis of the ith feature is true (A_i=0) given the statistics T_i. The alternative hypothesis is true if A_i=1. For example, in gene expression data analysis, if the null hypothesis is true, this would mean that the genes are not differentially expressed.

The output returns three lists. It returns the NFDR, CFDR, and RFDR estimators:

NFDR	nonlocal FDR
CFDR	corrected FDR
RFDR	re-ranked FDR

Code: Abbas Rahal.
Documentation: Anna Akpawu, Justin Chitpin and Abbas Rahal.
Maintainer: Abbas Rahal <Abbas.Rahal13@gmail.com>

Bickel, D.R., Rahal, A. (2019). Correcting false discovery rates for their bias toward false positives. Communications in Statistics - Simulation and Computation, https://tinyurl.com/kkdc9rk8.

Bickel, D. R. (2015). Corrigendum to: Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions. Statistical Applications in Genetics and Molecular Biology, 2015, 14, 225.

Bickel, D. R. (2013). Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions. Statistical Applications in Genetics and Molecular Biology, 2013, 12, 529-543.

#The examples below are from the "ProData" package.
#In order to use the "Prodata" input you would first need to install the ProData package.
#You will also need the function exprs in this package.
#First, make sure that the ProData package is properly installed:
#source("https://bioconductor.org/biocLite.R")
#biocLite("ProData")
#library(ProData)
#data("f45cbmk")
#q1<- quantile(as(exprs(f45cbmk[, pData(f45cbmk)$GROUP == "B"]), "numeric"), probs = 0.25)
#logish<- function(x){log(x + q1)}
#Vectors of proteins for 20 patients ER/PR-positive and Healthy
#Y<- logish(exprs(f45cbmk[, pData(f45cbmk)$GROUP == "B"])) # Control (Healthy)
#X.ER<- logish(exprs(f45cbmk[, pData(f45cbmk)$GROUP == "C"])) # Case ER/PR-positive
#pvalue<- NULL
#for (i in 1:nrow(X.ER))
#{
# t<-t.test(x=X.ER[i,], y=Y[i,], alternative = "two.sided")
# pvalue[i]<- t$p.value
#}

#The pvalues obtained from the t-test:
pvalue<- c(0.1981, 0.3794, 0.000001443, 0.02325, 0.03264, 0.07263, 0.02965, 0.8016, 0.8888,
          0.9133, 0.2971, 0.4573, 0.2815, 0.0007119, 0.5743, 0.927, 0.369, 0.8478, 0.38, 0.9904)
output<- EstimatorsFDR(pvalue)
#Three lists
output$NFDR
output$CFDR
output$RFDR