README.md
In StoreyLab/fFDR: Functional FDR for multiple hypothesis testing

fFDR: Functional False Discovery Rate

This fFDR package implements the functional false discovery rate (FDR) methodology and estimates FDR from a collection of p-values and observations from an informative variable. The informative variable may affect the likelihood of a true null hypothesis or the power of a statistical test, and the methodology models the likelihood or power as a function of the informative variable. When the informative variable does not affect the likelihood or power, it reduces to the traditional q-value based FDR methodology. The functional FDR methodology induces and employs the functional q-value. At a pre-specified threshold for the functional q-value (which is in general equivalent to a nominal FDR level), a null hypothesis is rejected if its associated functional q-value is less than or equal to the threshold.

An overview of the functional FDR methodology can be found in the preprint ``The Functional False Discovery Rate with Applications to Genomics'' authored by Xiongzhi Chen, David G. Robinson and John D. Storey and available at bioRxiv. We recommend reading the package vignette for users of the fFDR package who want a quick start.

To install, open R and type:

install.packages("devtools")
library("devtools")
devtools::install_github("StoreyLab/fFDR")

The vignette can be viewed by typing:

browseVignettes(package = "fFDR")

fqvalue: Estimate functional q-value based on p-value and an informative variable.
estimate_fpi0: Estimate the functional proportion; a tuning parameter lambda will be used for this purpose.
plot: Plot the estimated functional proportion and/or construct a scatter plot of p-values and quantiles of the informative variable

First, the built-in function simulate_t_tests generates m=2000 hypotheses, their associated p-values (as p.value) that are induced by t-tests, and (as z) quantile transformed sample sizes of the Normal observations. Note that the power of a t-test is affected by the sample size, which in this setting is an informative variable.

library(fFDR)
ttests_example <- simulate_t_tests(m = 2000)
p.value <- ttests_example$p.value
z <- ttests_example$n

Once p-values and observations from an informative are available, fqvalue implements the functional FDR methodology, and creates a fqvalue object fq.

fq <- fqvalue(p.value, z)

The functional q-value associated with each hypothesis testing can be extract by:

fqvalues <- fq$table$fq.value

With the individual functional q-values, at FDR level 0.05, null hypotheses that are rejected and the number of rejections can be found by:

fqvalues <- fq$table$fq.value
which(fqvalues < .05)
sum(fqvalues < .05)

The fqvalue object fq can be visualized via 2 panels in a vertical layout: the top panel is a scatter plot of p-values against quantiles of the informative variable; the bottom shows the estimated functional proportion for different values of the tuning parameter lambda, for which the solid curve is the estimated corresponding to the optimal choice of lambda.