# lfdr: Estimate local False Discovery Rate (FDR) In qvalue: Q-value estimation for false discovery rate control

## Description

Estimate the local FDR values from p-values.

## Usage

 1 2 lfdr(p, pi0 = NULL, trunc = TRUE, monotone = TRUE, transf = c("probit", "logit"), adj = 1.5, eps = 10^-8, ...)

## Arguments

 p A vector of p-values (only necessary input). pi0 Estimated proportion of true null p-values. If NULL, then pi0est is called. trunc If TRUE, local FDR values >1 are set to 1. Default is TRUE. monotone If TRUE, local FDR values are non-decreasing with increasing p-values. Default is TRUE; this is recommended. transf Either a "probit" or "logit" transformation is applied to the p-values so that a local FDR estimate can be formed that does not involve edge effects of the [0,1] interval in which the p-values lie. adj Numeric value that is applied as a multiple of the smoothing bandwidth used in the density estimation. Default is adj=1.0. eps Numeric value that is threshold for the tails of the empirical p-value distribution. Default is 10^-8. ... Additional arguments, passed to pi0est.

## Details

It is assumed that null p-values follow a Uniform(0,1) distribution. The estimated proportion of true null hypotheses pi_0 is either a user-provided value or the value calculated via pi0est. This function works by forming an estimate of the marginal density of the observed p-values, say f(p). Then the local FDR is estimated as lFDR(p) = pi_0/f(p), with adjustments for monotonicity and to guarantee that lFDR(p) <= 1. See the Storey (2011) reference below for a concise mathematical definition of local FDR.

## Value

A vector of estimated local FDR values, with each entry corresponding to the entries of the input p-value vector p.

John D. Storey

## References

Efron B, Tibshirani R, Storey JD, and Tisher V. (2001) Empirical Bayes analysis of a microarray experiment. Journal of the American Statistical Association, 96: 1151-1160.
http://www.tandfonline.com/doi/abs/10.1198/016214501753382129

Storey JD. (2003) The positive false discovery rate: A Bayesian interpretation and the q-value. Annals of Statistics, 31: 2013-2035.
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aos/1074290335

Storey JD. (2011) False discovery rates. In International Encyclopedia of Statistical Science.
http://genomine.org/papers/Storey_FDR_2011.pdf
http://www.springer.com/statistics/book/978-3-642-04897-5