# 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

`qvalue`, `pi0est`, `hist.qvalue`
 ```1 2 3 4 5 6 7 8``` ```# import data data(hedenfalk) p <- hedenfalk\$p lfdrVals <- lfdr(p) # plot local FDR values qobj = qvalue(p) hist(qobj) ```