concaveFDR: Estimate (Local) False Discovery Rates For Diverse Test...

In b-klaus/concaveFDR: Estimation of false discovery rates via log-concave densities

Description

concaveFDR takes a vector of z-scores (or of correlations, p-values, or t-statistics), and estimates for each case both the tail area-based Fdr as well as the density-based fdr (=q-value resp. local false discovery rate). The parameters of the null distribution are estimated adaptively from the data (except for the case of p-values where this is not necessary).

Usage

concaveFDR(x, statistic = c("normal", "correlation", "pvalue"), plot = TRUE,
  color.figure = TRUE, verbose = TRUE, theo = FALSE, scale_param = NULL,
  alternative = c("grenander", "log-concave"), cutoff.method = c("fndr",
  "pct0", "locfdr", "smoothing"), pct0 = 0.75)

Arguments

x	vector of the observed test statistics.
statistic	one of "normal" (default), "correlation", "pvalue". This species the null model.
plot	plot a figure with estimated densities, distribution functions, and (local) false discovery rates.
color.figure	determines whether a color figure or a black and white figure is produced (defaults to "TRUE", i.e. to color figure).
verbose	print out status messages.
theo	Should the theoretical null model be used? In this case no null model scale parameters (e.g. sigma for z-scores) are estimated. Note that the df and the kappa parameters for t-statistics and the correlation statistics have to be set manually as they depeden on the original sample sizes.
scale_param	scale parameter used when calculating the statistics, only needs to be specified if theo is set to TRUE and the statistics are t-scores or correlations. See dcor0 for details on how to set this for correlations. For t-statistics, this depedends on the type of t-test performed.
alternative	The estimation algorithm used for estimation of the alternative densitiy. "Grenander" corresponds to the method implemented in fdrtool, while "log-concave" is new method introduced in the package
cutoff.method	one of "fndr" (default), "pct0", "locfdr".
pct0	fraction of data used for fitting null model - only if cutoff.method="pct0"

Details

The algorithm implemented in this function proceeds as follows:

1. A suitable cutoff point is determined. If cutoff.method is "fndr" then first an approximate null model is fitted and subsequently a cutoff point is sought with false nondiscovery rate as small as possible (see fndr.cutoff). If cutoff.method is "pct0" then a specified quantile (default value: 0.75) of the data is used as the cutoff point. If cutoff.method equals "locfdr" then the heuristic of the "locfdr" package (version 1.1-6) is employed to find the cutoff (z-scores and correlations only). If cutoff.method is "smoothing" the a smoothed b-spline is fitted to the eta0 estimates at various cutoff points and flat regions are found by inspecting local minima of the smoothed b-spline curve.

2. The parameters of the null model are estimated from the data using censored.fit. This results in estimates for scale parameters und and proportion of null values (eta0). Not that choosing theo = TRUE will results in using the theoretical null model without a scale parameter.

3. Subsequently the corresponding p-values are computed, and a modified grenander or log-concave density estimation algorithm is employed to obtain the overall density and distribution function (note that this respects the estimated eta0). The choice of the density estimation algorithm can be made by using the alternative argument.

4. Finally, q-values and local fdr values are computed for each case.

The assumed null models all have (except for p-values) one free scale parameter. Note that the z-scores and the correlations are assumed to have zero mean.

Value

A list with the following components:

pval	a vector with p-values for each case.
qval	a vector with q-values (Fdr) for each case..
lfdr	a vector with local fdr values for each case.
statistic	the specified type of null model.
param	a vector containing the estimated parameters (the null proportion eta0 and the free parameter of the null model).

Author(s)

Bernd Klaus, Korbinian Strimmer (http://strimmerlab.org).

References

Strimmer, K. (2008a). A unified approach to false discovery rate estimation. BMC Bioinformatics 9: 303. Available from http://www.biomedcentral.com/1471-2105/9/303/.

Strimmer, K. (2008b). fdrtool: a versatile R package for estimating local and tail area- based false discovery rates. Bioinformatics 24: 1461-1462. Available from http://bioinformatics.oxfordjournals.org/cgi/content/abstract/24/12/1461.

See Also

pval.estimate.eta0, censored.fit.

Examples

# load "fdrtool" library and p-values
library("fdrtool")
data(pvalues)


# estimate fdr and Fdr from p-values

data(pvalues)
fdr <- concaveFDR(pvalues, statistic="pvalue")
fdr$qval.log # estimated Fdr values using log-concave density estimation
fdr$qval.gr # estimated local fdr using Grenander density estimation

# the same but with black and white figure
fdr <- concaveFDR(pvalues, statistic="pvalue", color.figure=FALSE)


# estimate fdr and Fdr from z-scores

sd.true = 2.232
n = 500
z = rnorm(n, sd=sd.true)
z = c(z, runif(30, 5, 10)) # add some contamination
fdr =  concaveFDR(z)

# you may change some parameters of the underlying functions
fdr =  concaveFDR(z, cutoff.method="pct0", pct0=0.9)

b-klaus/concaveFDR documentation built on May 11, 2019, 5:20 p.m.