limma (version 3.28.14)

propTrueNull: Estimate Proportion of True Null Hypotheses

Description

Estimate the proportion of true null hypotheses from a vector of p-values.

Usage

propTrueNull(p, method="lfdr", nbins=20, ...)
convest(p, niter=100, plot=FALSE, report=FALSE, file="", tol=1e-6)

Arguments

p

numeric vector of p-values.

method

estimation method. Choices are "lfdr", "mean", "hist" or "convest".

nbins

number of histogram bins (if method="hist").

niter

number of iterations to be used in fitting the convex, decreasing density for the p-values.

plot

logical, should updated plots of fitted convex decreasing p-value density be produced at each iteration?

report

logical, should the estimated proportion be printed at each iteration?

file

name of file to which to write the report. Defaults to standard output.

tol

accuracy of the bisectional search for finding a new convex combination of the current iterate and the mixing density

...

other arguments are passed to convest if method="convest".

Value

Numeric value in the interval [0,1] representing the estimated proportion of true null hypotheses.

Details

The proportion of true null hypotheses in a collection of hypothesis tests is often denoted pi0. This function estimates pi0 from a vector of p-values.

method="lfdr" implements the method of Phipson (2013) based on averaging local false discovery rates across the p-values.

method="mean" is a very simple method based on averaging the p-values. It gives a slightly smaller estimate than 2*mean(p).

method="hist" implements the histogram method of Mosig et al (2001) and Nettleton et al (2006).

method="convest" calls convest, which implements the method of Langaas et al (2005) based on a convex decreasing density estimate.

References

Langaas, M, Ferkingstad, E, and Lindqvist, B (2005). Estimating the proportion of true null hypotheses, with application to DNA microarray data. Journal of the Royal Statistical Society Series B 67, 555-572. Preprint at http://www.math.ntnu.no/~mettela/pi0.imf

Mosig MO, Lipkin E, Khutoreskaya G, Tchourzyna E, Soller M, Friedmann A (2001). A whole genome scan for quantitative trait loci affecting milk protein percentage in Israeli-Holstein cattle, by means of selective milk DNA pooling in a daughter design, using an adjusted false discovery rate criterion. Genetics 157, 1683-1698.

Nettleton D, Hwang JTG, Caldo RA, Wise RP (2006). Estimating the number of true null hypotheses from a histogram of p values. Journal of Agricultural, Biological, and Environmental Statistics 11, 337-356.

Phipson, B (2013). Empirical Bayes Modelling of Expression Profiles and Their Associations. PhD Thesis, University of Melbourne, Australia. http://repository.unimelb.edu.au/10187/17614

Ritchie, ME, Phipson, B, Wu, D, Hu, Y, Law, CW, Shi, W, and Smyth, GK (2015). limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Research 43, e47. http://nar.oxfordjournals.org/content/43/7/e47

See Also

See 08.Tests for other functions for producing or interpreting p-values.

Examples

# Test statistics
z <- rnorm(200)

# First 40 are have non-zero means
z[1:40] <- z[1:40]+2

# True pi0
160/200

# Two-sided p-values
p <- 2*pnorm(-abs(z))

# Estimate pi0
propTrueNull(p, method="lfdr")
propTrueNull(p, method="hist")