propTrueNull: Estimate Proportion of True Null Hypotheses
In hdeberg/limma: Linear Models for Microarray Data

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2	propTrueNull(p, method="lfdr", nbins=20, ...) convest(p, niter=100, plot=FALSE, report=FALSE, file="", tol=1e-6)

`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"`.

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.

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

Belinda Phipson and Gordon Smyth for propTrueNull. Egil Ferkingstad, Mette Langaas and Marcus Davy for convest.

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.

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

# 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")