propTrueNull {limma} | R Documentation

## 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"`.

### 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.

### Value

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

### Author(s)

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

### 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.

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")

[Package limma version 3.42.2 Index]