Estimate Proportion of True Null Hypotheses
Estimate the proportion of true null hypotheses from a vector of p-values.
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 |
nbins |
number of histogram bins (if |
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 |
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")
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