multipleTestingCorrections: Multiple corrections for multiple testing
In jvanheld/stats4bioinfo: Utilities for the book "Statistics for bioinformatics"

Description Usage Arguments Details Value Author(s) References Examples

Apply various multiple testing corrections on a list of P-values, report all of them in a table with one row per test and one column per correction, and optionally draw illutrative figures.

In particular, we apply the elegant strategy from Storey & Tibshirani (2003) to estimate the respective proportions of true and alternative hypotheses among the tests.

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multipleTestingCorrections(p.values, feature.names = NULL, lambda = 0.5,
  alpha = 0.05, main = "Multitesting corrections", run.qvalue = FALSE,
  plots = FALSE)

`p.values`	list of p-values
`feature.names=NULL`	Names associated to the p.value list (will be used as row.names for to result table)
`lambda=0.5`	lambda parameter for estimating pi0 = m0/m
`alpha=0.05`	Threshold of significance (alpha).
`main='Multitesting`	corrections' Prefix for the main title of the plots
`run.qvalue=FALSE`	For the sake of comparison, compute FDR and generate graphs using Storey's qvalue library (http://genomics.princeton.edu/storeylab/qvalue/).
`plots=FALSE`	If true, generate illutrsative plots
`plot.pch=c(p.value=2,`	fdr=4, qval.0=3, e.value=1, fwer=20) point type (character) associated to each statistics for the plot
`plot.col=c(p.value='black',`	fdr='blue', qval.0='darkviolet', e.value='darkbrown', fwer='orange') color for the plot
`plot.elements=c("p.value",`	"fdr", "qval.0","e.value", "fwer") Elements to draw on the plots (can be any subet of the default list).

First version: 2012-02-10 Last modification: 2015-02

A list comprizing the following elements:

`lambda`	Value provided for the input parameter lambda.
`alpha`	Value provided for the input parameter threshold (alpha).
`m`	total number of tests (= number of elements in the input list of p-values). m = m0 + m1.
`m0.est`	Estimation of the number of cases under null hypothesis.
`m1.est`	Estimation of the number of cases that do not comply with the null hypothesis (m1.est = m - m0.est).
`pi0`	Estimated proportion of trully null cases among all tests. pi0 = m0.est / m.
`nb.signif`	Number of tests declared significant above the specified alpha threshold
`multitest.table`	A table with one row per test, and one column per statistics (the fields described below).
`p.value`	P-value = probability to observe an at least as significant result under the null hypothesis. This column contains a replica of the input vector of p-values.
`rank`	rank by increasing P-value
`e.value`	E-value = expected number of false positives
`fdr`	False Discovery Rate = expected proportion of truly null hypotheses among the cases declared positives. The FDR is estimated using Storey and Tibshirani procedure.
`fwer`	Family-Wise Error Rate = probability to observe at least one FP among all the tests, assuming all of them are under null hypothesis.
`qval.0`	FDR assuming that all the tests are under null hypothesis (Benjamini-Hochberg approach).

Jacques van Helden (Jacques.van-Helden@univ-amu.fr)

1. Benjamini, Y. and Hochberg, Y. (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. JOURNAL-ROYAL STATISTICAL SOCIETY SERIES B. 2. Storey, J.D. and Tibshirani, R. (2003) Statistical significance for genomewide studies. Proc Natl Acad Sci USA, 100, 9440–9445.

## Generate a vector of 10,000 fake p-values
## with a given proportion of trully null (m0=9,000) and
## non-null (m1=1,000) cases.
my.p.values <- c(runif(n=9000, min=0, max=1),
                 runif(n=1000, min=0, max=1e-2))

multitest.result <- multipleTestingCorrections(my.p.values)
attributes(multitest.result)

## In principle, m0 should be ~9,000
print(paste("m0.est =", multitest.result$m0.est))

## In principle, m1 should be ~1,000
print(paste("m1.est =", multitest.result$m1.est))

## In principle, pi0 should be ~0.9
print(paste("pi0 =", multitest.result$pi0))

## Plot P-value distributions
mulitpleTestingCorrections.plotPvalDistrib(multitest.result)

## Compare the different multiple testing corrections (Y axis)
## versus the nominal p-value (X axis).
mulitpleTestingCorrections.plotCorrectedVsPval(multitest.result)

## Plot the number of significant features for different
## multiple testing corrections
mulitpleTestingCorrections.plotSignifFeatures(multitest.result)