LBE: Estimation of the false discovery rate.

In LBE: Estimation of the false discovery rate.

Description

LBE is an efficient procedure for estimating the proportion of true null hypotheses, the false discovery rate and the q-values.

Usage

LBE(pval, a = NA, l = 0.05, ci.level = 0.95, qvalues = TRUE, plot.type = "main", FDR.level = 0.05, n.significant = NA)

Arguments

pval	Numerical vector of p-values (only necessary input).
a	Real value used in [-ln (1-pi)]^a (see details). If a == NA (default), then the value of a is automatically calculated as the greatest value such that the upper bound of the asymptotic standard deviation of the estimator of pi0 is smaller than the threshold l. If a >= 1, the value of a is used in [-ln (1-pi)]^a (see details). If a < 1, the identity function is used for transforming the p-values.
l	Threshold for the upper bound of the asymptotic standard deviation (only used if a == NA).
ci.level	Level for the confidence interval of pi0.
qvalues	Logical value for estimating the qvalues and the FDR. If qvalues = FALSE, only the proportion pi0 of true null hypotheses is estimated.
plot.type	If plot.type = "none", no graphic is displayed. If plot.type = "main", the estimated q-values versus the p-values are plotted together with the histogram of the p-values. If plot.type = "multiple", several graphics are displayed: 1. The histogram of the p-values 2. The estimated q-values versus the p-values 3. The number of significant tests versus each qvalue cutoff 4. The number of expected false positives versus the number of significant tests.
FDR.level	Level at which to control the FDR (only used if n.significant == NA).
n.significant	If specified, the FDR is estimated for the rejection region defined by the "n.significant" smallest p-values.

Details

The procedure LBE is based on the expectation of a particular transformation of the p-values leading to a straightforward estimation of the key quantity pi0 that is the proportion of true null hypotheses:

pi0(a)=\{(1/m)*∑_{i=1}^m[-\ln(1-pi)]^a\}/Γ(a+1), where a belongs to the interval [1;inf).

Value

A list containing:

call	Function call.
FDR	Level at which to control the FDR (if n.significant == NA) or estimated FDR (if n.significant != NA).
pi0	Estimated value of pi0, the proportion of true null hypotheses.
pi0.ci	Confidence interval for pi0.
ci.level	Level for the confidence interval of pi0.
a	Value used in [-\ln (1-pi)]^a (see details).
l	Upper bound of the asymptotic standard deviation for pi0.
qvalues	Vector of the estimated q-values.
pvalues	Vector of the original p-values.
significant	Indicator of wether the null hypothesis is rejected.
n.significant	Number of rejected null hypotheses.

Note

LBE is an alternative method to the one proposed by Storey and Tibshirani (2003) for estimating the q-values, this latter method being implemented in the package qvalue.

Author(s)

Cyril Dalmasso

References

Dalmasso C, Broet P, Moreau T (2005). A simple procedure for estimating the false discovery rate. Bioinformatics. Bioinformatics, 21: 660 - 668.

Storey JD and Tibshirani R. (2003). Statistical significance for genome-wide studies. Proc Natl Acad Sci, 100, 9440-9445.

See Also

LBEplot, LBEsummary, LBEwrite, LBEa

Examples

## start
data(hedenfalk.pval)
res=LBE(hedenfalk.pval)
data(golub.pval)
res=LBE(golub.pval)
## end

LBE documentation built on Nov. 8, 2020, 5:58 p.m.