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).

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.

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.

Value

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.

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

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.

Examples

Run this code

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

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