metaRNASeq (version 0.4)

invnorm: P-value combination using the inverse normal method

Description

Combines one sided p-values using the inverse normal method.

Usage

invnorm(indpval, nrep, BHth = 0.05)

Arguments

indpval

List of vectors of one sided p-values to be combined.

nrep

Vector of numbers of replicates used in each study to calculate the previous one-sided p-values.

BHth

Benjamini Hochberg threshold. By default, the False Discovery Rate is controlled at 5%.

Value

• DEindices
  Indices of differentially expressed genes at the chosen Benjamini Hochberg threshold.
• TestStatistic
  Vector with test statistics for differential expression in the meta-analysis.
• rawpval
  Vector with raw p-values for differential expression in the meta-analysis.
• adjpval
  Vector with adjusted p-values for differential expression in the meta-analysis.

Details

For each gene g, let $$N_g = \sum_{s=1}^S \omega_s \Phi^{-1}(1-p_{gs}),$$ where $p_{gs}$ corresponds to the raw p-value obtained for gene g in a differential analysis for study s (assumed to be uniformly distributed under the null hypothesis), $\Phi$ the cumulative distribution function of the standard normal distribution, and $\omega_s$ a set of weights. We define the weights $\omega_s$ as in Marot and Mayer (2009): $$\omega_s = \sqrt{\frac{\sum_c R_{cs}}{\sum_\ell \sum_c R_{c\ell}}},$$ where $\sum_c R_{cs}$ is the total number of biological replicates in study s. This allows studies with large numbers of biological replicates to be attributed a larger weight than smaller studies. Under the null hypothesis, the test statistic $N_g$ follows a N(0,1) distribution. A unilateral test on the righthand tail of the distribution may then be performed, and classical procedures for the correction of multiple testing, such as that of Benjamini and Hochberg (1995), may subsequently be applied to the obtained p-values to control the false discovery rate at a desired level $\alpha$.

References

Y. Benjamini and Y. Hochberg (1995). Controlling the false discovery rate: a pratical and powerful approach to multiple testing. JRSS B (57): 289-300. Hedges, L. and Olkin, I. (1985). Statistical Methods for Meta-Analysis. Academic Press. Marot, G. and Mayer, C.-D. (2009). Sequential analysis for microarray data based on sensitivity and meta-analysis. SAGMB 8(1): 1-33. A. Rau, G. Marot and F. Jaffrezic (2012). Differential meta-analysis of RNA-seq data. (Manuscript in progress)

See Also

metaRNASeq

Examples

data(rawpval)
## 8 replicates simulated in each study
invnormcomb <- invnorm(rawpval,nrep=c(8,8), BHth = 0.05)       
DE <- ifelse(invnormcomb$adjpval<=0.05,1,0)
hist(invnormcomb$rawpval,nclass=100)

## A more detailed example is given in the vignette of the package:
## vignette("metaRNASeq")