bcaFDR: BCa Confidence Upper Bound for the FDR
In acde: Artificial Components Detection of Differentially Expressed Genes

Description Usage Arguments Value Author(s) References See Also Examples

For internal use in function stp. Computes a BCa confidence upper bound for the FDR following Algorithm 2 in the vignette.

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bcaFDR(Z, design, th = NULL, B = 100, 
    lambda = 0.5, PER = FALSE, R = 1000, 
    gamma = 0.95, Q = NULL, ...)

`Z`	a matrix or data.frame representing genes' expression levels. The rows of Z correspond to the genes in the experiment, and the columns correspond to the replicates. Treatment replicates are to the left, control replicates to the right.
`design`	a vector of length equal to the number of columns in `Z` with 1's for the treatment replicates and 2's for the control replicates (1, …, 1, 2, …, 2).
`th`	Threshold values for estimating the FDR. If `NULL`, the values from `abs(ac2(Z,design))` are used.
`B`	Number of bootstrap or permutation replications for estimating the FDR at each iteration (as passed from `stp`).
`lambda`	Parameter for the estimation of pi0 and the FDR as passed from `stp` (see Storey, 2002).
`R`	Number of bootstrap replications for the computation of the FDR's BCa confidence upper bound (as passed from `stp`).
`gamma`	Confidence level for the FDR's BCa upper confidence bound (as passed from `stp`).
`PER`	If `FALSE` (default), bootstrap replications are used to estimate the FDR. If `TRUE`, permutation replications are used instead (as passed from `stp`).
`Q`	Estimated FDR as returned in object `\$Q` from `fdr` function (passed from call to `stp`). For internal use.
`...`	additional arguments for parallel computation in `boot` function as passed from `stp` (see `stp` help page for details).

`cbound`	BCa upper confidence bound for the FDR for each threshold value in `th`.
`warnings`	warning messages generated from use of `boot.ci` function from package `boot`.

Juan Pablo Acosta (jpacostar@unal.edu.co).

Acosta, J. P. (2015) Strategy for Multivariate Identification of Differentially Expressed Genes in Microarray Data. Unpublished MS thesis. Universidad Nacional de Colombia, Bogot\'a.

Storey, J. D. (2002) A direct approach to false discovery rates. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(3): 479–498.

Efron B. and Tibshirani R. J. (1994) An Introduction to the Bootstrap. Chapman & Hall/CRC, 1993.

stp.

## Single time point analysis for 50 genes with 10 treatment 
## replicates and 10 control replicates
n <- 50; p <- 20; p1 <- 10
des <- c(rep(1, p1), rep(2, (p-p1)))
mu <- as.matrix(rexp(n, rate=1))
Z <- t(apply(mu, 1, function(mui) rnorm(p, mean=mui, sd=1)))
### 5 up regulated genes
Z[1:5,1:p1] <- Z[1:5,1:p1] + 5
### 10 down regulated genes
Z[6:15,(p1+1):p] <- Z[6:15,(p1+1):p] + 5

resFdr <- fdr(Z, des)
bca <- bcaFDR(Z, des, Q=resFdr$Q, B=50, R=500)
plot(resFdr$th, resFdr$Q, type="l", col="blue")
lines(resFdr$th, bca$cbound, col="green")
legend(x="topright", legend=c("FDR", "BCa upper bound"), 
    lty=c(1,1), col=c("blue", "green"))
## Note: Discontinuities in the BCa upper bound are due to warnings
## generated during computations with function \code{boot.ci} 
## from package \code{boot}.