acde (version 1.2.0)

bcaFDR: BCa Confidence Upper Bound for the FDR

Description

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

Usage

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

Arguments

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 $(1, \ldots, 1, 2, \ldots, 2)$.

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).

Value

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.

References

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 Unpublished MS thesis.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.

See Also

stp.

Examples

## 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}.