ssa (version 1.0.0)

fsdr: False simultaneous discovery rate control

Description

Given two sequences of paired test statistics, returns the optimal rectangular rejection that identifies the largest number of simultaneous signals while controlling the false discovery rate.

Usage

fsdr(T1, T2, alpha, m1 = 10000, m2 = 10000, p1 = TRUE, p2 = TRUE,
  jitter = NULL)

Arguments

T1, T2

paired vectors of test statistics, both must be the same length; can be p-values or otherwise; must contain only positive values

alpha

desired false simultaneous discovery rate

m1, m2

search only up the m1th (m2th) most significant test statistic in T1 (T2)

p1, p2

TRUE if T1 (T2) is a vector of p-values

jitter

NULL if no jittering is desired to resolve ties, otherwise a jitter of runif(0,jitter) will be added to all entries of T1 and T2

Value

• two-component vector; the first component is the optimal threshold for T1 and the second is for T2

Examples

## generate paired test statistics
p <- 10^6; ## total number of pairs
X <- c(rep(0,p-30),rep(1,10),rep(2,10),rep(3,10));
## X=0: no signal in either sequence of tests
## X=1: signal in sequence 1 only
## X=2: signal in sequence 2 only
## X=3: simultaneous signal
set.seed(1);
Z1 <- rnorm(p,0,1); Z1[X==1|X==3] <- rnorm(20,3,1);
Z2 <- rnorm(p,0,1); Z2[X==2|X==3] <- rnorm(20,4,1);
## convert to p-value
P1 <- 2*pnorm(-abs(Z1));
P2 <- 2*pnorm(-abs(Z2));
## run different version of fsdr()
out.pp <- fsdr(P1,P2,alpha=0.05);
out.zp <- fsdr(abs(Z1),P2,p1=FALSE,alpha=0.05);
out.pz <- fsdr(P1,abs(Z2),p2=FALSE,alpha=0.05);
out.zz <- fsdr(abs(Z1),abs(Z2),p1=FALSE,p2=FALSE,alpha=0.05);
## discovered simultaneous features
R1 <- which(P1<=out.pp[1]&P2<=out.pp[2]);
R2 <- which(abs(Z1)>=out.zp[1]&P2<=out.zp[2]);
R3 <- which(P1<=out.pz[1]&abs(Z2)>=out.pz[2]);
R4 <- which(abs(Z1)>=out.zz[1]&abs(Z2)>=out.zz[2]);