TrialSize (version 1.4)

TwoSide.fixEffect: Two-Sided Tests with fixed effect sizes

Description

Two-sided tests

Ho: \(\delta_j = 0\)

Ha: \(\delta_j \) is not equal to 0

Usage

TwoSide.fixEffect(m, m1, delta, a1, r1, fdr)

Arguments

m

m is the total number of multiple tests

m1

m1 = m - m0. m0 is the number of tests which the null hypotheses are true ; m1 is the number of tests which the alternative hypotheses are true. (or m1 is the number of prognostic genes)

delta

\(\delta_j\) is the constant effect size for jth test. \( \delta_j=(E(Xj)-E(Yj))/\sigma_j\). \(X_{ij}(Y_{ij})\) denote the expression level of gene j for subject i in group 1( and group 2, respectively) with common variance \(\sigma_{j}^{2}\). We assume \(\delta_j=0,~ j~ in~ M0\) and \(\delta_j >0, ~j~ in~ M1\)=effect size for prognostic genes.

a1

a1 is the allocation proportion for group 1. a2=1-a1.

r1

r1 is the number of true rejection

fdr

fdr is the FDR level.

Details

alpha_star=r1*fdr/((m-m1)*(1-fdr)), which is the marginal type I error level for r1 true rejection with the FDR controlled at f.

beta_star=1-r1/m1, which is equal to 1-power.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

# NOT RUN {
Example.12.2.3<-TwoSide.fixEffect(m=4000,m1=40,delta=1,a1=0.5,r1=24,fdr=0.01)
Example.12.2.3
# n=73
# }