One-Sided Tests with varying effect sizes

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Description

One-sided tests

Ho: δ_j = 0

Ha: δ_j > 0

Usage

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OneSide.varyEffect(s1, s2, m, m1, delta, a1, r1, fdr)

Arguments

s1

We use bisection method to find the sample size, which let the equation h(n)=0. Here s1 and s2 are the initial value, 0<s1<s2. h(s1) should be smaller than 0.

s2

s2 is also the initial value, which is larger than s1 and h(s2) should be larger than 0.

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

δ_j is the constant effect size for jth test. δ_j=(E(Xj)-E(Yj))/σ_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 σ_{j}^{2}. We assume δ_j=0,~ j~ in~ M0 and δ_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

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delta=c(rep(1,40/2),rep(1/2,40/2));

Example.12.2.2 <- OneSide.varyEffect(100,150,4000,40,delta,0.5,24,0.01)
Example.12.2.2
# n=148 s1<n<s2, h(s1)<0,h(s2)<0

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