Two-sided tests
Ho:
Ha:
TwoSide.varyEffect(s1, s2, m, m1, delta, a1, r1, fdr)
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 is also the initial value, which is larger than s1 and h(s2) should be larger than 0.
m is the total number of multiple tests
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)
a1 is the allocation proportion for group 1. a2=1-a1.
r1 is the number of true rejection
fdr is the FDR level.
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.
Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003
# NOT RUN {
delta=c(rep(1,40/2),rep(1/2,40/2));
Example.12.2.4<-TwoSide.varyEffect(s1=100,s2=200,m=4000,m1=40,delta=delta,a1=0.5,r1=24,fdr=0.01)
Example.12.2.4
# n=164 s1<n<s2, h(s1)<0,h(s2)<0
# }
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