Ho: \( \mu_{1j}-\mu_{2j} = 0 \)
Ha: \( \mu_{1j}-\mu_{2j} > 0 \)
Multiple.Testing(s1, s2, m, p, D, delta, BCS, pho, K, alpha, beta)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
p=n1/n. n1 is the sample size for group 1, n2 is the sample size for group 2, n=n1+n2.
D is the number of predictive genes.
\( \delta_j \) is the fix effect size among the predictive genes. We assume \( \delta_j = delta, j =1,...,D\) and \(\delta_j =0, j =D+1,....,m\).
BCS means block compound symmetry, which is the length of each blocks. If we only have one block, BCS=m, which is refer to compound symmetry(CS).
pho is the correlation parameter. If j and j' in the same block, \(\rho_{jj'}=pho\) ; otherwise \(\rho_{jj'} = 0 \).
K is the number of replicates for the simulation.
here alpha is the adjusted Familywise error rate (FWER)
here power is a global power. power=1-beta
Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003