This function computes the power for an analysis of \(m\) multiple tests with a control of the q-gFWER by a Bonferroni procedure.
Psirms(r, m, p = m, nE, nCovernE = 1, delta, SigmaC, SigmaE,
alpha = 0.05, q = 1, asympt = FALSE,
maxpts = 25000, abseps = 0.001, releps = 0, nbcores = 1, LB = FALSE)integer, r = 1, ..., m. Desired number of endpoints to be declared significant.
integer. Number of endpoints.
integer, p = 1, ..., m. Indicates the number of false null hypotheses.
integer. Sample size for the experimental (test) group.
Ratio of nC over nE.
vector of length m equal to muE - muC - d.
matrix giving the covariances between the m primary endpoints in the control group.
matrix giving the covariances between the m primary
endpoints in the experimental (test) group.
a value which corresponds to the chosen q-gFWER type-I control bound.
integer. Value of 'q' (q=1,...,m) in the q-gFWER of Romano et
al., which is the probability to make at least q false
rejections. The default value q=1 corresponds to the classical FWER control.
logical. TRUE for the use of the asymptotic approximation by a
multivariate normal distribution or FALSE for the multivariate
Student distribution.
convergence parameter used in the GenzBretz
function. A suggested choice is min(25000 * true.complexity, .Machine$integer.max)
where true.complexity is computed with the complexity function. But note that this might considerably increase the
computation time!
convergence parameter used in the GenzBretz
function. A suggested choice is max(0.001 / true.complexity, 1e-08)
where true.complexity is computed with the complexity function. But note that this might considerably increase the
computation time!
relative error tolerance as double used in the
GenzBretz function.
integer. Number of cores to use for parallel computations.
logical. Should we use a load balancing parallel computation.
List with two components:
The computed power.
The total sum of the absolute estimated errors for each call
to the pmvt (or pmvnorm) function. The number of such
calls is given (in the non exchangeable case) by the function complexity. Note that in the
exchangeable case, some probabilities are weighted. So an error
committed on such a probability is also inflated with the same weight. Note also that this global error does not take into account
the signs of the individual errors and is thus most certainly higher
than the true error. In other words, you are 99 percent sure that
the true power is between 'pow' - 'error' and 'pow' + 'error', but
it is also probably much closer to 'pow', particularly if the
complexity is large.
Delorme P., Lafaye de Micheaux P., Liquet B., Riou, J. (2015). Type-II Generalized Family-Wise Error Rate Formulas with Application to Sample Size Determination. Submitted to Statistics in Medicine.
Romano J. and Shaikh A. (2006) Stepup Procedures For Control of Generalizations of the Familywise Error Rate. The Annals of Statistics, 34(4), 1850--1873.