integer, r = 1, ..., m. Desired number of endpoints to be declared significant.
m
integer. Number of endpoints.
p
integer, p = 1, ..., m. Indicates the number of false null hypotheses.
nE
integer. Sample size for the experimental (test) group.
nCovernE
Ratio of nC over nE.
delta
vector of length m equal to muE - muC - d.
SigmaC
matrix giving the covariances between the m primary endpoints in the control group.
SigmaE
matrix giving the covariances between the m primary
endpoints in the experimental (test) group.
alpha
a value which corresponds to the chosen q-gFWER type-I control bound.
q
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.
asympt
logical. TRUE for the use of the asymptotic approximation by a
multivariate normal distribution or FALSE for the multivariate
Student distribution.
maxpts
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!
abseps
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!
releps
relative error tolerance as double used in the
GenzBretz function.
nbcores
integer. Number of cores to use for parallel computations.
LB
logical. Should we use a load balancing parallel computation.
orig.Hochberg
logical. To use the standard Hochberg's procedure.
Value
List with two components:
pow
The computed power.
error
The 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.
Note
Note that we use critical values involving the D1 term in formula
(11) of Romano et al. in order to control strongly the q-FWER.
If you want to use the original Hochberg's
procedure, set orig.Hochberg to TRUE. Even for
q=1, this is a bad idea except when the p-values can be assumed
independent.
Results can differ from one time to another because the results of the
function pmvt are random. If this is the case, you should
consider increasing maxpts and decreasing abseps.
Author(s)
P. Lafaye de Micheaux, B. Liquet and J. Riou
References
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.