Psirmu {rPowerSampleSize}

Computation of power for step-up (Hochberg) procedure.

Description

This function computes the power for an analysis of m multiple tests with a control of the q-gFWER with the Hochberg procedure.

Usage

Psirmu(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,
orig.Hochberg = FALSE)

Arguments

r

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.

See Also

indiv.analysis,