indiv.analysis {rPowerSampleSize}

Data analysis using an individual testing procedure controlling the q-gFWER in the context of m multiple continuous endpoints

Description

This function aims at analysing some multiple continuous endpoints with individual testing procedures (Bonferroni, Holm, Hochberg). These procedures, based on a Union-Intersection test procedure, allow to take into account the correlation between the different endpoints in the analysis. This function uses critical values from Romano et al. to control the q-gFWER. Different structures of the covariance matrices between endpoints are considered.

Usage

indiv.analysis(method, XE, XC, d, matrix.type, equalSigmas, alpha =
0.05, q = 1, rho = NULL, alternative = "greater", orig.Hochberg = FALSE)

Arguments

method

"Bonferroni", "Holm" or "Hochberg". When method = "Hochberg", 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.

XE

matrix (of size n_E \times m) of the outcome for the experimental (test) group.

XC

matrix (of size n_C \times m) of the outcome for the control group.

d

vector of length m indicating the true value of the differences in means under the null hypothesis.

matrix.type

integer value equal to 1, 2, 3, 4 or 5. A value of 1 indicates multisample sphericity. A value of 2 indicates multisample variance components. A value of 3 indicates multisample compound symmetry. A value of 4 indicates multisample compound symmetry with unequal individual (endpoints) variances. A value of 5 indicates unstructured variance components.

equalSigmas

logical. Indicates if \Sigma_E is equal to \Sigma_C.

alpha

value which corresponds to the chosen q-gFWER type-I error rate 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.

rho

NULL or should be provided only if matrix.type is equal to 3 or 4. This is the value of correlation for the compound symmetry case.

alternative

NOT USED YET. Character string specifying the alternative hypothesis, must be one of "two.sided", "greater" or "less".

orig.Hochberg

logical. To use the standard Hochberg's procedure.

Value

list(stat = statvec, pvals = pvals, AdjPvals = pvals.adj, sig2hat = varhatvec)

stat

individual test statistic values.

pvals

non corrected p-values.

pvals.adj

corrected p-values.

sig2hat

estimated variance (i.e., square of denominator of the test statistic.

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.rm.ssc,