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.
indiv.analysis(method, XE, XC, d, matrix.type, equalSigmas, alpha =
0.05, q = 1, rho = NULL, alternative = "greater", orig.Hochberg = FALSE)"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.
matrix (of size \(n_E \times m\)) of the outcome for the experimental (test) group.
matrix (of size \(n_C \times m\)) of the outcome for the control group.
vector of length m indicating the true value of the differences in means
under the null hypothesis.
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.
logical. Indicates if \(\Sigma_E\) is equal to \(\Sigma_C\).
value which corresponds to the chosen q-gFWER type-I error rate 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.
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.
NOT USED YET. Character string specifying the alternative hypothesis, must be one of "two.sided", "greater" or "less".
logical. To use the standard Hochberg's procedure.
list(stat = statvec, pvals = pvals, AdjPvals = pvals.adj, sig2hat = varhatvec)
individual test statistic values.
non corrected p-values.
corrected p-values.
estimated variance (i.e., square of denominator of the test statistic.
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.