Weighted parametric test
Description
It is assumed that under the global null hypothesis
(Φ^{1}(1p_1),...,Φ^{1}(1p_m)) follow a multivariate normal
distribution with correlation matrix correlation
where
Φ^{1} denotes the inverse of the standard normal distribution
function.
Usage
1 2  parametric.test(pvalues, weights, alpha = 0.05, adjPValues = TRUE,
verbose = FALSE, correlation, ...)

Arguments
pvalues 
A numeric vector specifying the pvalues. 
weights 
A numeric vector of weights. 
alpha 
A numeric specifying the maximal allowed type one error rate. If 
adjPValues 
Logical scalar. If 
verbose 
Logical scalar. If 
correlation 
Correlation matrix. For parametric tests the pvalues
must arise from onesided tests with multivariate normal distributed test
statistics for which the correlation is (partially) known. In that case a
weighted parametric closed test is performed (also see

... 
Further arguments possibly passed by 
Details
For example, this is the case if p_1,..., p_m are the raw pvalues
from onesided ztests for each of the elementary hypotheses where the
correlation between ztest statistics is generated by an overlap in the
observations (e.g. comparison with a common control, groupsequential
analyses etc.). An application of the transformation Φ^{1}(1p_i)
to raw pvalues from a twosided test will not in general lead to a
multivariate normal distribution. Partial knowledge of the correlation
matrix is supported. The correlation matrix has to be passed as a numeric
matrix with elements of the form: correlation[i,i] = 1 for diagonal
elements, correlation[i,j] = ρ_{ij}, where ρ_{ij} is the
known value of the correlation between Φ^{1}(1p_i) and
Φ^{1}(1p_j) or NA
if the corresponding correlation is
unknown. For example correlation[1,2]=0 indicates that the first and second
test statistic are uncorrelated, whereas correlation[2,3] = NA means that
the true correlation between statistics two and three is unknown and may
take values between 1 and 1. The correlation has to be specified for
complete blocks (ie.: if cor(i,j), and cor(i,j') for i!=j!=j' are specified
then cor(j,j') has to be specified as well) otherwise the corresponding
intersection null hypotheses tests are not uniquely defined and an error is
returned.
For further details see the given references.
References
Bretz F., Posch M., Glimm E., Klinglmueller F., Maurer W., Rohmeyer K. (2011): Graphical approaches for multiple endpoint problems using weighted Bonferroni, Simes or parametric tests. Biometrical Journal 53 (6), pages 894913, Wiley. http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000239/full