generateTest(g, w, cr, al)cr where $\Phi^{-1}$ denotes the inverse of the standard
normal distribution function. For example, this is the case if $p_1,..., p_m$ are the raw p-values
from one-sided z-tests for each of the elementary hypotheses
where the correlation between z-test statistics is generated by
an overlap in the observations (e.g. comparison with a common
control, group-sequential analyses etc.). An application of the
transformation $\Phi^{-1}(1-p_i)$ to raw p-values from a
two-sided 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: $cr[i,i] = 1$ for
diagonal elements, $cr[i,j] = \rho_{ij}$, where $\rho_{ij}$
is the known value of the correlation between
$\Phi^{-1}(1-p_i)$ and $\Phi^{-1}(1-p_j)$ or NA if
the corresponding correlation is unknown. For example cr[1,2]=0
indicates that the first and second test statistic are
uncorrelated, whereas cr[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,k) for i!=j!=k are specified
then cor(j,k) has to be specified as well) otherwise the
corresponding intersection null hypotheses tests are not uniquely
defined and an error is returned.
The parametric tests in (Bretz et al. (2011)) are defined such that
the tests of intersection null hypotheses always exhaust the full
alpha level even if the sum of weights is strictly smaller than
one. This has the consequence that certain test procedures that do
not test each intersection null hypothesis at the full level alpha
may not be implemented (e.g., a single step Dunnett test). If
exhaust is set to FALSE (default) the parametric
tests are performed at a reduced level alpha of sum(w) * alpha and
p-values adjusted accordingly such that test procedures with
non-exhaustive weighting strategies may be implemented. If set to
TRUE the tests are performed as defined in Equation (3) of
(Bretz et al. (2011)).
## Define some graph as matrix
g <- matrix(c(0,0,1,0,
0,0,0,1,
0,1,0,0,
1,0,0,0), nrow = 4,byrow=TRUE)
## Choose weights
w <- c(.5,.5,0,0)
## Some correlation (upper and lower first diagonal 1/2)
c <- diag(4)
c[1:2,3:4] <- NA
c[3:4,1:2] <- NA
c[1,2] <- 1/2
c[2,1] <- 1/2
c[3,4] <- 1/2
c[4,3] <- 1/2
## Test function for further use:
myTest <- generateTest(g,w,c,.05)
myTest(c(3,2,1,2))Run the code above in your browser using DataLab