Global test for groups of variables via model comparisons // The
association between a variable of interest (e.g. two groups)
and the global pattern of a group of variables (e.g. a gene
set) is tested via a global F-test. We give the following
arguments in support of the GlobalAncova approach: After
appropriate normalisation, gene-expression-data appear rather
symmetrical and outliers are no real problem, so least squares
should be rather robust. ANCOVA with interaction yields
saturated data modelling e.g. different means per group and
gene. Covariate adjustment can help to correct for possible
selection bias. Variance homogeneity and uncorrelated residuals
cannot be expected. Application of ordinary least squares gives
unbiased, but no longer optimal estimates (Gauss-Markov-
Aitken). Therefore, using the classical F-test is
inappropriate, due to correlation. The test statistic however
mirrors deviations from the null hypothesis. In combination
with a permutation approach, empirical significance levels can
be approximated. Alternatively, an approximation yields
asymptotic p-values. The framework is generalized to groups of
categorical variables or even mixed data by a likelihood ratio
approach. Closed and hierarchical testing procedures are
supported. This work was supported by the NGFN grant 01 GR
0459, BMBF, Germany and BMBF grant 01ZX1309B, Germany.