On the behavior of multiple comparison procedures in complex parametric designs

The framework for simultaneous inference by Hothorn, Bretz, and
Westfall (2008) allows for a unified treatment of multiple
comparisons in general parametric models where the study questions
are specified as linear combinations of elemental model parameters.
However, due to the asymptotic nature of the reference distribution
the procedure controls the error rate across all comparisons only
for sufficiently large samples. This thesis evaluates the small
samples properties of simultaneous inference in complex parametric
designs. These designs are necessary to address questions from
applied research and include nonstandard parametric models or data
in which the assumptions of classical procedures for multiple
comparisons are not met. This thesis first treats multiple
comparisons of samples with heterogeneous variances. Usage of a
heteroscedastic consistent covariance estimation prevents an
increase in the probability of false positive findings for
reasonable sample sizes whereas the classical procedures show
liberal or conservative behavior which persists even with
increasing sample size. The focus of the second part are multiple
comparisons in survival models. Multiple comparisons to a control
can be performed in correlated survival data modeled by a frailty
Cox model under control of the familywise error rate in sample
sizes applicable for clinical trials. As a further application,
multiple comparisons in survival models can be performed to
investigate trends. The procedure achieves good power to detect
different dose-response shapes and controls the error probability
to falsely detect any trend. The third part addresses multiple
comparisons in semiparametric mixed models. Simultaneous inference
in the linear mixed model representation of these models yields an
approach for multiple comparisons of curves of arbitrary shape. The
sections on which curves differ can also be identified. For
reasonably large samples the overall error rate to detect any
non-existent difference is controlled. An extension allows for
multiple comparisons of areas under the curve. However the
resulting procedure achieves an overall error control only for
sample sizes considerably larger than available in studies in which
multiple AUC comparisons are usually performed. The usage of the
evaluated procedures is illustrated by examples from applied
research including comparisons of fatty acid contents between
Bacillus simplex lineages, comparisons of experimental drugs with a
control for prolongation in survival of chronic myelogeneous
leukemia patients, and comparisons of curves describing a
morphological structure along the spinal cord between variants of
the EphA4 gene in mice.