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