Universität zu Köln

Hagemann, Niklas ORCID: 0000-0001-7751-9941 (2025). Modeling techniques and statistical inference for multidimensional effects. PhD thesis, Universität zu Köln.

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Abstract

The increasing complexity of biostatistical research questions requires statistical methods that can effectively address multidimensional problems.This thesis addresses issues arising from multidimensionality in statistical testing and modeling, with a focus on model-based equivalence tests and hazard regression models. Specifically, it examines three directions of multidimensionality: multivariate outcomes, model uncertainty, and multidimensional covariate effects. Four contributions discuss the necessity of adapting model-based equivalence tests and hazard regression models to account for these three aspects of multidimensionality. The first contribution extends model-based equivalence tests to multivariate, potentially mixed-scale outcomes using generalized joint regression models. This approach overcomes the limitations of a previous approach that is only capable of bivariate binary outcomes and relies on the intersection-union principle leading to an overly conservative test, particularly for small sample sizes. In contrast, a new maximum of maxima approach is used to increase the power in finite samples while maintaining asymptotic validity. The second contribution addresses model uncertainty, a common issue in applied research where often the true model is unknown. By incorporating model averaging to model-based equivalence tests and deploying a confidence interval-based testing approach, the proposed method offers a robust and numerically feasible alternative that retains the asymptotic properties. The third and fourth contributions shift the focus to multidimensional covariate effects. In the third article, functional random coefficients are introduced to model heterogeneously time-varying covariate effects. Such coefficients are not only capable of time-varying and subgroup-specific covariate effects but also of covariate effects in which the time-variation itself is heterogeneous. The functional random coefficients are constructed as tensor product interactions of heterogeneity and time. While the third contribution introduces these effects to generalized additive models, the fourth article discusses their applicability in survival analysis by incorporating such effects into hazard regression models. The methods are evaluated through simulations outlining their flexibility while either retaining the asymptotic properties of the model-based equivalence test or the prevention of overfitting of the regression models. The practical relevance of the proposed methods is demonstrated using case studies from pharmacology, toxicology, and oncology. This thesis thus contributes novel approaches that enhance the flexibility and applicability of statistical methods in multidimensional biostatistical research.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Hagemann, Niklas UNSPECIFIED orcid.org/0000-0001-7751-9941 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-783606
Date:	2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Biostatistics English Multidimensionality English Statistical modeling English
Date of oral exam:	23 May 2025
Referee:	Name Academic Title Möllenhoff, Kathrin Prof. Dr. Schwender, Holger Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/78360