Universität zu Köln

Ameis, Lucia ORCID: 0009-0002-9420-6984 (2026). From risk to alerts: Statistical methods across changing questions and data structures. PhD thesis, Universität zu Köln.

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Abstract

As biostatistical research becomes more specialized and diverse, a careful alignment between research question, data structure, and methodology is required for valid statistical conclusions. This necessitates the development of flexible approaches that are simultaneously tailored to the research question, while accounting for the underlying data structure. This thesis comprises three contributions that discuss the interplay between data, research questions, and methodology for two major thematic areas: risk estimation for time-to-event data, and alert identification for continuous covariates. The first contribution introduces a nonparametric estimator for the relative risk of two groups to experience the event. By directly estimating the relative risk, the proposed method avoids problems that arise from the misinterpretation of the odds ratio or the hazard ratio as the relative risk, which is often found in practice. Therefore, it is better aligned with the research question of primary interest. The procedure utilizes the Kaplan-Meier estimator. In contrast to an existing approach, it thus avoids parametric assumptions and merely assumes proportional risks, that is, a constant risk ratio over time. As a result, it remains mostly interpretable even when this assumption is violated and is applicable to a broader spectrum of data. The second and third contributions introduce model-based approaches for the identification of alerts, at which a pre-specified threshold of the response variable is exceeded. Both methods use hypothesis tests, enabling inference based on statistical significance. The second contribution extends existing methods by shifting from the identification of the onset of an effect to the identification of entire covariate regions, such as time intervals, over which the response changes. This approach retains the advantages of parametric model-based methods, including interpolation between observed covariate values and applicability to a broad range of data structures. This is achieved by basing the analysis on the first derivative of the parametric model. The third contribution extends model-based alert identification to two continuous covariates and generalizes naturally to higher-dimensional settings. The proposed approach enables the identification of an alert for one covariate while the other is fixed, or alternatively, an alert relationship between the covariates, depending on the research question. To accommodate the increased complexity of multidimensional data, the approach incorporates the flexible framework of generalized additive models for location, scale, and shape. Each method is evaluated by means of a simulation study, and its practical relevance is investigated by case studies from diabetes research or toxicology. Collectively, these contributions provide methodological advances that improve the alignment between research questions and statistical analysis, while accounting for the underlying data structure.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Ameis, Lucia UNSPECIFIED https://orcid.org/0009-0002-9420-6984 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-813654
Date:	2026
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:	General statistics Mathematics
Uncontrolled Keywords:	Keywords Language Biostatistics English Alert identification English Time-to-event English
Date of oral exam:	21 September 2026
Referee:	Name Academic Title Möllenhoff, Kathrin Prof. Dr. Schwender, Holger Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/81365