Montag, 01. Juni 2026 um 12:00 Uhr spricht:

Prof. Dr. Kathrin Möllenhoff (Universität zu Köln)

im Mathematischen Institut, Weyertal 86-90, Köln in Seminarraum 2 (Raum 204)

zum Thema:

When Does It Matter? Detecting Critical Threshholds and Changes in Data

Abstract:

Detecting meaningful changes and critical thresholds in complex data is a central
challenge in fields such as toxicology, (pre-)clinical research, and pharmacokinetics.
In practice, analyses are often based on multiple hypothesis tests at observed time
points or concentrations, which limits the ability to accurately identify when changes
occur and where relevant thresholds are crossed. Moreover, such approaches typically
fail to fully exploit the common structure of continuous covariates such as time and
dose. In this talk, we propose a flexible, model-based framework for identifying both
significant changes and alert thresholds in time-, concentration-, and multivariate
response settings. The approach is based on fitting parametric models to the underlying
response curves and deriving inference from confidence bands constructed via a robust
bootstrap methodology. By analyzing the first derivative of time-response relationships,
we are able to detect time intervals of significant change, including their onset and
duration. In parallel, we introduce methods for identifying alert concentrations at which
a pre-specified response threshold is exceeded, even at unobserved points. Extending
this idea to multidimensional data, we further develop a framework for estimating alert
relationships across multiple continuous covariates, such as time and dose. Using flexible
regression frameworks, we construct confidence bands and surfaces that allow for the
characterization of complex response dynamics and the estimation of alerts in higher-
dimensional settings. The proposed methods are validated through simulation studies
and illustrated using applications to gene expression data and toxicological experiments.
Overall, the framework enables a more precise and comprehensive understanding of
when and under which conditions relevant changes and thresholds occur in complex
biological systems.
 

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