Estimating effect thresholds and beyond: A flexible framework for multivariate alert detection

2026-04-14

AI Summary

This study addresses the challenge of estimating effect thresholds—such as ED50—in multivariate settings like time–dose–response relationships, where direct observations are often unavailable for many covariate combinations. The authors propose a parametric framework based on Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to flexibly fit multidimensional response surfaces, enabling estimation and extrapolation of effect thresholds across arbitrary covariate configurations. This work represents the first systematic application of GAMLSS to multidimensional threshold modeling, supporting the construction of two-dimensional confidence bands or three-dimensional confidence planes. By coherently integrating information across dimensions, the approach enhances the reliability of extrapolations. Simulations and analyses of primary human hepatocyte cytotoxicity data demonstrate that the method accurately captures the joint effects of exposure duration and dose on toxicity.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Evaluating the influence of continuous covariates, like exposure time or dose, on a response variable is a pivotal objective in the assessment of a compound's effect, particularly when determining toxicity in pre-clinical research or pharmacokinetics in clinical trials. The determination of an alert, such as the ED50 value, at which a pre-specified threshold of the response variable is crossed, is an important tool for the evaluation process. In practice, response data might be available for combinations of different covariates and the alert depending on both is of interest. In this case, it is crucial to use all available information and extrapolate between cases to ensure the optimal utilization of the data. In this paper, we introduce a parametric approach that allows alerts to be estimated in a multidimensional setting. For time-dose-response data, for instance, alert doses at a given time can be determined, even when there are no measurements available at that exact time. Likewise, it allows estimation of alert times for a given dose. More generally, the method makes it possible to characterize the complete alert relationship between covariates by leveraging all available data. This is achieved by fitting a parametric model and constructing either a confidence band for the two-dimensional curve given for example a fixed time or dose or by constructing a confidence plane for the three-dimensional model fit. The initial model fit is achieved by the flexible framework of Generalized Additive Models for Location, Scale and Shape (GAMLSS), which offers the possibility to account for a plethora of complex three-dimensional data structures. We demonstrate the validity of our approach through a simulation study and present an application to data from a study investigating the relevance of the exposure duration on cytotoxicity in primary human hepatocytes.

Problem

• effect threshold
• multivariate alert detection
• time-dose-response
• extrapolation
• toxicity assessment

Innovation

• multivariate alert detection
• GAMLSS
• effect threshold estimation
• time-dose-response modeling
• confidence surface