Hierarchical modeling meets mechanistic models. A molecular TKTD case study

Florian Schunck
University of Osnabrück
A large amount of diverse toxicological data from experiments in the past decades exists, and increasingly available on public repositories. Mechanistic models are well suited to integrate heterogeneous data sources because they are built on biophysical relationships that encode causal relationships in the data.
Recently this was shown at the example of transcription data, internal concentration and survival data from over 30 experiments with zebrafish embryos, which can be integrated in one mechanistic TKTD model to approximate toxicodynamic damage (https://arxiv.org/abs/2406.12949). While successful as a proof of principle, the variability structure in the data could not be represented well by the employed complete pooling approach (i.e. fitting one set of parameters on all experiments). Two major challenges for integrating heterogeneous data types from multiple experiments into mechanistic models remain: 1. Data sparsity: While many datasets exist, they are not exhaustive. Experimental data have a high dimensional data structure (experiment, treatment, measurement variable). But, due to experimental limitations, only sparse information exist in the ideal combinatorial observation matrix. 2. Data variability: Datasets from multiple sources and times are subject to experimental noise, biological variation and measurement errors from e.g. experimenter or batch organism effects. To overcome these challenges, hierarchical models were employed to integrate sparse data while accounting for the inter-experimental biological variability due to batch effects of test organisms, and to account for experimental errors in the external concentration. In the department seminar, I will briefly outline the molecular TKTD approach and introduce the pymob (https://github.com/flo-schu/pymob/) package that facilitates the computation. Then I will go on to show and discuss in depth the opportunities and challenges of using a hierarchical approach for mechanistic modeling.