Hierarchical Approaches for Integrating Sparse, Multivariate Toxicological Effect Data in Whole Organism Molecular Dynamics Models

MotivationIntegrating time-resolved toxicity data observed along multiple steps along the whole-organism exposure-to-effect pathway into mechanistic ordinary differential equation (ODE) models promises improved chemical risk assessment and predictive toxicology. However, effective incorporation of such multivariate observations is mainly hindered by the inherent sparsity and variability of observation matrices characterized by low overlap in observation types between different experiments, due to tissue consumption and cost of whole-organism experiments. ResultsWe analyzed the potential of bayesian hierarchical ODE models to estimate model parameters from sparse, non-overlapping, multivariate, time resolved datasets subject to experimental variability. The dataset in this study consisted of time series of chemical residue, gene-expression and survival obtained from 5 years of chemical exposure experiments with zebrafish embryos. Using the hierarchical approach, it was possible to increase the number of observations used in the model because experimental deviations in the exposure concentration could be accounted for. We identified inadequate dynamics of the uptake and metabolization kinetics in the ODE system, which led to strong overfitting when coupled to the hierarchical approach when wide prior distributions for the experimental error were used. In contrast, narrow distribution for the experimental error successfully avoided overfitting, despite model inadequacy. An additional simulation study of an adequate model confirmed that hierarchical models estimate parameters with low (< 10%) bias even under complete sparsity (i.e. no experimental overlap between measured variables); filling even small amounts (2.5%) of the missing information further reduced the parameter bias to (< 5%). Availability and ImplementationThe ODE model used in this study was implemented in the pymob model-building framework (https://github.com/flo-schu/pymob/), which provides the infrastructure for specifying high-dimensional ODE models and provides tools for bayesian inference. The case-study is available under https://github.com/flo-schu/hierarchical_molecular_tktd. The snakemake workflow for fitting pymob models is available under https://github.com/flo-schu/pymob-workflow. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=86 SRC="FIGDIR/small/652942v1_ufig1.gif" ALT="Figure 1"> View larger version (27K): org.highwire.dtl.DTLVardef@a68678org.highwire.dtl.DTLVardef@c66e29org.highwire.dtl.DTLVardef@16a85beorg.highwire.dtl.DTLVardef@72a193_HPS_FORMAT_FIGEXP M_FIG C_FIG