Survival is a relevant endpoint for many questions related to the effects of chemicals in the environment. Making sense of mortality, as a process over time, requires mechanism-based models, known as toxicokinetic-toxicodynamic (TKTD) models. All published TKTD models for survival can now be viewed as members of an over-arching framework: GUTS.
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2 Description of GUTS
3 Mathematical treatment
4 Case study: dieldrin in guppies
5 Case study: propiconazole in amphipods
6 Use cases
7 Ring test
8 Model evaluation
The General Unified Threshold model for Survival (GUTS) integrates previously published toxicokinetic-toxicodynamic models and estimates survival with explicitly defined assumptions. Importantly, GUTS accounts for time-variable exposure to the stressor. We performed three studies to test the ability of GUTS to predict survival of aquatic organisms across different pesticide exposure patterns, time scales and species. Firstly, using synthetic data, we identified experimental data requirements which allow for the estimation of all parameters of the GUTS proper model. Secondly, we assessed how well GUTS, calibrated with short-term survival data of Gammarus pulex exposed to four pesticides, can forecast effects of longer-term pulsed exposures. Thirdly, we tested the ability of GUTS to estimate 14-day median effect concentrations of malathion for a range of species and use these estimates to build species sensitivity distributions for different exposure patterns. We find that GUTS adequately predicts survival across exposure patterns that vary over time. When toxicity is assessed for time-variable concentrations species may differ in their responses depending on the exposure profile. This can result in different species sensitivity rankings and safe levels. The interplay of exposure pattern and species sensitivity deserves systematic investigation in order to better understand how organisms respond to stress, including humans. (open access, Nature Scientific Reports)
Why do some individuals survive after exposure to chemicals while others die? Either, the tolerance threshold is distributed among the individuals in a population, and its exceedance leads to
certain death, or all individuals share the same threshold above which death occurs stochastically. The previously published General Unified Threshold model of Survival (GUTS) established a
mathematical relationship between the two assumptions. According to this model stochastic death would result in systematically faster compensation and damage repair mechanisms than individual
tolerance. Thus, we face a circular conclusion dilemma because inference about the death mechanism is inherently linked to the speed of damage recovery. We provide empirical evidence that the
stochastic death model consistently infers much faster toxicodynamic recovery than the individual tolerance model. Survival data can be explained by either, slower damage recovery and a wider
individual tolerance distribution, or faster damage recovery paired with a narrow tolerance distribution. The toxicodynamic model parameters exhibited meaningful patterns in chemical space, which
is why we suggest toxicodynamic model parameters as novel phenotypic anchors for in vitro to in vivo toxicity extrapolation. GUTS appears to be a promising refinement of traditional survival
curve analysis and dose response models. (Published in Environmental Science & Technology, open access)
Toxicokinetic-toxicodynamic models (TKTD models) simulate the time-course of processes leading to toxic effects on organisms. Even for an apparently simple endpoint as survival, a large number of very different TKTD approaches exist. These differ in their underlying hypotheses and assumptions, although often the assumptions are not explicitly stated. Thus, our first objective was to illuminate the underlying assumptions (individual tolerance or stochastic death, speed of toxicodynamic damage recovery, threshold distribution) of various existing modeling approaches for survival and show how they relate to each other (e.g., critical body residue, critical target occupation, damage assessment, DEBtox survival, threshold damage). Our second objective was to develop a general unified threshold model for survival (GUTS), from which a large range of existing models can be derived as special cases. Specific assumptions to arrive at these special cases are made and explained. Finally, we illustrate how special cases of GUTS can be fitted to survival data. We envision that GUTS will help increase the application of TKTD models in ecotoxicological research as well as environmental risk assessment of chemicals. It unifies a wide range of previously unrelated approaches, clarifies their underlying assumptions, and facilitates further improvement in the modeling of survival under chemical stress. (link at journal) or (download here)
Using the General Unified Threshold model of Survival this study systematically investigates how well different ways of using the model perform when it comes to predicting survival: "Toxicokinetic-toxicodynamic modelling of survival of Gammarus pulex in multiple pulse exposures to propiconazole: model assumptions, calibration data requirements and predictive power." Ecotoxicology (link to paper, free access)
Toxicokinetic-toxicodynamic (TKTD) models quantify the time-course of internal concentration, which is defined by uptake, elimination and biotransformation (TK), and the processes which lead to the toxic effects (TD). TKTD models show potential in predicting pesticide effects in fluctuating concentrations, but the data requirements and validity of underlying model assumptions are not known. We calibrated TKTD models to predict survival of Gammarus pulex in propiconazole exposure and investigated the data requirements. In order to assess the need of TK in survival models, we included or excluded simulated internal concentrations based on pre-calibrated TK. Adding TK did not improve goodness of fits. Moreover, different types of calibration data could be used to model survival, which might affect model parameterization. We used two types of data for calibration: acute toxicity (standard LC50, 4 d) or pulsed toxicity data (total length 10 d). The calibration data set influenced how well the survival in the other exposure scenario was predicted (acute to pulsed scenario or vice versa). We also tested two contrasting assumptions in ecotoxicology: stochastic death and individual tolerance distribution. Neither assumption fitted to data better than the other. We observed in 10-d toxicity experiments that pulsed treatments killed more organisms than treatments with constant concentration. All treatments received the same dose, i.e. the time-weighted average concentration was equal. We studied mode of toxic action of propiconazole and it likely acts as a baseline toxicant in G. pulex during 10-days of exposure for the endpoint survival.
The General Unified Threshold model of Survival (GUTS) provides a consistent mathematical framework for survival analysis. However, the calibration of GUTS models is computationally challenging. We present a novel algorithm and its fast implementation in our R package, GUTS, that help to overcome these challenges. We show a step-by-step application example consisting of model calibration and uncertainty estimation as well as making probabilistic predictions and validating the model with new data. Using self-defined wrapper functions, we show how to produce informative text printouts and plots without effort, for the inexperienced as well as the advanced user. The complete ready-to-run script is available as supplemental material. We expect that our software facilitates novel re-analysis of existing survival data as well as asking new research questions in a wide range of sciences. In particular the ability to quickly quantify stressor thresholds in conjunction with dynamic compensating processes, and their uncertainty, is an improvement that complements current survival analysis methods. PLoS Comput Biol 12(6): e1004978.