Robust Fit of Toxicokinetic–Toxicodynamic Models Using Prior Knowledge Contained in the Design of Survival Toxicity Tests

Toxicokinetics–toxicodynamic (TKTD) models have emerged as a powerful means to describe survival as a function of time and concentration in ecotoxicology. They are especially powerful to extrapolate survival observed under constant exposure conditions to survival predicted under realistic fluctuating exposure conditions. But despite their obvious benefits, these models have not yet been adopted as a standard to analyze data of survival toxicity tests. Instead simple dose–response models are still often used although they only exploit data observed at the end of the experiment. We believe a reason precluding a wider adoption of TKTD models is that available software still requires strong expertise in model fitting. In this work, we propose a fully automated fitting procedure that extracts prior knowledge on parameters of the model from the design of the toxicity test (tested concentrations and observation times). We evaluated our procedure on three experimental and 300 simulated data sets and showed that it provides robust fits of the model, both in the frequentist and the Bayesian framework, with a better robustness of the Bayesian approach for the sparsest data sets

Robust Fit of Toxicokinetic–Toxicodynamic Models Using Prior Knowledge Contained in the Design of Survival Toxicity Tests

Toxicokinetics–toxicodynamic (TKTD) models have emerged as a powerful means to describe survival as a function of time and concentration in ecotoxicology. They are especially powerful to extrapolate survival observed under constant exposure conditions to survival predicted under realistic fluctuating exposure conditions. But despite their obvious benefits, these models have not yet been adopted as a standard to analyze data of survival toxicity tests. Instead simple dose–response models are still often used although they only exploit data observed at the end of the experiment. We believe a reason precluding a wider adoption of TKTD models is that available software still requires strong expertise in model fitting. In this work, we propose a fully automated fitting procedure that extracts prior knowledge on parameters of the model from the design of the toxicity test (tested concentrations and observation times). We evaluated our procedure on three experimental and 300 simulated data sets and showed that it provides robust fits of the model, both in the frequentist and the Bayesian framework, with a better robustness of the Bayesian approach for the sparsest data sets

Statistical Handling of Reproduction Data for Exposure-Response Modeling

Reproduction data collected through standard bioassays are classically analyzed by regression in order to fit exposure-response curves and estimate EC_<i>x</i> values (<i>x</i>% effective concentration). But regression is often misused on such data, ignoring statistical issues related to (i) the special nature of reproduction data (count data), (ii) a potential inter-replicate variability, and (iii) a possible concomitant mortality. This paper offers new insights in dealing with those issues. Concerning mortality, particular attention was paid not to waste any valuable databy dropping all the replicates with mortalityor to bias EC_<i>x</i> values. For that purpose we defined a new covariate summing the observation periods during which each individual contributes to the reproduction process. This covariate was then used to quantify reproductionfor each replicate at each concentrationas a number of offspring per individual-day. We formulated three exposure-response models differing by their stochastic part. Those models were fitted to four data sets and compared using a Bayesian framework. The individual-day unit proved to be a suitable approach to use all the available data and prevent bias in the estimation of EC_<i>x</i> values. Furthermore, a nonclassical negative-binomial model was shown to correctly describe the inter-replicate variability observed in the studied data sets