Shape and steepness of toxicological dose–response relationships of continuous endpoints

A re-analysis of a large number of historical dose-response data for continuous endpoints indicates that an exponential or a Hill model with four parameters adequately describes toxicological dose-responses. No exceptions were found for the datasets considered, which related to a wide variety of endpoints and to both in vivo and in vitro studies of various types. For a given endpoint/study type dose-response shapes were found to be homogenous among chemicals in the in vitro studies considered, while a mild among-chemical variation in the steepness parameter seemed to be present in the in vivo studies. Our findings have various practical consequences. For continuous endpoints, model selection in the BMD approach is not a crucial issue. The often applied approach of using constraints on the model parameters to prevent "infinite" slopes at dose zero in fitting a model is not in line with our findings, and appears to be unjustified. Instead, more realistic ranges of parameter values could be derived from re-analyses of large numbers of historical dose-response datasets in the same endpoint and study type, which could be used as parameter constraints in future individual datasets. This approach will be particularly useful for weak datasets (e.g. few doses, much scatter). In addition, this approach may open the way to use fewer animals in future studies. In the discussion, we argue that distinctions between linear, sub/supralinear or thresholded dose-response shapes, based on visual inspection of plots, are not biologically meaningful nor useful for risk assessment.