A general best-fit method for concentration-response curves and the estimation of low-effect concentrations

Risk assessments of toxic chemicals currently rely heavily on the use of no-observed-effect concentrations (NOECs). Due to several crucial flaws in this concept, however, discussion of replacing NOECs with statistically estimated low-effect concentrations continues. This paper describes a general best-fit method for the estimation of effects and effect concentrations by the use of a pool of 10 different sigmoidal regression functions for continuous toxicity data. Due to heterogeneous variabilities in replicated data (i.e., heteroscedasticity), the concept of generalized least squares is used for the estimation of the model parameters, whereas a nonparametric variance model based on smoothing spline functions is used to describe the heteroscedasticity. To protect the estimates against outliers, the generalized least-squares method is improved by winsorization. On the basis of statistical selection criteria, the best-fit model is chosen individually for each set of data. Furthermore, the bootstrap methodology is applied for constructing confidence intervals for the estimated effect concentrations. The best-fit method for the estimation of low-effect concentrations is validated by a simulation study, and its applicability is demonstrated with toxicity data for 64 chemicals tested in an algal and a bacterial bioassay. In comparison with common methods of concentration-response analysis, a clear improvement is achieved.