Statistical cautions when estimating DEBtox parameters

DEBtox (Dynamic Energy Budget in toxicology) models have been designed to analyse various results from classic tests in ecotoxicology. They consist of a set of mechanistic models describing how organisms manage their energy, when they are exposed to a contaminant. Until now, such a biology-based modeling approach has not been used within the regulatory context. However, these methods have been promoted and discussed in recent guidance documents on the statistical analysis of ecotoxicity data. Indeed, they help us to understand the underlying mechanisms. In this paper, we focused on the 21 day Daphnia magna reproduction test. We first aimed to clarify and detail the model building process leading to DEBtox models. Equations were rederived step by step, and for some of them we obtained results different from the published ones. Then, we statistically evaluated the estimation process quality when using a least squares approach. Using both experimental and simulated data, our analyses highlighted several statistical issues related to the fitting of DEBtox models on OECD-type reproduction data. In this case, particular attention had to be paid to parameter estimates and the interpretation of their confidence intervals.