Identifying alert concentrations using a model-based bootstrap approach.

The determination of alert concentrations, where a pre-specified threshold of the response variable is exceeded, is an important goal of concentration-response studies. The traditional approach is based on investigating the measured concentrations and attaining statistical significance of the alert concentration by using a multiple t-test procedure. In this paper, we propose a new model-based method to identify alert concentrations, based on fitting a concentration-response curve and constructing a simultaneous confidence band for the difference of the response of a concentration compared to the control. In order to obtain these confidence bands, we use a bootstrap approach which can be applied to any functional form of the concentration-response curve. This particularly offers the possibility to investigate also those situations where the concentration-response relationship is not monotone and, moreover, to detect alerts at concentrations which were not measured during the study, providing a highly flexible framework for the problem at hand.