Four-parameter nonlinear regression and maximum achievable effect in ecotoxicology: Just visually appealing or relevant for risk assessment?

ABSTRACT

In ecotoxicology, ECx refers to the concentration that causes x% effect (Organisation for Economic Co-operation and Development, 2006a). This seems to be a precise definition, but is typically only clear for ECx values calculated for inhibitions of metric variables from two and three parameter regressions, as they assume that the minimum of the affected variable is zero. In contrast, some four-parameter-regression (4PR) assume that the maximum achievable effect levels off at a value of the affected variable greater than zero. As a consequence, two types of ECx can then be calculated. While the absolute ECx considers effects always as a change compared to the control level, the relative ECx is related to the maximum achievable response to a stressor. In literature and in common software such as the drc package of R, the question whether absolute or relative ECx should be calculated is not handled in a uniform way. Based on a sensitivity analysis, it is shown, that depending on the steepness of the curve and the level of the lower limit, a relative ECx from 4PR can be considerably lower than the corresponding absolute ECx. Thus, the question of whether to use absolute or relative ECx should not be left to the preference of the user or arbitrary settings of the used software, but requires consistent and binding regulatory guidance.

This paper does not advocate for absolute or relative ECx from 4PR, but outlines the characteristics and consequences of each approach. The objective is to highlight the need for discussion and to provide information for an informed decision. Future guidelines should address this issue in detail to ensure consistency, clarity and transparency in data interpretation.