The use of canonical dose–response models for benchmark dose analysis of continuous toxicological data

The benchmark dose (BMD) approach employs dose-response modeling to determine the dose associated with a small change in response relative to the background response. Here, we introduce a conceptual framework for modeling continuous data that is based on key risk assessment principles and requirements. Based on this framework, we define a class of dose-response models sharing the same four biologically interpretable model parameters, while exhibiting five common properties that are essential from a risk assessment perspective: such models are denoted as "canonical" models. The first two canonical properties are straightforward: property 1. The models should predict positive values only (as measurements of continuous endpoints are typically positive) and property 2. the outcomes should not depend on the measurement unit. Canonical property 3 reflects the observation that toxicological dose-response data related to different subgroups (e.g. species, sexes, and exposure durations) are typically (at least approximately) parallel on a log-dose scale, which is at the same time an implicit assumption in defining fundamental toxicological concepts, such as extrapolation factors, relative potency factors (RPFs), and relative sensitivity factors (RSFs). Property 4 is needed to enable comparisons of the sensitivity of endpoints differing in maximum response. A fifth canonical property reflects our view that choices regarding the dose-response model expression, the assumed distribution for the within-group variation, and the benchmark response (BMR) that is being used should be internally consistent. The canonical models that we discuss are suitable to fit parallel dose-response curves to combined datasets related to different subgroups (e.g. species, sexes, and exposure durations). Doing so provides a tool to check canonical property 3 of the particular data analyzed. We provide a review of empirical evidence indicating that this property has general validity, which is highly fortunate, as this legitimizes the use of extrapolation factors and RPFs in risk assessment. We then evaluate to what extent the approaches in current BMD guidance by European Food Safety Authority (EFSA) or U.S. Environmental Protection Agency (US-EPA) comply with the principles of canonical dose-response modeling, concluding that this is only partly the case. The latter can have unfavorable and sometimes far-reaching consequences. For instance, some of the recommended non-canonical models result in different BMDs when changing the measurement unit (e.g. µg to mg). As another example, the BMD tool recently developed by EFSA implements covariate analysis in such a way that canonical property 3 cannot possibly be represented by any of the models. As another disadvantage, non-canonical models preclude the effective development and use of prior distributions in a Bayesian approach. Finally, we argue that a concomitant but important advantage of only using canonical models is that BMD methodology will be more transparent, so that risk assessors will be better able to understand it, and BMDs with high societal impact can be more easily defended. The present paper may be a helpful tool for toxicologists and risk assessors to critically follow the developments in BMD methodology at the conceptual level.