Hixon JG, Thompson C, Bichteler A, Abraham L. 2014. Smoothing regression splines as the basis for dose-response modeling. Presented at the Society of Toxicology’s 53rd Annual Meeting, March 23-27, Phoenix, AZ.
In its current state, dose-response modeling employs analytical methods that include numerous candidate mathematical functions from which the analyst must choose in order to develop toxicity values such as reference doses and cancer slope factors. Smoothing regression splines offer a much simpler approach to dose-response modeling and have a number of desirable properties. They are flexible, require no pre-specification of a functional form, achieve optimal fit under a wide range of circumstances, and need little-to-no intervention by the analyst. In addition, the same smoothing regression splines can be used to unambiguously identify various types of points of departure (e.g. threshold and benchmark doses), as well as address important questions about a dose-response curve such as its overall non-linearity and non-linearity within specific regions. We compared more traditional modeling approaches with smoothing splines to illustrate how the latter provide a unified mathematical framework for estimating dose-response functions and critical quantities and often provide superior performance. For example, we compared threshold doses estimated via smoothing regression splines with other published bilinear models. Although smoothing regression splines regularly provide similar results to older approaches, when differences emerge the smoothing spline results are often clearly superior. They are more faithful to the underlying data as indexed by their solutions tracking more closely to the key visual characteristics of the plotted data, and they frequently offer narrower confidence intervals. Finally, we introduce an R package that facilitates the use of smoothing regression splines for dose-response modeling.