Quantitative risk assessment proceeds by first estimating a dose-response model and then inverting this model to estimate the dose that corresponds to some prespecified level of response. The parametric form of the dose-response model often plays a large role in determining this dose. Consequently, the choice of the proper model is a major source of uncertainty when estimating such endpoints. While methods exist that attempt to incorporate the uncertainty by forming an estimate based upon all models considered, such methods may fail when the true model is on the edge of the space of models considered and cannot be formed from a weighted sum of constituent models. We propose a semiparametric model for dose-response data as well as deriving a dose estimate associated with a particular response. In this model formulation, the only restriction on the model form is that it is monotonic. We use this model to estimate the dose-response curve from a long-term cancer bioassay, as well as compare this to methods currently used to account for model uncertainty. A small simulation study is conducted showing that the method is superior to model averaging when estimating exposure that arises from a quantal-linear dose-response mechanism, and is similar to these methods when investigating nonlinear dose-response patterns.