FastBMD currently offers 10 statistical models. Among them, Nhe NTP recommends using all of the models other than Poly3 and Poly4. While these higher degree polynomials often give good fits, there are concerns that allowing too many changes of direction may over fit the data. However, of the remaining models (Exp2-5, Linear, Polynomial degree 2, Power, and Hill), only Poly 2 allows for non-monotonic behaviour. Thus, if you expect non-monotonic behaviour, you may wish to include higher order polynomials.
The NTP report suggests that future implementations of dose-response software should include the ability to constrain Poly3 and Poly4 models to only change direction once. We plan to include this feature in future updates to FastBMD.