Often when we carry out dose-response modelling we want to estimate the dose required to elicit a predetermined response (i.e. response ~ dose). Typically this is done with inverse regression techniques (i.e. after-fitting / reparameterisation), but sometimes these impose constraints or come with a greater degree of uncertainty.
Is there any statistical reason that we shouldn't instead just swap the terms (I.e. dose ~ response), if the goal of the exercise is fit a model with the most accurate predictions?
I understand that it is very unorthodox (at least) to suggest that an applied treatment is dependent on the response and goes against the underlying theory but is there any mathematical reason we should not do this if it gives more accurate predictions.