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Context:

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.

Question:

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.

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Yes, there is a reason not to do it.

Nonlinear regression is based on the assumption that the distribution of the differences between the actual Y values and the predicted Y values (the curve) is Gaussian. If that assumption is reasonable, then it is unlikely that the distribution of the difference between actual concentrations and the predicted concentrations would be Gaussian. If the assumption is far off, then so are the results.

It is easy enough to fit the curve conventionally and then interpolate the values you need.

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  • $\begingroup$ What about with models like SVMs? $\endgroup$ – André.B Mar 21 at 19:37
  • $\begingroup$ What does SVM stand for? $\endgroup$ – Harvey Motulsky Mar 22 at 18:21
  • $\begingroup$ Support Vector Machine $\endgroup$ – André.B Mar 23 at 23:06

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