An often used model for the shape of a drug's dose–response relationship is the following: the curve increases to a certain dose until a plateau is reached. In this situation, the minimum dose with maximum effect can be seen as a change point in a regression model. We present four estimators for the change point and compare their performance with respect to selection rates and loss function based criteria by extensive simulations. The choice of the loss function depending on the practical situation is discussed. Application of the estimators is illustrated by an example.