Simultaneous confidence bounds in monotone dose–response studies

In dose–response studies, one of the most important issues is the identification of minimum effective dose (MED), where the MED is defined as the lowest dose such that the mean response is better than the mean response of a zero-dose control by a clinically significant difference. Dose–response curves are sometimes monotonic in nature. In this paper, we propose a new method to construct simultaneous confidence lower bounds for the differences between the mean response of any non-zero dose level and that of the control under the monotonicity assumption to identify the MED. The evaluation of the lower confidence bounds is a concave programming problem subject to homogeneous linear inequality constraints. A necessary and sufficient condition for the solution and its simplified expressions are derived. An efficient computing algorithm is proposed. A real data example from a dose–response study is used to illustrate the method.