We consider identifying the minimum effective dose (MED) in a dose-response study, where the MED is defined to be the lowest dose level producing an effect over that of the zero-dose control. Proposed herein is a nonparametric procedure based on the Mann-Whitney statistic incorporated with the step-down closed testing scheme. A numerical example demonstrates the feasibility of the proposed nonp...

introduction: nowadays ionizing radiation has a considerable contribution in medical diagnostic and treatment. using ionizing radiation is increasing rapidly, so biological effects of ionizing radiation should be considered more. x-rays in the range of diagnostic radiology have hazardous effects and risks that are defined as random effects. these effects obey the lnt hypothesis that occur at lo...