Two-stage design of quantal response studies

In a quantal response study, there may be insufficient knowledge of the response relationship for the stimulus (or dose) levels to be chosen properly. Information from such a study can be scanty or even unreliable. A two-stage design is proposed for such studies, which can determine whether and how a follow-up (i.e., second-stage) study should be conducted to select additional stimulus levels to compensate for the scarcity of information in the initial study. These levels are determined by using optimal design theory and are based on the fitted model from the data in the initial study. Its advantages are demonstrated using a fishery study.