Optimal Designs for Estimating the ED₅₀ When Response Functions Have a Downturn

The is the dose which, on average, produces 50% of the maximum possible response. In many cases, dose-response functions have a downturn at higher doses. If researchers ignore the downturn and try to select doses below the peak dose, there is some loss of information. This study analyzes the loss of information and changes in optimal designs for estimating the due to restricting the dose range. We assume that responses are continuous and doses to be used are restricted to be between some fixed minimum and maximum doses. For biologically motivated models that incorporate a downturn in the response function, c-optimal designs for estimating the and the c-optimal designs using the restricted dose range are obtained and compared. This article also presents a two-stage optimal design for estimating the that is not substantially affected by restricting the dose range.