Sequential Bayesian design for estimation of ED_p

Maximum likelihood recursions of Wu can be used to estimate extreme percentiles of a dose-quantal effective curve. For certain choices of initial designs, Wu's method performs well. In bioassay, there often exist some different initial designs which are known as the up-and-down designs. Based on the existing data set from such a design, we propose three sequential empirical Bayesian designs by quickly and efficiently exploiting the information in the testing data and known knowledge. The improvement obtained by using the new procedures for the estimation of extreme percentiles is substantial.