Optimal Bayesian sequential estimation of the median effective dose

Abstract

This paper concerns the sequential design of experiments for estimating the median lethal dose parameter of a quantal, logistic dose response curve. Bayesian decision theory is used to provide a stopping rule and terminal decision rule to minimize the prior expectation of the total cost of observation plus estimation loss. Special cases in which trials can only be performed at one, two or three dose levels are considered, and optimal strategies are evaluated numerically. The expected losses are compared with those of the up and down method using a fixed sample size equal to the prior expectation of the number of trials under the sequential design. The up and down method is shown to be surprisingly good, having efficiency usually in excess of 90 %.