Sequential method of estimating the LD50 using a modified up-and-down rule

In this paper, the original up-and-down method, modified up-and-down method, the Robbins-Monro method, and a fixed-sample Spearman-Kärber method are compared for the point estimator as well as the confidence interval of LD50. In particular, three different designs of the modified up-and-down approach based on the combination of experiments on one test space and reduced test space are investigated. The standard normal distribution and chi-square distribution are used as tolerance distributions. Simulation results indicate that the modified up-and-down method tends to be somewhat better than the original up-and-down method in terms of the mean squared error under normal tolerance distribution. In case of chi-square distribution, the modified method is shown to be substantially better when the test space is wide and the initial dose is further away from the LD50.