Sequential estimation of the mean logistic response function

In this paper we show that the maximum likelihood estimators of LD50 and th e scale parameter in the logistic case are equivalent to the Spearman-Karbe r type of estimators, when the subsample sizes at each dose level are equal . We derive a simple expression for the asymptotic variance-covariance matr ix of the estimators. We also obtain correction terms to the bias and the v ariance of the Spearman-Karber estimator of LD50. Using these we construct sequential fixed-width and risk-efficient procedures for LD50. Numerical ca lculations show that these procedures are simple to carry out and stop at f ewer dose levels than those proposed earlier by Nanthakumar and Govindaraju lu (1994, 1999).