Corrigendum: The Median Lethal Dose-Design and Estimation

Abstract

I am grateful to Graham Healey, Huntingdon Life Sciences Limited, and Jochen Mueller-Cohrs, Aventis Behring GmbH, Marburg, for pointing out the following error. Owing to a computing error in calculating the deviance the results on the likelihood ratio (LR) method in Table 1 were incorrect. It has now been recomputed and is shown below. Section 4 should be corrected as follows. In Table 1 when the maximum likelihood (ML) estimate existed all methods gave finite intervals. We note that both Newton's method and the grid search gave identical results for the LR intervals. Apart from the configuration a = 30 and ,3 =-15, the true confidence probability of the LR interval tended to fall below the nominal level. This was also shown by Williams (1986). The LR method did converge and gave the 95% confidence interval (1.8154, 1.9273) for the data set 10, 10, 6, 2, 1, 0, 0, 0. Also Newton's algorithm did converge for the data set 10, 10, 7, 0, 3, 0, 0, 0. The coverage probability of the LR interval was always between that of Fieller's method and the bootstrap, with Fieller's method being conservative. For most simulations the LR interval lay within the Fieller interval. The mean width and standard deviation of the width of the LR intervals were intermediate between those of Fieller and the bootstrap. In the second paragraph of Section 5 it should be stated that the precision of the LR intervals is intermediate between that of the Fieller and the bootstrap methods. The LR intervals performed better than the bootstrap in terms of coverage probability but Fieller's method is the only method that provides a probability of a type 1 error below the nominal level.