The median lethal dose and its estimation

Abstract

An important paper by Zbinden and Fluri-Roversi (1981) has shown the many weaknesses in any policy or regulatory system that regards an estimated LD₅₀ in an animal species as an adequate guide to toxicity in man. The present paper draws attention to some statistical aspects of LD₅₀ estimation that are too often neglected or misunderstood when this quantity is wanted. It is solely concerned with practice when a LD₅₀ must be estimated, and deliberately does not approach the broader issues of whether the LD₅₀ should be estimated.

A first need is clear distinction between the true but unknown form of dependence of mortality on dose and the estimate of it (or of a particular property such as the LD₅₀) that is obtainable from an experiment. Some assumptions are necessary before any estimation is possible. The graphical and semi-graphical methods that once were popular because of their simplicity and speed are today only reasonable as a last resort, when data are wholly inadequate and all that can be found is a very rough preliminary indication. Many “simple” arithmetical methods have been shown to be inherently bad, in that equally simple alternatives are usually more precise and less subject to bias. The Spearman-Kärber method remains as a useful possibility, demanding little knowledge of the form of the response curves but often needing other unverifiable assumptions. For most purposes, maximum likelihood estimation of a parametric formulation of the response curve is the best choice, not only because of theoretical merits but also because it can now be performed on a microcomputer in a very few seconds.