Estimating LD50s without a computer

Quantitative analysis of dose-related effects, such as mosquitoes killed by insecticide or parasites killed by a drug, usually involves estimating the dose which kills, on average, 50% of the subjects. This quantity is often termed the LD(50) (LD for lethal dose), or the ED(50) (ED for effective dose). Other specified response levels, such as the LD(90) - the dose that kills 90% of subjects - may also be derived. Dose-related effects of this type follow an S-shaped curve because, clearly, doses lower than those giving zero response will also give zero response, while at the other end of the curve, doses above those giving a maximum response can also only give a maximum response. In other words the curve flattens out at both ends. The mathematics of fitting a suitable S-shaped curve to such data - for example by probit analysis - is quite simple in principle but can be arduous and time-consuming without a suitably programmed computer. In this article, Michael Healy explains an alternative approach which is particularly applicable to field observations where computers are unavailable.