An accurate method for estimating an approximate lethal dose with few animals, tested with a Monte Carlo procedure

A reliable but not necessarily precise indication of the toxicity of a chemical product is frequently needed for the determination of its class of toxicity. Estimations of the LD50 carried out for this purpose often have a precision which is higher than necessary and so is the number of laboratory animals used. Alternative methods estimating an approximate lethal dose (ALD) have been proposed, but too little is known about their accuracy and precision. The method of Deichmann and LeBlanc (1943) for estimating an ALD has a systematic error, dependent upon the magnitude of the unknown variance of the log tolerance. A new method was developed in which this systematic error was removed. Its performance was tested in a model with Monte Carlo techniques. The model is based on the log-normal distribution of individual tolerance, i.e. the lowest dose that is lethal for an individual of the species under study. A hypothetical substance was created with a mean tolerance between 1 and 5,000 mg per kg and a standard deviation of log tolerance between 0.1 and 1.5 (in natural logarithms). This substance was then subjected to a sequential test, by repeatedly drawing a random element from the population of normally distributed log tolerance values and testing whether this element is smaller or greater than the dose administered according to the method's protocol. The method of Lorke (1983) was tested with a similar simulation model. In series of 100 simulations no systematic error was found. For a standard deviation of log tolerance exceeding 0.85 the new method was less precise than that of Lorke, but for smaller values the new method was more precise; it required on average less than ten animals, against 13 required in Lorke's method.