WEIGHTED APPROXIMATION METHOD FOR DETERMING LD_x

It is agreed by most statisticians that in determing the LD_x of a drug the probir method would give a satisfactory solution. However, the computation required for probit analysis with maximum likelihood method is tedious and time consuming. Research workers are clearly justified in pressing statisticians to invent simpler methods of analysis.This article presents an alternative method of probit analysis for determing LD_x, the "weighted approximation method". This is much simpler than the method of maximum likelihood and is a good approximation to the latter.Let x₁, x₂, …, x_k be the k logarithm doses with equally spaced I; p₁, P₂,…, P_k, the corresponding percentage of positive responses; y₁, y₂,…, y_k, the probits and w₁, w₂,…, w_k, the weights of corresponding probits, in which y and w may be obtained from the tables listed in the text.With the analysis of weighted linear regression, the slope of weighted regression lineb= CA/IB (1) then and the standard deviation of M (2)there C=1 for an odd number of doses, C=2 for an even number of doses, the calculation of A and B are tabulated as follows:With polynomial coefficients λ of linear regression, formulae (1) and (2) may be for an arbitrary number of doses.An example is described which describes that the weighted approximation method has a negligible error, while the simplified probit method already recommended by Gu Hanyi has an unnegligible error as compared with the maximum likelihood method.A criticism of "simplified probit method" is presented in the appendix.