徐端正. 求LDx的加权近似法J. 药学学报, 1979, 14(5): 293-301.
引用本文: 徐端正. 求LDx的加权近似法J. 药学学报, 1979, 14(5): 293-301.
Xu Duanzheng. WEIGHTED APPROXIMATION METHOD FOR DETERMING LDxJ. Acta Pharmaceutica Sinica, 1979, 14(5): 293-301.
Citation: Xu Duanzheng. WEIGHTED APPROXIMATION METHOD FOR DETERMING LDxJ. Acta Pharmaceutica Sinica, 1979, 14(5): 293-301.

求LDx的加权近似法

WEIGHTED APPROXIMATION METHOD FOR DETERMING LDx

  • 摘要: 求LDx的最大或然性方法被公认为是最佳方法,但由于计算繁琐而费时往往迫使药理及生物检定工作者要求在不失其精确度的条件下,用简便的方法代替。本文提出用加权近似法求LDx,并有一套定型的公式以利计算。它略去最大或然性法的叠代过程,使计算大为简化。该法对最大或然性法是极好的近似,为了说明两者的近似程度,用加权近似法,最大或然性法以及顾汉颐氏提出的简化概率单位法作比较。最后,文章附录对简化概率单位法的不足提出评论。

     

    Abstract: It is agreed by most statisticians that in determing the LDx 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 LDx, 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, …, xk be the k logarithm doses with equally spaced I; p1, P2,…, Pk, the corresponding percentage of positive responses; y1, y2,…, yk, the probits and w1, w2,…, wk, 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.

     

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