An algorithm for the calculation of distribution parameters in an analysis of the dose-effect curve

Conclusion

An algorithm is proposed for calculating the parameters of the statistical distribution of the dose-effect curve on the basis of the principle of piecewise-linear approximation. The computer program enables an estimate of the mean dose (equivalent to the value ED₅₀ as applied to a normal distribution) and the error of its determination to be obtained; a check on the hypothesis of the normality of the statistical distribution is carried out by the method of moments and Kolmogorov's criterion; if this hypothesis is correct, the values of ED₀₂₅ and ED₉₇₅ are calculated. Since the algorithm is not connected with any a priori hypothesis concerning the nature of the distribution of the probability of the effect, the estimate obtained by using it is free from the distortions inherent in the method of probit anaylsis [1]. At the same time, the possibility of approximating the empirical distribution by the normal distribution is taken into account and is checked by the extremely strict criterion of moments and Kolmogorov's criterion. The corresponding check has shown that some of the empirical distributions of the probability of a lethal effect of antibiotics that we have encountered in acute experiments on mice definitely do not belong to the normal type. In this case, the estimate of the mean dose cannot be expressed by the idea of ED₅₀, which is quite permissible for a normal distribution in which the mathematical expectation and the median coincide. In addition to the variance of the distribution of the probability of the effect, we also calculated the variance of the summed binomial distribution of the tests of various doses, which estimates the error in the estimate of the mean dose. This estimate is weakly connected with the nonuniformity of the distribution of the symptom of sensitivity to the preparation in the population and therefore permits the approximation of the binomial distributions to the normal distribution to a considerably greater extent. It is proposed to calculate the confidence intervals for the estimate of the mean dose for the 5% level of significance on the basis of the latter program.