PROBIT-METOD

PROBIT-METOD (English. probability unit - probabilistic unit) — one of methods of mathematical statistics applied in medical researches. The hl is used. obr. for definition of effective or lethal doses of biologically active compounds. This method consists in the analysis of experimental curves of efficiency or mortality on the basis of a function graph of integral of probability.

In experimental pharmacology and chemotherapy, toxicology, radiobiology and microbiology as parameters of efficiency of pharmaceuticals or harm of the damaging agents effective use averages (ED 50 ) or averages deadly (DL 50 ) doses (see). For their definition on several groups of animals study action of consistently increasing doses of substance (or ionizing radiation, etc.), registering in each group quantity of animals at whom the studied effect is observed (e.g., spasms, death, etc.). Placing in system of coordinates the frequency of emergence of effect in groups (on axis U, percentage of quantity of animals in group) against logarithms of the corresponding doses (on axis X), receive the symmetric S-shaped «characteristic curves» which are graphically expressing distribution of individual sensitivity of animals to this agent. On the basis of characteristic curves find ED5 values 0 or DL 30 , using the methods offered by Berens (V. of Behrens, 1929), Berens and Shlosser (V. of Behrens, L. Schlosser, 1957), and also Kerber's formula. However the linear interpolation allowing not only to define, but also to compare ED values is more convenient 50 or DL 50 for several substances at parallelism of straight lines.

As «characteristic curves» are symmetric, as well as a curve of the saved-up details (kumulyat) of normal distribution of Gauss, we will apply a method of rectification of a normal curve to them. Follows from the equation of a Gaussian curve that p = F(H-H 50 ) / ∑, where r — a share option at alternative distribution, F — integral of probabilities, X 50 = lg ED 50 (or lg DL 50 ); ∑ — a standard deviation. Using instead of value at — ψp, i.e. function, the return to integral of probabilities, we have the equation at = (X-X 50 ) / ∑, Krom can give a type of the equation of a straight line. Therefore, X 50 there is an abscissa of that point of a straight line, edges has ordinate ψp — 0. At at = — X correspond to 1 and +1 values X 50 — ∑ and X 50 + ∑, i.e. X 16 and X 84 . To avoid negative values at, it is replaced with size at' = at + 5 as at at = ψp + the 5th absolute value at’ exceeds all negative values ψp which can meet in practice. Sizes at' call probitam. Values of the probit corresponding to the percent of effect (mortality) established in an experiment in group of animals determine by special tables.

To find size X 50 , and from it ED 50 (or DL 50 ), in system of coordinates postpone are punched against the corresponding values of logarithms of the doses (X) used in an experiment. The received points are located on the straight line having an inclination 1/δ. For definition of X 50 it is necessary to find an abscissa of that point of a straight line, ordinate a cut at' = 5 (since it corresponds at = 0 and r = 0,5). Abscissae which ordinates are equal in a scale of probit 4 and 6 correspond to lged 16 and lged 84 . Errors of a method depend on inaccuracy of carrying out a straight line through the found points. To draw the straight line which is best answering to experimental points apply Litchfild and Uilkokson's graphical method (J. T. Litchfield, F. Wilcoxon, 1949) pl V. B. Prozorovsky's (1962) way based on use of a method of least squares for is punched - the analysis of curves a dose — the answer and not demanding creation of the schedule.

Bibliography: White M. L. Elements of quantitative assessment of pharmacological effect, L., 1963; Prozorovsky V B. Use of a method of least squares for it is punched - the analysis of curves of a lethality, Pharm. and toksikol., t. 25, century 1, page 115, 1962; At r-@ and x V. Yu. Biometric methods, M., 1964; Finney D. J. Probit analysis, Cambridge, 1952; Litchfield J. T. a. Wilcoxon F. A simp’ified method of evaluating dose-effect experiments, J. Pharmacol, exp. Ther., v. 96, p. 99, 1949; W an u d D. R. Analysis of dose-response curves, Naunyn-Schmiedeberg’s Arch. exp. Path. Pharmak.P Bd 308, Suppl., S. 1, 1979.

I. V. Komissarov.