The error of determination of toxicity / by J.W. Trevan.

  • Trevan, J. W. (John William)
Date:
1927?]
Catalogue details

Licence: In copyright

Credit: The error of determination of toxicity / by J.W. Trevan. Source: Wellcome Collection.

    17/36 page 497
    Let N be the number of animals injected with a dose near the LD 50, D the deviation of dose (reckoned as a percentage of the dose) corresponding to three times the standard deviation of the mortality, K the ratio of the percentage increase of dose to percentage increase in mortality, and p the probability of survival, and q that of death, with the dose injected, p and q being 0-5 for the average lethal dose. Then let three times the standard deviation of deaths = d. d = 3V pgN. Let d be reckoned as percentage of N = d'. d' = 3VWn x 100_ N Since D/d' = K, for parts of the curve which approximate to straight lines, then DN DVN 300 V^N ~ * 300 Vpq = K’ 300 Ky/pq “ D 90,000 K2 pq D2 For cocaine, the value, for the median lethal dose, of K is 0-510 and for N = 30, the error of the average lethal dose is D2 _ 90,000 X (0-510)2 X 0-5 X 0-5 30 D = ± 14-05, as against + 17*75 or — 12-2, as worked out by the graphic method (p. 493). The formula applies to values of D not larger than about 20 per cent., provided that only the ££ straight ” part of the characteristic is involved in the calculation. For very small values (up to 5 per cent.) of D, it is applicable to any part of the curve—the value of K being the ratio of the percentage increment of dose at the point under investigation to the percentage increment in mortality. The estimate of the accuracy of the determination of the toxicity clearly depends on the liability of casual groups of animals of sufficient size to give characteristics of the same shape, and average lethal doses of the same magnitude. Observations on the toxicity of cocaine over a period of more than twelve months have shown that at different intervals the percentage mortality for any given dose does not vary significantly from that given in the curve.
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