Letter | Published:

Quantal Responses to Mixtures of Drugs

Naturevolume 180pages712713 (1957) | Download Citation



THE joint action of two drugs can be termed ‘non-interactive’ if, when applied together, neither modifies the physiological action of the other that leads to the response under consideration1. We have previously formulated the relation between dose and quantal response for the extreme forms of this type of joint action, namely, simple similar action1, in which the drugs act on the same physiological system, and independent action1,2, in which they act on different systems. The relation for independent action allowed different degrees of correlation of the tolerances for the respective drugs ; but the relation for simple similar action allowed only their complete positive correlation. We have now extended this work, first to cover types of non-interactive joint action intermediate between the extreme forms, and secondly, to permit any degree of correlation of tolerances for every form of non-interactive joint action. Since interactive joint action can be formulated as a generalization of non-interactive1, the whole theory of quantal responses to mixtures of drugs is thereby unified.

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  1. 1

    Plackett, R. L., and Hewlett, P. S., J. Roy. Statist. Soc., Ser. B. 14, 141 (1952).

  2. 2

    Plackett, R. L., and Hewlett, P. S., Ann. App. Biol., 35, 347 (1948).

  3. 3

    Turner, N., Connecticut Agric. Exp. Sta. Bull. No. 594 (1955).

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  1. Pest Infestation Laboratory, Slough

    • P. S. HEWLETT
  2. Department of Applied Mathematics, University of Liverpool

    • R. L. PLACKETT


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