Inherently Low Precision of Infectivity Titrations Using a Quantal Response

Infectivity* and pharmacological titrations appear at first sight to be very similar, not only in execution but also in interpretation. In both, the test preparation is serially diluted, a group of subjects is inoculated with each dilution and, in the case of quantal responses, to which this discussion is confined, the niumber of subjects responding to each dilution is recorded. The proportion of subjects responding is usually related to the logarithm of dose by a sigmoid curve which is roughly symmetrical. Finally, the potency of the preparation is often expressed in terms of the ED50, the dose causing 50% of subjects to responid, the precision with which this is dolne being clearly governed by the 'steepness' of the dose-response curve. The purpose of this paper is to suggest that the interpretations of infectivity and pharmacological titrations differ fundamentally owing to the completely different mechanisms by which the response is produced in the two cases and that infective particles act in a manner which restricts the steepness of the dose-response curve and consequently restricts the precision with which the ED50 of an infective preparation can be estimated. It will be shown that the greateAt precision predicted for infectivity titrations is considerably less than that attainable in pharmacological titrationis performed under the same conditions. The production of ani infective response is usually accoun-ted for by a hypothesis derived from pharmacology which postulates that there exists an lndividual Effective Dose (I.E.D.) for each subject such that a subject is certain to respond if it receives a dose equal to or greater than its I.E.D. The shape of the dose-responise curve is considered to be governed solely by the distributioln of I.E.D.s amongst the subjects (Finney [1952a], Wilson and Miles [1955]), assuming that errors in dosage can be ignored. This hypothesis offers a reasonable explanation for responses to particles, such as drug molecules, which are not selfreproducing. Such particles must cooperate to produce the response