Analysis of Quantal Response Assays with Dosage Errors

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Abstract
This paper is concerned with the problem of estimating the parameters of a tolerance distribution when the dose is subject to error of administration, and when observation is limited to the quantal, or all-or-none, response. The case when the errors in dose follow the Poisson law with known mean equal to the nominal dose is considered as a numerical example. To put the problem in parametric form, a log-normal distribution function is postulated which coincides with the necessarily discrete tolerance distribution function at each possible integral value for the actual dose. The method of maximum likelihood is applied to obtain the estimating equations for the 2 parameters of the log-normal distribution, and these are solved by a series of iterative calculations. Hypothetical data are employed to illustrate the procedure. In principle, the computational procedure developed would require consideration of an infinite number of possible actual doses for each nominal dose employed. Two devices for dealing with this problem are suggested.

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