Serially balanced sequences in bioassay

Abstract

Some bioassay techniques involve applying a long sequence of doses on one or more subjects and measuring the response that occurs each time. In order to prevent trends in the responsiveness of a subject from inflating the experimental error, randomized block and Latin square designs have been adapted to these experiments. Such constraints take no account of any residual effect of a dose tending to increase or diminish the response associated with the subsequent dose. A serially balanced sequence for any specified number of different doses has a constraint like that of randomized blocks and an additional property that each dose is balanced in respect of the doses that immediately precede it in its several repetitions. A number of properties of these sequences have been investigated and certain simple categories have been enumerated. Sequences for four different doses are likely to be the most useful for parallel line bioassays. The statistical analysis of such assays, under a simple model for residual effects, is discussed, with particular reference to the choice of validity tests and of potency estimators. Tables have been prepared that enable the tests and estimates to be formed immediately from linear functions of the responses. Subsequent sections are concerned with the extension of these methods to assays involving a greater number of different doses, limitations on the utility of the sequences, and applications to other types of experiment. The paper ends with brief notes on the selection of a randomized sequence.