D. J. Finney

Serially Balanced Sequences in Bioassay

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.

Cross-over designs in bioassay

The precision of biological assays is increased if each subject can be tested with several different doses of the materials under assay, so that the estimate of relative potency is based upon intra-subject comparison of responses. In some assay techniques, doses can be given simultaneously at different sites on a subject. In others, a time-sequence of doses is inevitable, and any response may be affected by the previous doses or responses of the same subject. Five models are elaborated, these involving combinations of error correlation, residual dose effects, and autoregressive effects of previous responses to represent mathematically the expected and observed responses. Cross-over designs, involving a balancing of dose sequences for different subjects, permit estimation of the important parameters of the models by analysis of variance and least-squares techniques. Three designs, each applicable to a 4-point parallel line assay, are discussed in detail. These are the twin cross-over, in which only two doses are tested on each subject, and the orthogonal square and serially balanced single-square designs in which each subject receives in turn all four doses. The construction of the analysis of variance, tests of assay validity and the formation of estimates of relative potency are described for each model. Despite their different logical bases, the model involving correlation and additive residual dose effects and that for a simple autoregressive scheme always lead to essentially the same statistical analysis; this analysis seems likely to be fairly insensitive to small deviations from the strict specifications of the models, and its use is an insurance against the possibility that one of the more complicated models is applicable. A final section describes the randomization necessary in the selection of a particular design.

Statistical science and effective scientific communication

Modern science increasingly uses sophisticated statistical techniques, yet papers in scientific journals are often defective in identification of methods used and in clear presentation of quantitative conclusions. The omission of essential information, ambiguities and misleading conclusions from ill-chosen methods often escape editorial challenge: referees, usually chosen for expertise in the substantive subject matter, may lack the statistical skill and experience needed for critical assessment. This paper makes proposals that might enable an editor and his referees more readily to detect the need for major revision before publication. Some matters have ethical components in addition to their implications for the advancement of knowledge in many disciplines.

A note on the history of regression

The first notion of statistical regression is usually attributed to Francis Galton. Recent work in a special field of applied statistics has brought to light the work of the neglected pioneer R. J. Adcock. Despite errors of execution, he deserves remembering in the history of our science. He came close to inventing linear regression; he also saw the need for specifying criteria for optimal estimation of parameters, and, with a little clearer understanding, he might have become the first recorded maximizer of likelihood.

Symbols and Terminology in Biometry

The many biologists whose work requires statistical science must be concerned for sound management and interpretation of quantitative data. Biometricians also need increased care for literacy and clarity in speech and writing, with precise phrasing for every numerical statement. This paper illustrates common confusions that arise from inexact terminology, or from words and symbols used without adequate definition. Careless statements on quantitative relations, or on probabilities, may be ambiguous; bad practices seriously pollute scientific journals and obstruct transmission of information. Such faults can affect daily life for a modem citizen. Pedantry is unwanted, and to be dogmatic about corrective measures would be stupid. This paper suggests that biologists and biometricians should examine the practicability of a system yet to be devised for standardizing use of symbols and the generally accepted terminology for the methods, techniques, and processes of statistical analysis. The outcome should influence all that we biometricians say and do - as authors, as consultants, and as referees for journals.

Design of Experiments

In earlier chapters, I have discussed a very simple experiment on two treatments. In many practical situations, the subjects or materials fall naturally into groups, or can be organized as groups.