An interaction of medical and statistical ethics.

It is argued that the practice of omitting outliers when calibrating thromboplastin time, as recommended by the World Health Organization, should not continue unless it can be justified statistically and that possible harmful effects of omitting such data should be investigated.

Statistical science and quantitative understanding.

Authors of papers in biological journals need to make their uses of statistical methods and software explicit and maximally comprehensible. Editors and referees have important responsibilities for this. Inexact use of technical terminology causes confusion. Computer software is invaluable but not infallible. Graphical presentation should not conceal numerical results. Tests of statistical significance should be reserved for specific needs, which will rarely include multiple comparison procedures. Experiments that involve repeated measurements need special care in statistical analysis. Full attention should be given to principles of statistical estimation as well as to choice of appropriate statistical technique. At all times, ethical standards of scientific integrity must contribute to precision and clarity. Clinical research that neglects well-established statistical principles may be intrinsically unethical.

Calibration of thromboplastins.

Anticoagulant therapy with coumarin drugs requires tests on the patient's blood to determine the dose rate for the drug. The tests involve measuring the effect of a preparation of a certain reagent, thromboplastin, in accelerating the clotting of the patient's blood. Features of the World Health Organization's recommendation on the appropriate laboratory procedure for a calibration assay and evaluation of results call for comment. The standard method involves estimation of a linear structural relation, a statistical technique long known but seldom finding practical application. This paper reviews its history, as a prelude to discussing strange mistakes in earlier publications; it also examines assessment of the precision of estimation and other aspects of the statistical method.

A statistician looks at met-analysis.

I begin by considering origins and meanings for the term met-analysis/meta-analysis. The underlying ideas have a long history, not only in medical but also in the agricultural and social sciences. Met-analysis is a form of critical review of research on a stated topic, distinctive for its emphasis on producing quantitative conclusions. It is not in itself a specific technique, but rather an approach to aggregating information with the aid of critical deployment of standard statistical techniques. I shall discuss types of data on which met-analysis may be practised. These may be published papers or reports on past research, or the complete data on which such publications were based, whether from well-designed experiments or from other sources, or even--least satisfactorily--from spontaneously submitted information. Particular dangers are bias arising from the manner in which component studies are chosen, possibly affected by publication bias, and the pernicious influence of the modern tendency to deify the statistical significance test. A further important issue is that of the scale to be used as a measure of the effect of the treatment (or treatments) under study. I end with general comments on the conduct of met-analyses.

Ethical aspects of statistical practice.

This paper embodies a personal view of the ethical considerations that the author believes should be continuously in the mind of any applied statistician or biometrician whose work involves extensive collaboration with other persons and organizations. It looks particularly at the contribution of the International Statistical Institute to the codification of principles, the duties of the statistician in relation to data and the interests of his employer or client, his responsibilities to his professional colleagues and towards society as a whole, and, by no means least; the responsibility of the client towards the statistician who works with him.

Repeated measurements: what is measured and what repeats?

This paper expresses a personal view of experiments involving repeated measurements; it attempts to classify types of experiment and approaches to statistical analysis: no novel procedures are proposed, only a systematic outlook on objectives and methods.

Guidelines for immunoassay data processing.

These guidelines outline the minimum requirements for a data-processing package to be used in the immunoassay laboratory. They include recommendations on hardware, software, and program design. We outline the statistical analyses that should be performed to obtain the analyte concentrations of unknown specimens and to ensure adequate monitoring of within- and between-assay errors of measurement.

The median lethal dose and its estimation.

An important paper by Zbinden and Fluri-Roversi (1981) has shown the many weaknesses in any policy or regulatory system that regards an estimated LD50 in an animal species as an adequate guide to toxicity in man. The present paper draws attention to some statistical aspects of LD50 estimation that are too often neglected or misunderstood when this quantity is wanted. It is solely concerned with practice when a LD50 must be estimated, and deliberately does not approach the broader issues of whether the LD50 should be estimated. A first need is clear distinction between the true but unknown form of dependence of mortality on dose and the estimate of it (or of a particular property such as the LD50) that is obtainable from an experiment. Some assumptions are necessary before any estimation is possible. The graphical and semi-graphical methods that once were popular because of their simplicity and speed are today only reasonable as a last resort, when data are wholly inadequate and all that can be found is a very rough preliminary indication. Many "simple" arithmetical methods have been shown to be inherently bad, in that equally simple alternatives are usually more precise and less subject to bias. The Spearman-Kärber method remains as a useful possibility, demanding little knowledge of the form of the response curves but often needing other unverifiable assumptions. For most purposes, maximum likelihood estimation of a parametric formulation of the response curve is the best choice, not only because of theoretical merits but also because it can now be performed on a microcomputer in a very few seconds.

Response curves for radioimmunoassay.

In quantitative estimates from radioimmunoassay, one of four types of response curves is usually used: a freehand curve, a spline function, an equation based upon mass-action considerations, or a logistic equation. This paper comments briefly on the subjectivity and labor of the first and on the overparametrization of the second. It is chiefly concerned to compare the single binding-site equation with a simple or modified logistic. Whatever the theoretical merits of the binding-site approach (these are not under discussion), estimation of parameters is difficult. The paper shows that under many but not all circumstances a four- or five-parameter logistic will fit data at least as well over a wide range of doses. This is particularly so when both the binding-site concentration and the equilibrium constant are small.

Between medicine and law.

A recent experience as an expert witness in a legal action intended to prevent the fluoridation of water supplies has emphasized to me some of the problems of explaining statistical reasoning to persons unfamiliar with the mode of thought. The procedures of cross-examination are not ideal for clarifying scientific truth, and regrettably the language of statistics offers much scope for misunderstanding when words used technically are read with more colloquial meaning. I illustrate this by discussing the meaning of significance tests and by examples relating to the combination of independent test results, the misunderstanding of independence, covariance analysis, the use of interpolation, the relation between source of data and interpretation, and spurious correlation.

The detection of adverse reactions to therapeutic drugs.

The risk that a drug newly introduced into medical use will occasionally cause adverse reactions is neither negligible nor totally avoidable. Only well organized systems of monitoring can bring early detection and appropriate action. These in turn require either detailed supervision or spontaneous reporting. The paper is concerned with statistical inference from reports spontaneously submitted, and its logical limitations; it discusses strengths and weaknesses of the UK system, the detection process, and automated signalling.

The questioning statistician.

Effective statistical help to biological and medical research demands thorough involvement of the statistician. The breadth of his activities can be illustrated by considering the questions he needs to discuss with his scientific colleagues in the course of planning a comparative experiment. The paper presents and comments on 22 such questions, showing their relation to the objectives of the experiment, the utilization of resources, and the subsequent statistical analysis. A final paragraph urges that proper attention to all these points forms an integral part of an ethical approach to experimentation.

Radioligand Assay.

In radioimmunoassay and immunoradiometric assay, potency estimation involves the relation between counts of radioactivity and dose. Many workers have found the regression function to be satisfactorily represented by a logistic curve with limits that are themselves unknown parameters. This paper discusses estimation of all the parameters under the supposition (supported by empirical evidence) that the variance of a count is proportional to UJ, where U is the mean count at a dose and J is a parameter that almost certainly lies between 1.0 and 2.0. Estimation is found to be very robust, both in respect of the value taken for J and over alternative forms of least squares and maximum likelihood procedures. Special attention is given to whether the assay uses one or more doses of each test preparation, the former having important limitations but permitting some simplification of formulae. Requirements for a comprehensive computer program, suitable for routine use by assayists lacking statistical expertise and designed to produce potency estimates for a series of test preparations in one assay, are described. Data from an assay of oestradiol are used to illustrate various points.

A computer program for parallel line bioassays.

PARLIN is a program for the statistical analysis of biological assays that are either completely randomized, or in randomized blocks, in which the regression on log dose is linear with a constant variance per response. An earlier program (McArthur et al., J. Pharmacol. Exp. Ther. 153: 573-580, 1966) has been completely rewritten, improved and extended in its facilities. PARLIN, written in FORTRAN IV, will handle up to 99 test preparations, up to 100 doses in all, and up to 50 responses per dose. It is designed with special attention to simplicity for routine use, versatility of facilities and output immediately available for all forms of reporting results. A wide choice of transformations of response is available. The output reproduces the data for verification and tabulates potency estimates with limits at probabilities .95, .99; optional output includes an analysis of variance, information on validity, values of residuals and a rough plot of the dose-response relation.

Point and interval estimation in the combination of bioassay results.

A procedure for combining evidence from different biological assays is shown to be equivalent both to generalized least-squares and to maximum-likelihood estimation. By appropriate nesting of hypotheses, the likelihood function can be used to test the agreement between the assays and to obtain probability limits for the combined estimate of potency. The properties of these limits are examined, with particular reference to the situation, unusual but not impossible in practice, in which the values of relative potency that they define consist of several disjoint segments instead of a single interval. The connection with general theory of estimating linear functional relations is pointed out.