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RESP-4647

The review of adaptive assignment methods by Simon (1977) follows a similar review by Bailar (1976). Both authors point out that recent theoretical developments in clinical trial methodology have been almost totally ignored by practitioners. They reach similar conclusions, to the effect that the practitioners are on the whole correct in their implied judgment; the new methods, they hold, are not really well suited to the clinical trial field. There is no doubt that there are difficult problems, both practical and theoretical, with which adaptive methods have yet to come to terms. One of these relates to trials in which the response takes a long time to declare itself, so that it is unrealistic to suppose that the response on the ith subject is known at the time at which the treatment for the (i + l)th subject is to be determined. This situation is routine in the cancer field (it is to be noted that both Bailar and Simon wrote from cancer research centres) and is common in trials relating to a variety of chronic conditions. Another problem especially concerns methods which make it difficult to conceal the nature of the treatment from those concerned with administering it and assessing its consequences. A third points to difficulties arising from non-stationarity; if conditions change unpredictably in the course of a trial, adaptive methods may give rise to substantial biases. I do not wish to comment on this set of problems, except to say that they seem to me not to be logically insuperable and so to represent a challenge to clinical trial theorists. As things stand, they do present a set of good reasons for not embarking upon an adaptive trial at this time. Rather, I want to comment briefly on some other reasons given by Simon and Bailar which seem to me to be less well founded. These in fact relate to clinical trials in general and are not at all specific to those using adaptive methods. Simon in particular is critical of 'selection theory' methods in which the trial culminates in an explicit decision to recommend one or another of the treatments in the trial. 'Clinical trials', he states, 'are complicated experiments in which the evaluation of the treatments requires a careful summarization of all evidence concerning relative eSects. If there is little evidence that the treatments differ substantially in efficacy, then such a conclusion must be stated. Significance tests of the null hypothesis play an important role in the analysis and have evidential content that is meaningful to a wide variety of clinical investigators. Statisticians . . . have not dented the importance to clinicians of null 'p values' in interpreting and reporting complicated clinical results . . . Any design which does not provide for a convincing test of the null hypothesis has little chance of being adopted for general use.' With a decisionbased approach, 'there is no provision for concluding that . . . results for the treatments do not diSer more than might be expected by chance.' One reaction to Simon's emphasis on the importance of significance levels is to ask just what the clinician is expected to do with them. Presumably if treatment A gives significantly better results than treatment B (always having regard to undesirable side eSects), treatment A should be adopted for future patients since the evidence is that it is truly the better

Assessment of Skeletal Maturity and Prediction of Adult Height (TW2 Method). By J. M. Tanner, R. H. Whitehouse, W. A. Marshall, M. J. R. Healy and H. Goldstein. London and New York, Academic Press, 1975. vii, 99p. 31 cm. £9·00.

For both scientific and administrative reasons it is of vital importance to forecast the future course of the AIDS epidemic. There are essentially two ways of doing this. On the one hand, a mathematical model of the spread of the disease can be constructed and used to provide forecasts for as far ahead as is desired. At the other end of the spectrum, numbers of recorded cases can be plotted against time and the resulting curve extrapolated forwards. The model-based forecasts rely upon estimates of the model parameters which must to some extent be supplied by reference to the case data; as will appear, the extrapolation forecasts are far from being model-free. The purpose of this paper is to describe the data available on the UK epidemic and to see to what extent extrapolation forecasts can be reliably made.

where the sum of squares are derived from the standard analysis of variance. It is well known that R2 is misleading when used to compare the fit of regressions involving different numbers of predictors. The regression sum of squares cannot decrease when new predictors are added to the equation, so that increasing the number of predictors will usually increase R2 even when the true values of the new regression coefficients are zero. In a recent article, Draper (1984) shows that R2 is normally reduced when new replicate values of y are introduced at existing values of x. The situation is clear in terms of the analysis of variance. Suppose we fit the relationship y = X,B with k predictors plus a constant term. Given m x-values with p replicates at each, we get

The Analysis of Time Series: Theory and Practice. By C. Chatfield. London, Chapman & Hall, 1975. xiv, 263 p. 814″ £4·35.

It is proposed to assess the surprisingness of the latest observation in a time series, when only a very few earlier observations are available, by comparing it with a prediction based on weighted linear regression with weights decreasing exponentially into the past. An enormous quantity of statistical material is collected on a routine basis and published at more or less regular intervals. The problem of presenting such figures to best advantage is not a simple one; almost by definition, the figures are not collected in order to answer a few well-defined questions but rather so as to be available when new questions arise or, better, in order to stimulate questions that otherwise would not be asked. This last role requires that a new reading in an on-going series should be scrutinized so that it can be labelled as surprising or non-surprising according as it invites the comment "that seems peculiar" or "much as would have been expected". This is the monitoring problem, and the second comment indicates that the solution lies in comparing the new observation with some kind of expected result based on the previous values in the series. There is a very large literature on the subject and many fairly elaborate methods (notably those based on the work of Box and Jenkins (1970)) have been developed. It is however quite common for the series concerned to be very short, no more perhaps than five to ten readings in all, and then there is a requirement for very simple methods whose assumptions are both few and appar- ent. This note describes one such method which is mainly designed for annual figures; modifications to cope with seasonal variations will be briefly mentioned below. The method supposes, then, that we have a small number of equally spaced observations and that we wish to assess the surprisingness of the next observation in the series. It will usually be too restrictive to assume that the readings are varying about a constant mean, but with a short series it may be adequate to suppose that any trend is roughly linear. The proposal is then merely to fit a straight line to the data points, to derive from the line an expected or predicted value for the new point, and to judge the new value by the size oI its departure from expectation. The line can be fitted by simple regression, but it is possible to recognize the time-series aspect of the data by doing a weighted regression with the recent past weighted more heavily than more remote points. One possibility suggested by exponentially weighted moving averages (Chatfield, 1975, section 5.2.2) is to use weights which decrease by a constant factor with each successive step backwards in time. A difficulty occurs with the assessment of the statistical significance (the surprisingness) of the calculated deviation. It is of course technically possible to estimate the scatter about the fitted line, but with the short series envisaged here such an estimate will itself be exceed- ingly imprecise. The proposed method will really be satisfactory only when the precision

Stem-and-Leaf Displays (J. Emerson & D. Hoaglin). Letter Values: A Set of Selected Order Statistics (D. Hoaglin). Boxplots and Batch Comparison (J. Emerson & J. Strenio). Transforming Data (J. Emerson & M. Stoto). Resistant Lines for y Versus x (J. Emerson & D. Hoaglin). Analysis of Two-Way Tables by Medians (J. Emerson & D. Hoaglin). Examining Residuals (C. Goodall). Mathematical Aspects of Transformation (J. Emerson). Introduction to More Refined Estimators (D. Hoaglin, et al.). Comparing Location Estimators: Trimmed Means, Medians, and Trimean (J. Rosenberger & M. Gasko). M-Estimators of Location: An Outline of the Theory (C. Goodall). Robust Scale Estimators and Confidence Intervals for Location (B. Iglewicz). Index.

In a standard technique for comparing two fly-repellant sprays, batches of mice are treated with the two materials under test and are subsequently exposed under anaesthetic to attack by flies of the genus Stomoxys. A control untreated batch is similarly exposed for purposes of comparison. If replicate tests are carried out on several occasions, it is found that the attack rates in the control and in the treated mice vary considerably, and the problem arises of finding some stable basis for comparison. In practice, five mice are used on each occasion for each treatment and for the controls, and each mouse is exposed to attack by 20 flies (this figure is not exact, but the variations in the number of flies are small enough to be neglected). The percentage attack rate is worked out for each mouse, and these rates are then averaged to give three mean attack rates for each occasion of testing. Full biological details of the method will be published elsewhere by Mr. L. C. Stones.

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