1

The scope of statistics

In one sense medical statistics are merely numerical statements about medical matters: how many people die from a certain cause each year, how many hospital beds are available in a certain area, how much money is spent on a certain medical service. Such facts are clearly of administrative importance. To plan the maternity-bed service for a community we need to know how many women in that community give birth to a child in a given period, and how many of these should be cared for in hospitals or maternity homes. Numerical facts also supply the basis for a great deal of medical research; examples will be found throughout this book. It is no purpose of the book to list or even to summarize numerical information of this sort. Such facts may be found in official publications of national or international health departments, in the published reports of research investigations and in textbooks and monographs on medical subjects. This book is concerned with the general rather than the particular, with methodology rather than factual information, with the general principles of statistical investigations rather than the results of particular studies.

Statistics may be defined as the discipline concerned with the treatment of numerical data derived from groups of individuals. These individuals will often be people-for instance, those suffering from a certain disease or those living in a certain area. They may be animals or other organisms. They may be different administrative units, as when we measure the case-fatality rate in each of a number of hospitals. They may be merely different occasions on which a particular measurement has been made.

Why should we be interested in the numerical properties of groups of people or objects? Sometimes, for administrative reasons like those mentioned earlier, statistical facts are needed: these may be contained in official publications; they may be derivable from established systems of data collection such as cancer registries or systems for the notification of congenital malformations; they may, however, require specially designed statistical investigations.

This book is concerned particularly with the uses of statistics in medical research, and here-in contrast to its administrative uses-the case for statistics has not always been free from controversy. The argument occasionally used to be heard that statistical information contributes little or nothing to the progress of medicine, because the physician is concerned at any one time with the treatment of a single patient, and every patient differs in important respects from every other patient. The clinical judgement exercised by a physician in the choice of treatment for an individual patient is based to an extent on theoretical considerations derived from an understanding of the nature of the illness. But it is based also on an appreciation of statistical information about diagnosis, treatment and prognosis acquired either through personal experience or through medical education. The important argument is whether such information should be stored in a rather informal way in the physician's mind, or whether it should be collected and reported in a systematic way. Very few doctors acquire, by personal experience, factual information over the whole range of medicine, and it is partly by the collection, analysis and reporting of statistical information that a common body of knowledge is built and solidified.

The phrase evidence-based medicine is often applied to describe the compilation of reliable and comprehensive information about medical care (Sackett et al., 1996). Its scope extends throughout the specialties of medicine, including, for instance, research into diagnostic tests, prognostic factors, therapeutic and prophylactic procedures, and covers public health and medical economics as well as clinical and epidemiological topics. A major role in the collection, critical evaluation and dissemination of such information is played by the Cochrane Collaboration, an international network of research centres (http://www.cochrane.org/).

In all this work, the statistical approach is essential. The variability of disease is an argument for statistical information, not against it. If the bedside physician finds that on one occasion a patient with migraine feels better after drinking plum juice, it does not follow, from this single observation, that plum juice is a useful therapy for migraine. The doctor needs statistical information showing, for example, whether in a group of patients improvement is reported more frequently after the administration of plum juice than after the use of some alternative treatment.

The difficulty of arguing from a single instance is equally apparent in studies of the aetiology of disease. The fact that a particular person was alive and well at the age of 95 and that he smoked 50 cigarettes a day and drank heavily would not convince one that such habits are conducive to good health and longevity. Individuals vary greatly in their susceptibility to disease. Many abstemious non-smokers die young. To study these questions one should look at the morbidity and mortality experience of groups of people with different habits: that is, one should do a statistical study.

The second chapter of this book is concerned mainly with some of the basic tools for collecting and presenting numerical data, a part of the subject usually called descriptive statistics. The statistician needs to go beyond this descriptive task, in two important respects. First, it may be possible to improve the quality of the information by careful planning of the data collection. For example, information on the efficacy of specific treatments is most reliably obtained from the experimental approach provided by a clinical trial (Chapter 18), and questions about the aetiology of disease can be tackled by carefully designed epidemiohgical surveys (Chapter 19). Secondly, the methods of statistical inference provide a largely objective means of drawing conclusions from the data about the issues under research. Both these developments, of planning and inference, owe much to the work of R.A. (later Sir Ronald) Fisher (1890-1962), whose influence is apparent throughout modern statistical practice.

Almost all the techniques described in this book can be used in a wide variety of branches of medical research, and indeed frequently in the non-medical sciences also. To set the scene it may be useful to mention four quite different investigations in which statistical methods played an essential part.

1 MacKie et al. (1992) studied the trend in the incidence of primary cutaneous malignant melanoma in Scotland during the period 1979-89. In assessing trends of this sort it is important to take account of such factors as changes in standards of diagnosis and in definition of disease categories, changes in the pattern of referrals of patients in and out of the area under study, and changes in the age structure of the population. The study group was set up with these points in mind, and dealt with almost 4000 patients. The investigators found that the annual incidence rate increased during the period from 3.4 to 7.1 per 100 000 for men, and from 6.6 to 10.4 for women. These findings suggest that the disease, which is known to be affected by high levels of ultraviolet radiation, may be becoming more common even in areas where these levels are relatively low. 2 Women who have had a pregnancy with a neural tube defect (NTD) are known to be at higher than average risk of having a similar occurrence in a future pregnancy. During the early 1980s two studies were published suggesting that vitamin supplementation around the time of conception might reduce this risk. In one study, women who agreed to participate were given a mixture of vitamins including folic acid, and they showed a much lower incidence of NTD in their subsequent pregnancies than women who were already pregnant or who declined to participate. It was possible, however, that some systematic difference in the characteristics of those who participated and those who did not might explain the results. The second study attempted to overcome this ambiguity by allocating women randomly to receive folic acid supplementation or a placebo, but it was too small to give clear-cut results. The Medical Research Council (MRC) Vitamin Study Research Group (1991) reported a much larger randomized trial, in which the separate effects could be studied of both folic acid and other vitamins. The outcome was clear. Of 593 women receiving folic acid and becoming pregnant, six had NTD; of 602 not receiving folic acid, 21 had NTD. No effect of other vitamins was apparent. Statistical methods confirmed the immediate impression that the contrast between the folic acid and control groups is very unlikely to be due to chance and can safely be ascribed to the treatment used. 3 The World Health Organization carried out a collaborative case-control study at 12 participating centres in 10 countries to investigate the possible association between breast cancer and the use of oral contraceptives (WHO Collaborative Study of Neoplasia and Steroid Contraceptives, 1990). In each hospital, women with breast cancer and meeting specific age and residential criteria were taken as cases. Controls were taken from women who were admitted to the same hospital, who satisfied the same age and residential criteria as the cases, and who were not suffering from a condition considered as possibly influencing contraceptive practices. The study included 2116 cases and 13 072 controls. The analysis of the association between breast cancer and use of oral...