Statistical Methods in Medical Research

Peter Armitage, Geoffrey Berry, J. N. S. Matthews

• Publisher: Wiley-Blackwell
• Year: 2013
• ISBN:
  9781118702581
• Edition: 4
• Topic: Medicina
• Subtopic: Bioestadística

The explanation and implementation of statistical methods for the medical researcher or statistician remains an integral part of modern medical research. This book explains the use of experimental and analytical biostatistics systems. Its accessible style allows it to be used by the non-mathematician as a fundamental component of successful research.

Since the third edition, there have been many developments in statistical techniques. The fourth edition provides the medical statistician with an accessible guide to these techniques and to reflect the extent of their usage in medical research.

The new edition takes a much more comprehensive approach to its subject. There has been a radical reorganization of the text to improve the continuity and cohesion of the presentation and to extend the scope by covering many new ideas now being introduced into the analysis of medical research data. The authors have tried to maintain the modest level of mathematical exposition that characterized the earlier editions, essentially confining the mathematics to the statement of algebraic formulae rather than pursuing mathematical proofs.

Received the Highly Commended Certificate in the Public Health Category of the 2002 BMA Books Competition.

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 contraceptives had to consider a number of other variables that are associated with breast cancer and which might differ between users and non-users of oral contraceptives. These variables included age, age at first live birth (2.7-fold effect between age 30 or older and less than 20 years), a socio-economic index (twofold effect), year of marriage and family history of breast cancer (threefold effect). After making allowance for these possible confounding variables as necessary, the risk of breast cancer for users of oral contraceptives was estimated as 1.15 times the risk for non-users, a weak association in comparison with the size of the associations with some of the other variables that had to be considered.

4 A further example of the use of statistical arguments is a study to quantify illness in babies under 6 months of age reported by Cole et al. (1991). It is important that parents and general practitioners have an appropriate method for identifying severe illness requiring referral to a specialist paediatrician. Whether this is possible can only be determined by the study of a large number of babies for whom possible signs and symptoms are recorded, and for whom the severity of illness is also determined. In this study the authors considered 28 symptoms and 47 physical signs. The analysis showed that it was sufficient to use seven of the symptoms and 12 of the signs, and each symptom or sign was assigned an integer score proportional to its importance. A baby’s illness score was then derived by adding the scores for any signs or symptoms that were present. The score was then considered in three categories, 0–7, 8–12 and 13 or more, indicating well or mildly ill, moderate illness and serious illness, respectively. It was predicted that the use of this score would correctly classify 98% of the babies who were well or mildly ill and correctly identify 92% of the seriously ill.

These examples come from different fields of medicine. A review of research in any one branch of medicine is likely to reveal the pervasive influence of the statistical approach, in laboratory, clinical and epidemiological studies. Consider, for instance, research into the human immunodeficiency virus (HIV) and the acquired immune deficiency syndrome (AIDS). Early studies extrapolated the trend in reported cases of AIDS to give estimates of the future incidence. However, changes in the incidence of clinical AIDS are largely determined by the trends in the incidence of earlier events, namely the original HIV infections. The timing of an HIV infection is usually unknown, but it is possible to use estimates of the incubation period to work backwards from the AIDS incidence to that of HIV infection, and then to project forwards to obtain estimates of future trends in AIDS. Estimation of duration of survival of AIDS patients is complicated by the fact that, at any one time, many are still alive, a standard situation in the analysis of survival data (Chapter 17). As possible methods of treatment became available, they were subjected to carefully controlled clinical trials, and reliable evidence was produced for the efficacy of various forms of combined therapy. The progression of disease in each patient may be assessed both by clinical symptoms and signs and by measurement of specific markers. Of these, the most important are the CD4 cell count, as a measure of the patient’s immune status, and the viral load, as measured by an assay of viral RNA by the polymerase chain reaction (PCR) method or some alternative test. Statistical questions arising with markers include their ability to predict clinical progression (and hence perhaps act as surrogate measures in trials that would otherwise require long observation periods); their variability, both between patients and on repeated occasions on the same patient; and the stability of the assay methods used for the determinations.

Statistical work in this field, as in any other specialized branch of medicine, must take into account the special features of the disease under study, and must involve close collaboration between statisticians and medical experts. Nevertheless, most of the issues that arise are common to work in other branches of medicine, and can thus be discussed in fairly general terms. It is the purpose of this book to present these general methods, illustrating them by examples from different medical fields.

Statistical investigations

The statistical investigations described above have one feature in common: they involve observations of a similar type being made on each of a group of individuals. The individuals may be people (as in 1–4 above), animals, blood samples, or even inanimate objects such as birth certificates or parishes. The need to study groups rather than merely single individuals arises from the presence of random, unexplained variation. If all patients suffering from the common cold experienced well-defined symptoms for precisely 7 days, it might be possible to demonstrate the merits of a purported drug for the alleviation of symptoms by administering it to one patient only. If the symptoms lasted only 5 days, the reduction could safely be attributed to the new treatment. Similarly, if blood pressure were an exact function of age, varying neither from person to person nor between occasions on the same person, the blood pressure at age 55 could be determined by one observation only. Such studies would not be statistical in nature and would not call for statistical analysis. Those situations, of course, do not hold. The duration of symptoms from the common cold varies from one attack to another; blood pressures vary both between individuals and between occasions. Comparisons of the effects of different medical treatments must therefore be made on groups of patients; studies of physiological norms require population surveys.

In the planning of a statistical study a number of administrative and technical problems are likely to arise. These will be characteristic of the particular field of research and cannot be discussed fully in the present context. Two aspects of the planning will almost invariably be present and are of particular concern to the statistician. The investigator will wish the inferences from the study to be sufficiently precise, and will also wish the results to be relevant to the questions being asked. Discussions of the statistical design of investigations are concerned especially with the general considerations that bear on these two objectives. Some of the questions that arise are: (i) how to select the individuals on which observations are to be made; (ii) how to decide on the numbers of observations falling into different groups; and (iii) how to allocate observations between different possible categories, such as groups of animals receiving different treatments or groups of people living in different areas.

It is useful to make a conceptual distinction between two different types of statistical investigation, the experiment and the survey. Experimentation involves a planned interference with the natural course of events so that its effect can be observed. In a survey, on the other hand, the investigator is a more passive observer, interfering as little as possible with the phenomena to be recorded. It is easy to think of extreme examples to illustrate this antithesis, but in practice the distinction is sometimes hard to draw. Consider, for instance, the following series of statistical studies:

1 A register of deaths occurring during a particular year, classified by the cause of death.

2 A survey of the types of motor vehicle passing a checkpoint during a certain period.

3 A public opinion poll.

4 A study of the respiratory function (as measured by various tests) of men working in a certain industry.

5 Observations of the survival times of mice of three different strains, after inoculation with the same dose of a toxic substance.

6 A clinical trial to compare the merits of surgery and conservative treatment for patients with a certain condition, the subjects being allotted randomly to the two treatments.

Studies 1 to 4 are clearly surveys, although they involve an increasing amount of interference with nature. Study 6 is equally clearly an experiment. Study 5 occupies an equivocal position. In its statistical aspects it is conceptually a survey, since the object is to observe and compare certain characteristics of three strains of mice. It happens, though, that the characteristic of interest requires the most extreme form of interference—the death of the animal—and the non-statistical techniques are more akin to those of a laboratory experiment than to those required in most survey work.

The general principles of experimental design will be discussed in §9.1, and those of survey design in §§19.2 and 19.4.

2

Describing data

2.1 Diagrams

One of the principal methods of displaying statistical information is the use of diagrams. Trends and contrasts are often more readily apprehended, and perhaps retained longer in the memory, by casual observation of a well-proportioned diagram than by scrutiny of the corresponding numerical data presented in tabular form. Diagrams must, however, be simple. If too much information is presented in one diagram it becomes too difficult to unravel and the reader is unlikely even to make the effort. Furthermore, details will usually be lost when data are shown in diagrammatic form. For any critical analysis of the data, therefore, reference must be made to the relevant numerical quantities.

Statistical diagrams serve two main purposes. The first is the presentation of statistical information in articles and other reports, when it may be felt that the reader will appreciate a simple, evocative display. Official statistics of trade, finance, and medical and demographic data are often illustrated by diagrams in newspaper articles and in annual reports of government departments. The powerful impact of diagrams makes them also a potential means of misrepresentation by the unscrupulous. The reader should pay little attention to a diagram unless the definition of the quantities represented and the scales on which they are shown are all clearly explained. In research papers it is inadvisable to present basic data solely in diagrams because of the loss of detail referred to above. The use of diagrams here should be restricted to the emphasis of important points, the detailed evidence being presented separately in tabular form.

The second main use is as a private aid to statistical analysis. The statistician will often have recourse to diagrams to gain insight into the structure of the data and to check assumptions which might be made in an analysis. This informal use of diagrams will often reveal new aspects of the data or suggest hypotheses which may be further investigated.

Various types of diagrams are discussed at appropriate points in this book. It will suffice here to mention a few of the main uses to which statistical diagrams are put, illustrating these from official publications.

1 To compare two or more numbers. The comparison is often by bars of different lengths (Fig. 2.1), but another common method (the pictogram) is to use rows of repeated symbols; for example, the populations of different countries may b...