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# Statistics in Medical Research

Statistical methods as applied to problems in medical research are, at first sight, no different from the application of such methods to any area of scientific endeavor. However, there are some important societal and technical aspects of medical research that warrant particular attention. At the societal level the issues relate to the impact on individual patients of intervention procedures, treatments and their side effects. The conduct and interpretation of medical trials is an extremely important issue, and decisions made regarding who is to be treated and how, and who is not to be treated, are often complex and can be distressing for all involved. Furthermore, inadequate design, implementation and reporting of trials can lead to erroneous conclusions, with potentially serious consequences. On a technical level there are specific techniques and protocols that have been developed to address many of these issues, but there remains continuing difficulties facing medical staff who need to understand and use appropriate statistical procedures whilst having an enormous number of other issues to deal with. Again, these problems can be addressed by early involvement of medical statisticians, although the scarcity of experienced specialists in this field is an additional concern. There is also an ongoing debate regarding the appropriateness of classical frequentist statistics, and even Bayesian statistics to many problems in medical research, bearing in mind the practical complexities and uncertainties associated with such work, especially for observational studies.

In 1937, the editor of The Lancet, writing in the foreword of Austin Bradford Hill's groundbreaking book "Principles of Medical Statistics" [BH1] summarized the position of statistics in medicine at that time as follows:

"In clinical medicine today there is a growing demand for adequate proof of the efficacy of this or that form of treatment. Often proof can come only by means of a collection of records of clinical trials devised on such a scale and in such a form that statistically reliable conclusions can be drawn from them. However great might be our aversion to figures, we cannot escape the conclusion that the solution of most of the problems of clinical or preventative medicine must ultimately depend on them"

Bradford Hill sought to provide an easily understood introduction to statistical concepts and methods for medical students, and his book [BH1] continued to be updated and published in many editions and in many translations, over a period of forty years. He was particularly concerned to ensure that the foundations of medical research benefited from sound underlying logical analysis and testing. To this end he was one of the initial proponents of randomized controlled trials (RCTs), which provide a key framework for current medical research exercises. In addition he devised a series of viewpoints on how suspected cause-effect relationships can be evaluated. Both of these areas are discussed in more detail below.

Bradford Hill was also extremely influential in bringing the idea of cohort studies to the fore through his work with Sir Richard Doll on the link between smoking and lung cancer. Their initial research was based on a case-control approach, but they then extended this work to a cohort study of over 30,000 British doctors. Cohort studies typically involve tracking the medical histories of a select group or cohort of individuals over many years. For example, in 2010 an international cohort study known as COSMOS was launched. The UK COSMOS cohort will follow the health of approximately 100,000 mobile phone users (18+ years old) for 20-30 years, and the international cohort will follow approximately 250,000 European mobile phone users over this period.

Considerable efforts have been made by many specialists with the aim of improving the understanding of statistics by medical professionals and in ensuring the quality of reporting in journal publications is of the highest standard (see especially, the excellent article and associated discussion in Altman and Bland, 1991 [ALT1], and the extensive set of short "Statistics Notes" by Altman, Bland and colleagues available via the British Medical Journal and more directly via Professor Bland's web page). The quality of published studies has been greatly aided by the production or adoption of guidelines by individual journals, and by the development of "statements" that explain how different types of research exercise should be reported. Perhaps the most important of these is CONSORT: "Consolidated Standards of Reporting Trials", which encompasses various initiatives to alleviate the problems arising from inadequate reporting of randomized controlled trials (RCTs). We discuss CONSORT further below. Other examples of such statements include STROBE "Strengthening the Reporting of Observational studies in Epidemiology", and the EQUATOR network, which is an international effort that seeks to "improve the reliability and value of medical research literature by promoting transparent and accurate reporting of research studies". Their 'reporting guidelines' section includes links to many useful websites and articles, including those already mentioned, and articles such as Olson et al. [OLS1] on the reporting of case-control studies.

As mentioned earlier, undertaking and reporting of medical research requires many specialized skills. Historically there has been insufficient training of medical researchers in statistical concepts and methods, and very real problems of communication between medical and statistical specialists. For example, the terms significance, variance and frequency may have a very different meaning to medical staff from those assigned by statisticians. To medics significance has the more usual interpretation of 'being significant' or important in the context of the medical problem under consideration — indeed, statisticians and medical journals now often play down the use of the term and the associated use of statistical significance levels (p-values). Estimation (identifying the typical range of values/effects) is rightly regarded as being of far greater relevance. For those involved in case-mix management (CMM) analysis of variance may refer to financial management (variation from targets) rather than having any statistical interpretation, whilst frequency can refer to how often a patient visits the toilet! As with many disciplines, technical terminology unfortunately may serve to confuse rather than clarify the subject.

There is no simple answer to these problems, although modern undergraduate and post-graduate teaching practice attempts to address the most important issues in a manner that medical specialists are likely to respond to and retain, long after the brief courses given have been completed. The leading medical journals, key medical reference web sites, the early involvement of medical statisticians, statistical consultancy and peer review, recently published precedents and the application of sound methodologies (such as the PPDAC model discussed earlier in this Handbook) will all serve to assist those engaging in medical research and trials for the first time.

The technical statistical procedures applicable to medical research are covered in the various main topics and sections of this Handbook. However, there are one or two specific topics that warrant further comment at this juncture. The two we have focused upon are Causation, and the Conduct and Reporting of Research. Each of these topics is discussed briefly in the subsections that follow.

An equally important topic, which is of particular relevance to medical research, is that of Bayesian analysis. We discuss aspects of Bayesian analysis at several points in this Handbook (e.g. see Yudowsky's example of breast cancer screening). Whilst not excluding classical frequentist statistics, a substantial number of scientists believe that Bayesian thinking is essential in the medical sphere — as Professor Campbell states in his commentary on Altman and Bland's paper (see also [CAM1]):

"Many doctors have an 'a priori' belief that the patient either has or does not have the disease and use the Bayesian paradigm to modify their beliefs. They find the idea of a null hypothesis existing without any probability attached to it counter-intuitive"

Other authors, including the leading Bayesian statistician Professor David Spiegelhalter, argue that for some problems only a Bayesian approach can provide a sensible answer, or in some instances, any answer at all.

We now take a closer look at the thorny question of causality, and how suspected cause-effect relationships can be identified and studied. We then consider some aspects of the conduct and reporting of medical research, including randomized controlled trials (RCTs), case-control studies and cohort studies. These procedures are a particular feature of modern medical research and RCT in particular is a development that has been largely championed in the medical statistics field.

References

[ALT1] Altman D G, Bland J M (1991) Improving Doctors' Understanding of Statistics. J of the Royal Stat. Soc., A, 154(2), 223-267

[BH1] Bradford Hill A (1937) Principles of Medical Statistics. The Lancet, London (issued in various editions until 1971. Then republished as "A Short Textbook of Medical Statistics" in 1977