How to present statistics in medical journals.

In the 1990s the movement for ‘evidence-based medicine’, that medical decisions should be based on objective evidence rather than simply on experience, took off. Since then the number of medical studies involving the analysis of data has rapidly increased. Data arise from a variety of types of studies: clinical trials, observational studies, meta-analyses and others. There is a range of readily accessible sources of recommendations on how to present statistics in medical journals. The instructions for authors for this journal (http://www. oxfordjournals.org/our_journals/ageing/for_authors/) refer to two sources: the Uniform Requirements of the International Committee of Medical Journal Editors (ICMJE) (http://www. icjme.org, 2010) and the CONSORT statement [1]. The Uniform Requirements of the ICMJE include basic guidelines for presenting statistical information and state, among other things, that statistical methods should be described ‘with enough detail to enable a knowledgeable reader with access to the original data to verify the reported results’. The CONSORT statement is specifically directed at the reporting of parallel group randomised trials. The guidelines comprise 25 items covering the whole range of the report, almost all of them having a bearing on statistics. Many of these items also apply to other types of study and will be discussed below. Those which have particular relevance in a randomised trial include guidance on reporting the method of randomisation and blinding. Other guidelines available include the PRISMA statement [2], for reporting systematic reviews and meta-analyses, the STARD statement [3], for reporting studies of diagnostic accuracy, and the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) statement [4]. The existence of the STROBE guidelines is particularly important. Observational studies are the most common type of study used in medical research, but are also more likely than randomized trials to lead to erroneous conclusions, typically because of confounding. A well-known example was the finding, based on observational studies, that hormone replacement therapy (HRT) provided protection against coronary heart disease [5]. This was subsequently contradicted following several large randomised controlled trials [6]. The earlier incorrect finding was probably due to the likelihood that both risk of coronary heart disease and use of HRT are associated with socioeconomic status [7]. The most wellconducted observational study can produce misleading results if important confounders are not known. The STROBE checklist for reporting observational studies includes specific recommendations relating to potential confounders. It also suggests that in Discussion authors should ‘discuss limitations...taking into account sources of potential bias’ and ‘give a cautious overall interpretation of results’. There are STROBE checklists specifically for cohort, case–control and cross-sectional studies. For readers to be able to evaluate the strength of the conclusions which have been based on statistical evidence presented in a journal article, they need to know the aims of the study, how the data were collected, and how they were analysed. Statistical reviewers will be checking (as far as possible) the validity of the statistical methods used, and whether they are adequately explained and whether the conclusions are reasonable. The first step in describing how the data were collected is to name the study design. This should appear in the title or the abstract. For an observational study, this will usually be one of cohort (longitudinal), cross-sectional or case–control. Sometimes adjustments are made for confounding variables in the design of a study by matching the treatment groups with respect to the confounders. You should state whether a study is matched, and, if so, which matching variables were used, and whether the matching is, for example, pair wise. A study which is simply described as ‘matched’ could mean that the matching is paired, implying that a special form of analysis must be applied. Alternatively, the matching could be at the group level, carried out to ensure that the groups have a similar overall composition in terms of confounding variables and lead to a different analysis. It is important to avoid overmatching, where a matching variable is not a true confounder, or is redundant because it is highly correlated with other matching variables. An example of overmatching is given by Marsh et al. [8]. They investigated the relationship between cumulative radiation dose at Sellafield nuclear power station and mortality from leukaemia using a case– control study, matching on a number of variables including date of birth and date of entry. The relationship was not found to be significant. The conclusion was reversed when date of entry was omitted from the analysis, the rationale being that, by matching on both date of birth and date of entry, workers in the same matched sets had similar radiation doses. This obscured the relationship between dose and mortality. In evaluating the statistical evidence in a research paper, it can be difficult to distinguish between errors in presentation and errors in analysis. Poor presentation, apart from blurring findings, could suggest that are serious problems