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Meta-analysis is the combination of data from several studies to produce a single estimate. From the statistical point of view, meta-analysis is a straightforward application of multifactorial methods. We have several studies of the same thing, which might be clinical trials or epidemiological studies, perhaps carried out in different countries. Each trial gives us an estimate of an effect. We assume that these are estimates of the same global population value. We check the assumptions of the analysis, and, if these assumptions are satisfied, we combine the separate study estimates to make a common estimate. This is a multifactorial analysis, where the treatment or risk factor is one predictor variable and the study is another, categorical, predictor variable.

The main problems of meta-analysis arise before we begin the analysis of the data. First, we must have a clear definition of the question so that we only include studies which address this. For example, if we want to know whether lowering serum cholesterol reduces mortality from coronary artery disease, we would not want to include a study where the attempt to lower cholesterol failed.. On the other hand, if we ask whether dietary advice lowers mortality, we would include such a study. Which studies we include may have a profound influence on the conclusions (Thompson 1993). Second, we must have all the relevant studies. A simple literature search is not enough. Not all studies which have been started are published; studies which produce significant differences are more likely to be published than those which do not (e.g. Pocock and Hughes 1990; Easterbrook et al. 1991). Within a study, results which are significant may be emphasized and parts of the data which produce no differences may be ignored by the investigators as uninteresting. Publication of unfavourable results may be discouraged by the sponsors of research. Researchers who are not native English speakers may feel that publication in the English language literature is more prestigious as it will reach a wider audience, and so try there first, only publishing in their own language if they cannot publish in English. The English language literature may thus contain more positive results than do other literatures. The phenomenon by which significant and positive results are more likely to be reported, and reported more prominently, than non-significant and negative ones is called {\bf publication bias}. Thus we must not only trawl the published literature for studies, but use personal knowledge of ourselves and others to locate all the unpublished studies. Only then should we carry out the meta-analysis.

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