Facilitating meta‐analyses by deriving relative effect and precision estimates for alternative comparisons from a set of estimates presented by exposure level or disease category

Epidemiological studies relating a particular exposure to a specified disease may present their results in a variety of ways. Often, results are presented as estimated odds ratios (or relative risks) and confidence intervals (CIs) for a number of categories of exposure, for example, by duration or level of exposure, compared with a single reference category, often the unexposed. For systematic literature review, and particularly meta-analysis, estimates for an alternative comparison of the categories, such as any exposure versus none, may be required. Obtaining these alternative comparisons is not straightforward, as the initial set of estimates is correlated. This paper describes a method for estimating these alternative comparisons based on the ideas originally put forward by Greenland and Longnecker, and provides implementations of the method, developed using Microsoft Excel and SAS. Examples of the method based on studies of smoking and cancer are given. The method also deals with results given by categories of disease (such as histological types of a cancer). The method allows the use of a more consistent comparison when summarizing published evidence, thus potentially improving the reliability of a meta-analysis.