Meta‐analytic approaches to dose‐response relationships, with application in studies of lung cancer and exposure to environmental tobacco smoke

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Abstract
This paper outlines several meta‐analytic approaches to the assessment of quantal dose—response relationships; that is, to the evaluation of an increase in the level of exposure to an agent and the associated relative risk of a disease when this is investigated over a number of different studies. Analysis is developed at two levels: first, a consistent method of evaluating the dose—response relationship is applied to each study, and second, an overall picture is obtained by comparing and combining these relationships. At the first stage, for an individual study, dose—response assessment involves choices of model and appropriate tests for trend, which are influenced by such issues as dose measurement and use of the unexposed group. At the second stage, different methods for pooling results across studies must be considered. These depend on the choices made in the first stage of analysis, with additional attention paid to heterogeneity, and possible bias due to studies included in meta‐analysis. We describe these meta‐analytic approaches for three methods of evaluating dose response. The approaches are illustrated by evaluating the relationship between lung cancer and levels of exposure to environmental tobacco smoke (ETS). The strength of this relationship has been a point of debate in recent assessment of evidence for an overall carcinogenic effect of ETS exposure. We find little indication of a consistent dose response, a result explained in terms of recent models for cancer and passive smoking developed by Darby and Pike, the current meta‐analysis results of overall risk‐ratios of current studies in Tweedie and Mengersen, and misclassification models developed by the United States Environmental Protection Agency (EPA).