Abstract

Background and aim: Two-stage designs have become standard tools in environmental epidemiology. These methods rely on the application of a random-effects meta-analysis to pool results from different locations. However, standard models do not account for potential correlation structures within and between locations, arising for example when pooling multi-parameter associations, multiple levels or hierarchies, and/or longitudinally and spatially-correlated estimates. In this contribution, we illustrate a unified framework and software for meta-analysis that flexibly extends the two-stage design to cover these and other applications.Methods: We extended the standard meta-analytic models along the lines of linear mixed-effects models, by allowing correlation between effect sizes to be modelled through a flexible random-effects structure. We derived (restricted) maximum likelihood estimators, and efficient computational strategies based on profiled methods alternating iterative generalized least squares and Newton-Raphson procedures. The analytic framework and inferential procedures are implemented in a new version of the R package mvmeta.Results: The modelling framework and its software implementation will be illustrated in a series of examples, using multi-city time series data for the analysis of health effects of air pollution and temperature. Various case studies will demonstrate different applications, such as: multilevel meta-analysis of effects across locations nested within countries; meta-analysis for spatially-correlated outcomes; longitudinal meta-analysis for repeatedly-measured effects to assess effect modification by time-varying predictors, such as air conditioning.Conclusions: The definition of a unified framework for meta-analysis, along with a freely-available software, will provide researchers with a flexible tool for addressing non-standard pooling problems in two-stage designs applied to environmental studies

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