Standard applications of meta-analysis consider a single effect-size estimated from independent studies. However, extensions to deal with more complex meta-analytical problems have been presented, such as multivariate, network, multilevel, dose-response, longitudinal meta-analysis and meta-regression. These extensions are characterised by non-independence among effect-sizes with a complex correlation structures that need to be modelled or accounted for. In my PhD, I reviewed and brought together these different extensions, developing a coherent extended mixed-effects framework for meta-analysis. The framework is built on the link between meta-analysis and linear mixed effects models, where patterns of effect sizes are modelled through a flexible structure of fixed and random terms. The extended mixed-effects framework for meta-analysis has been implemented in the R package mixmeta. Meta analytic models are often applied to environmental epidemiology using two-stage designs. In this setting, location-specific exposure-response associations are estimated in the first stage, and then the estimates are pooled using meta-analytic methods in the second stage. In my PhD, I illustrated multiple design extensions of the classical two-stage method, all implemented using the extended mixed-effects framework described above. In addition, I applied the framework and related software to show the advantages of using the extended two-stages design in environmental epidemiology studies, allowing a clearer characterisation of the short-term health effects of environmental stressors. In these applications, I first explored the role of urban characteristics in modifying the effects of temperature on health. Then I used a multi-country, multi-city, longitudinal design to quantify the independent role of air conditioning in the attenuation of heath related health risk. Finally, I developed a twostage ecological modelling approach to examine the impact of meteorological variables on SARS-CoV-2 transmission. The extended mixed-effects framework for meta-analysis and related software has proved to be a valid and useful analytical tool to address research questions on environmental health risks and beyond.
