Extended two-stage designs for environmental research

The two-stage design has become a standard tool in environmental epidemiology to model multi-location data. However, its standard form is rather inflexible and poses important limitations for modelling complex risks associated with environmental factors. In this contribution, we illustrate multiple design extensions of the classical two-stage method, all implemented within a unified analytic framework.

We extended standard two-stage meta-analytic models along the lines of linear mixed-effects models, by allowing location-specific estimates to be pooled through flexible fixed and random-effects structures. This permits the analysis of associations characterised by combinations of multivariate outcomes, hierarchical geographical structures, repeated measures, and/or longitudinal settings. The analytic framework and inferential procedures are implemented in the R package mixmeta.

The design extensions are illustrated in examples using multi-city time series data collected as part of the National Morbidity, Mortality and Air Pollution Study (NMMAPS). Specifically, four case studies demonstrate applications for modelling complex associations with air pollution and temperature, including non-linear exposure-response relationships, effects clustered at multiple geographical levels, differential risks by age, and effect modification by air conditioning in a longitudinal analysis.

The definition of several design extensions of the classical two-stage design within a unified framework, along with its implementation in freely-available software, will provide researchers with a flexible tool to address novel research questions in two-stage analyses of environmental health risks.