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.

中文翻译：

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用于环境研究的扩展两阶段设计

两阶段设计已成为环境流行病学中对多地点数据进行建模的标准工具。然而，它的标准形式相当不灵活，并且对与环境因素相关的复杂风险进行建模具有重要限制。在这篇文章中，我们说明了经典两阶段方法的多个设计扩展，所有这些都在统一的分析框架内实现。我们沿着线性混合效应模型扩展了标准的两阶段元分析模型，允许通过灵活的固定和随机效应结构汇集特定位置的估计。这允许分析以多变量结果、分层地理结构、重复测量和/或纵向设置的组合为特征的关联。分析框架和推理过程在 R 包 mixmeta 中实现。使用作为国家发病率、死亡率和空气污染研究 (NMMAPS) 的一部分收集的多城市时间序列数据的示例说明了设计扩展。具体而言，四个案例研究展示了对与空气污染和温度的复杂关联进行建模的应用，包括非线性暴露-反应关系、在多个地理层面聚集的影响、按年龄划分的不同风险以及纵向分析中空调对影响的影响。在统一框架内定义经典两阶段设计的几个设计扩展，以及在免费提供的软件中实现，