BACKGROUND Distributed lag non-linear models (DLNMs) are the reference framework for modelling lagged non-linear associations. They are usually used in large-scale multi-location studies. Attempts to study these associations in small areas either did not include the lagged non-linear effects, did not allow for geographically-varying risks or downscaled risks from larger spatial units through socioeconomic and physical meta-predictors when the estimation of the risks was not feasible due to low statistical power. METHODS Here we proposed spatial Bayesian DLNMs (SB-DLNMs) as a new framework for the estimation of reliable small-area lagged non-linear associations, and demonstrated the methodology for the case study of the temperature-mortality relationship in the 73 neighbourhoods of the city of Barcelona. We generalized location-independent DLNMs to the Bayesian framework (B-DLNMs), and extended them to SB-DLNMs by incorporating spatial models in a single-stage approach that accounts for the spatial dependence between risks. RESULTS The results of the case study highlighted the benefits of incorporating the spatial component for small-area analysis. Estimates obtained from independent B-DLNMs were unstable and unreliable, particularly in neighbourhoods with very low numbers of deaths. SB-DLNMs addressed these instabilities by incorporating spatial dependencies, resulting in more plausible and coherent estimates and revealing hidden spatial patterns. In addition, the Bayesian framework enriches the range of estimates and tests that can be used in both large- and small-area studies. CONCLUSIONS SB-DLNMs account for spatial structures in the risk associations across small areas. By modelling spatial differences, SB-DLNMs facilitate the direct estimation of non-linear exposure-response lagged associations at the small-area level, even in areas with as few as 19 deaths. The manuscript includes an illustrative code to reproduce the results, and to facilitate the implementation of other case studies by other researchers.

中文翻译：

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用于小区域暴露-滞后-反应流行病学建模的空间贝叶斯分布滞后非线性模型 (SB-DLNM)。


背景技术分布式滞后非线性模型（DLNM）是用于对滞后非线性关联进行建模的参考框架。它们通常用于大规模多地点研究。在小区域研究这些关联的尝试要么不包括滞后的非线性效应，要么不考虑地理变化的风险，或者当风险估计不可行时，通过社会经济和物理元预测因子缩小较大空间单位的风险由于统计功效低。方法在这里，我们提出了空间贝叶斯 DLNM（SB-DLNM）作为估计可靠小区域滞后非线性关联的新框架，并演示了该地区 73 个邻域温度与死亡率关系案例研究的方法。巴塞罗那市。我们将位置无关的 DLNM 推广到贝叶斯框架 (B-DLNM)，并通过在单阶段方法中合并空间模型来将其扩展到 SB-DLNM，该方法考虑了风险之间的空间依赖性。结果 案例研究的结果强调了将空间成分纳入小区域分析的好处。从独立的 B-DLNM 获得的估计值不稳定且不可靠，特别是在死亡人数非常低的社区。 SB-DLNM 通过合并空间依赖性来解决这些不稳定性，从而产生更合理、更连贯的估计并揭示隐藏的空间模式。此外，贝叶斯框架丰富了可用于大区域和小区域研究的估计和测试范围。结论 SB-DLNM 解释了小区域风险关联的空间结构。 通过对空间差异进行建模，SB-DLNM 有助于直接估计小区域水平的非线性暴露-反应滞后关联，甚至在死亡人数少至 19 人的地区也是如此。该手稿包括一个说明性代码，用于重现结果，并促进其他研究人员实施其他案例研究。