Spatial Bayesian distributed lag non-linear models (SB-DLNM) for small-area exposure-lag-response epidemiological modelling

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.

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.

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.

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.