The Annals of Applied Statistics

A locally adaptive process-convolution model for estimating the health impact of air pollution

Duncan Lee

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Most epidemiological air pollution studies focus on severe outcomes such as hospitalisations or deaths, but this underestimates the impact of air pollution by ignoring ill health treated in primary care. This paper quantifies the impact of air pollution on the rates of respiratory medication prescribed in primary care in Scotland, which is a proxy measure for the prevalence of less severe respiratory disease. A novel bivariate spatiotemporal process-convolution model is proposed, which: (i) has increased computational efficiency via a tapering function based on nearest neighbourhoods; and (ii) has locally adaptive weights that outperform traditional distance-decay kernels. The results show significant effects of particulate matter on respiratory prescription rates which are consistent with severe endpoint studies.

Article information

Ann. Appl. Stat., Volume 12, Number 4 (2018), 2540-2558.

Received: October 2017
Revised: February 2018
First available in Project Euclid: 13 November 2018

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Air pollution bivariate spatiotemporal modelling process-convolution models respiratory medication rates


Lee, Duncan. A locally adaptive process-convolution model for estimating the health impact of air pollution. Ann. Appl. Stat. 12 (2018), no. 4, 2540--2558. doi:10.1214/18-AOAS1167.

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Supplemental materials

  • Supplement A: Additional results and data analysis. Section 1 contains additional data summaries, while Section 2 presents predictive analysis for the pollution data. Section 3 presents exploratory analysis of the prescription data, while Section 4 presents the reproducibility materials. Section 5 provides theoretical results, while Section 6 presents sensitivity analyses.
  • Supplement B: Supplementary data and code. Code and data for applying the model proposed in Section 3 to the GP data.