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**A locally adaptive process-convolution model for estimating the health impact of air pollution.**
*(English)*
Zbl 1412.62163

Summary: 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.

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62P12 | Applications of statistics to environmental and related topics |

62H11 | Directional data; spatial statistics |

### Keywords:

air pollution; bivariate spatiotemporal modelling; process-convolution models; respiratory medication rates### References:

[1] | Banerjee, S., Gelfand, A. E., Finley, A. O. and Sang, H. (2008). Gaussian predictive process models for large spatial data sets. J. R. Stat. Soc. Ser. B. Stat. Methodol.70 825-848. · Zbl 1533.62065 · doi:10.1111/j.1467-9868.2008.00663.x |

[2] | Bhopal, R., Steiner, M., Cezard, G., Bansal, N., Fischbacher, C., Simpson, C., Douglas, A. and Sheikh, A. (2015). Risk of respiratory hospitalization and death, readmission and subsequent mortality: Scottish health and ethnicity linkage study. Eur. J. Public Health25 769-774. |

[3] | Blangiardo, M., Finazzi, F. and Cameletti, M. (2016). Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions. Spatial Spatio-temporal Epidemiol.18 1-12. |

[4] | Congdon, P. (2005). Bayesian Models for Categorical Data. Wiley, Chichester. · Zbl 1079.62036 |

[5] | Datta, A., Banerjee, S., Finley, A. O. and Gelfand, A. E. (2016). Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets. J. Amer. Statist. Assoc.111 800-812. |

[6] | Dibben, C. and Clemens, T. (2015). Place of work and residential exposure to ambient air pollution and birth outcomes in Scotland, using geographically fine pollution climate mapping estimates. Environ. Res.140 535-541. |

[7] | Dominici, F., Samet, J. and Zeger, S. (2000). Combining evidence on air pollution and daily mortality from the 20 largest US cities: A hierarchical modelling strategy. J. Roy. Statist. Soc. Ser. A163 263-302. |

[8] | Furrer, R., Genton, M. G. and Nychka, D. (2006). Covariance tapering for interpolation of large spatial datasets. J. Comput. Graph. Statist.15 502-523. |

[9] | Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian Data Analysis, 2nd ed. Chapman & Hall/CRC, Boca Raton, FL. · Zbl 1039.62018 |

[10] | Higdon, D. (1998). A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environ. Ecol. Stat.5 173-190. |

[11] | Huang, G., Lee, D. and Scott, E. (2018). Multivariate space-time modelling of multiple air pollutants and their health effects accounting for exposure uncertainty. Stat. Med.. 37. 1134-1148. |

[12] | Lee, D. (2018). Supplement to “A locally adaptive process-convolution model for estimating the health impact of air pollution.” DOI:10.1214/18-AOAS1167SUPPA, DOI:10.1214/18-AOAS1167SUPPB. · Zbl 1412.62163 |

[13] | Lee, D., Mukhopadhyay, S., Rushworth, A. and Sahu, S. (2017). A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health. Biostatistics18 370-385. |

[14] | Liechty, J. C., Liechty, M. W. and Müller, P. (2004). Bayesian correlation estimation. Biometrika91 1-14. · Zbl 1132.62314 · doi:10.1093/biomet/91.1.1 |

[15] | Lu, H., Reilly, C. S., Banerjee, S. and Carlin, B. P. (2007). Bayesian areal wombling via adjacency modeling. Environ. Ecol. Stat.14 433-452. |

[16] | Meyer, S. and Held, L. (2014). Power-law models for infectious disease spread. Ann. Appl. Stat.8 1612-1639. · Zbl 1304.62135 · doi:10.1214/14-AOAS743 |

[17] | Riebler, A., Held, L. and Rue, H. (2012). Estimation and extrapolation of time trends in registry data—Borrowing strength from related populations. Ann. Appl. Stat.6 304-333. · Zbl 1235.62030 · doi:10.1214/11-AOAS498 |

[18] | Royal College of Physicians (2016). Every breath we take: The lifelong impact of air pollution. Available at https://www.rcplondon.ac.uk/projects/outputs/every-breath-we-take-lifelong-impact-air-pollution. |

[19] | Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res.11 3571-3594. · Zbl 1242.62024 |

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