A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health.

In the United Kingdom, air pollution is linked to around 40000 premature deaths each year, but estimating its health effects is challenging in a spatio-temporal study. The challenges include spatial misalignment between the pollution and disease data; uncertainty in the estimated pollution surface; and complex residual spatio-temporal autocorrelation in the disease data. This article develops a two-stage model that addresses these issues. The first stage is a spatio-temporal fusion model linking modeled and measured pollution data, while the second stage links these predictions to the disease data. The methodology is motivated by a new five-year study investigating the effects of multiple pollutants on respiratory hospitalizations in England between 2007 and 2011, using pollution and disease data relating to local and unitary authorities on a monthly time scale.

A spatio-temporal model for estimating the long-term effects of air pollution on respiratory hospital admissions in Greater London.

It has long been known that air pollution is harmful to human health, as many epidemiological studies have been conducted into its effects. Collectively, these studies have investigated both the acute and chronic effects of pollution, with the latter typically based on individual level cohort designs that can be expensive to implement. As a result of the increasing availability of small-area statistics, ecological spatio-temporal study designs are also being used, with which a key statistical problem is allowing for residual spatio-temporal autocorrelation that remains after the covariate effects have been removed. We present a new model for estimating the effects of air pollution on human health, which allows for residual spatio-temporal autocorrelation, and a study into the long-term effects of air pollution on human health in Greater London, England. The individual and joint effects of different pollutants are explored, via the use of single pollutant models and multiple pollutant indices.

A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution.

Estimation of the long-term health effects of air pollution is a challenging task, especially when modeling spatial small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial autocorrelation structure in these data, which is accounted for using random effects modeled by a globally smooth conditional autoregressive model. These smooth random effects confound the effects of air pollution, which are also globally smooth. To avoid this collinearity a Bayesian localized conditional autoregressive model is developed for the random effects. This localized model is flexible spatially, in the sense that it is not only able to model areas of spatial smoothness, but also it is able to capture step changes in the random effects surface. This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models. These results are established using a simulation study, and are then illustrated with our motivating study on air pollution and respiratory ill health in Greater Glasgow, Scotland in 2011. The model shows substantial health effects of particulate matter air pollution and nitrogen dioxide, whose effects have been consistently attenuated by the currently available globally smooth models.

Flexible regression models over river networks.

Many statistical models are available for spatial data but the vast majority of these assume that spatial separation can be measured by Euclidean distance. Data which are collected over river networks constitute a notable and commonly occurring exception, where distance must be measured along complex paths and, in addition, account must be taken of the relative flows of water into and out of confluences. Suitable models for this type of data have been constructed based on covariance functions. The aim of the paper is to place the focus on underlying spatial trends by adopting a regression formulation and using methods which allow smooth but flexible patterns. Specifically, kernel methods and penalized splines are investigated, with the latter proving more suitable from both computational and modelling perspectives. In addition to their use in a purely spatial setting, penalized splines also offer a convenient route to the construction of spatiotemporal models, where data are available over time as well as over space. Models which include main effects and spatiotemporal interactions, as well as seasonal terms and interactions, are constructed for data on nitrate pollution in the River Tweed. The results give valuable insight into the changes in water quality in both space and time.

Distributed lag models for hydrological data.

The distributed lag model (DLM), used most prominently in air pollution studies, finds application wherever the effect of a covariate is delayed and distributed through time. We specify modified formulations of DLMs to provide computationally attractive, flexible varying-coefficient models that are applicable in any setting in which lagged covariates are regressed on a time-dependent response. We investigate the application of such models to rainfall and river flow and in particular their role in understanding the impact of hidden variables at work in river systems. We apply two models to data from a Scottish mountain river, and we fit to some simulated data to check the efficacy of our model approach. During heavy rainfall conditions, changes in the influence of rainfall on flow arise through a complex interaction between antecedent ground wetness and a time-delay in rainfall. The models identify subtle changes in responsiveness to rainfall, particularly in the location of peak influence in the lag structure.