Duncan Lee

A comparison of conditional autoregressive models used in Bayesian disease mapping

Disease mapping is the area of epidemiology that estimates the spatial pattern in disease risk over an extended geographical region, so that areas with elevated risk levels can be identified. Bayesian hierarchical models are typically used in this context, which represent the risk surface using a combination of available covariate data and a set of spatial random effects. These random effects are included to model any overdispersion or spatial correlation in the disease data, that has not been accounted for by the available covariate information. The random effects are typically modelled by a conditional autoregressive (CAR) prior distribution, and a number of alternative specifications have been proposed. This paper critiques four of the most common models within the CAR class, and assesses their appropriateness via a simulation study. The four models are then applied to a new study mapping cancer incidence in Greater Glasgow, Scotland, between 2001 and 2005.

Spatial Modeling of Air Pollution in Studies of Its Short-Term Health Effects

In studies that estimate the short-term effects of air pollution on health, daily measurements of pollution concentrations are often available from a number of monitoring locations within the study area. However, the health data are typically only available in the form of daily counts for the entire area, meaning that a corresponding single daily measure of pollution is required. The standard approach is to average the observed measurements at the monitoring locations, and use this in a log-linear health model. However, as the pollution surface is spatially variable this simple summary is unlikely to be an accurate estimate of the average pollution concentration across the region, which may lead to bias in the resulting health effects. In this article, we propose an alternative approach that jointly models the pollution concentrations and their relationship with the health data using a Bayesian spatio-temporal model. We compare this approach with the simple spatial average using a simulation study, by investigating the impact of spatial variation, monitor placement, and measurement error in the pollution data. An epidemiological study from Greater London is then presented, which estimates the relationship between respiratory mortality and four different pollutants.

Estimating exposure response functions using ambient pollution concentrations

This paper presents an approach to estimating the health effects of an environmental hazard. The approach is general in nature, but is applied here to the case of air pollution. It uses a computer model involving ambient pollution and temperature input to simulate the exposures experienced by individuals in an urban area, while incorporating the mechanisms that determine exposures. The output from the model comprises a set of daily exposures for a sample of individuals from the population of interest. These daily exposures are approximated by parametric distributions so that the predictive exposure distribution of a randomly selected individual can be generated. These distributions are then incorporated into a hierarchical Bayesian framework (with inference using Markov chain Monte Carlo simulation) in order to examine the relationship between short-term changes in exposures and health outcomes, while making allowance for long-term trends, seasonality, the effect of potential confounders and the possibility of ecological bias. The paper applies this approach to particulate pollution (PM 10 ) and respiratory mortality counts for seniors in greater London (≥65 years) during 1997. Within this substantive epidemiological study, the effects on health of ambient concentrations and (estimated) personal exposures are compared. The proposed model incorporates within day (or between individual) variability in personal exposures, which is compared to the more traditional approach of assuming a single pollution level applies to the entire population for each day. Effects were estimated using single lags and distributed lag models, with the highest relative risk, RR = 1.02 (1.01-1.04), being associated with a lag of two days ambient concentrations of PM 10 . Individual exposures to PM 10 for this group (seniors) were lower than the measured ambient concentrations with the corresponding risk, RR = 1.05 (1.01-1.09), being higher than would be suggested by the traditional approach using ambient concentrations.

Boundary detection in disease mapping studies

In disease mapping, the aim is to estimate the spatial pattern in disease risk over an extended geographical region, so that areas with elevated risks can be identified. A Bayesian hierarchical approach is typically used to produce such maps, which represents the risk surface with a set of random effects that exhibit a single global level of spatial smoothness. However, in complex urban settings, the risk surface is likely to exhibit localized rather than global spatial structure, including areas where the risk varies smoothly over space, as well as boundaries separating populations that are geographically adjacent but have very different risk profiles. Therefore, this paper proposes an approach for capturing localized spatial structure, including the identification of such risk boundaries. The effectiveness of the approach is tested by simulation, before being applied to lung cancer incidence data in Greater Glasgow, UK, between 2001 and 2005.

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.

Identifying clusters in Bayesian disease mapping

Disease mapping is the field of spatial epidemiology interested in estimating the spatial pattern in disease risk across [Formula: see text] areal units. One aim is to identify units exhibiting elevated disease risks, so that public health interventions can be made. Bayesian hierarchical models with a spatially smooth conditional autoregressive prior are used for this purpose, but they cannot identify the spatial extent of high-risk clusters. Therefore, we propose a two-stage solution to this problem, with the first stage being a spatially adjusted hierarchical agglomerative clustering algorithm. This algorithm is applied to data prior to the study period, and produces [Formula: see text] potential cluster structures for the disease data. The second stage fits a separate Poisson log-linear model to the study data for each cluster structure, which allows for step-changes in risk where two clusters meet. The most appropriate cluster structure is chosen by model comparison techniques, specifically by minimizing the Deviance Information Criterion. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland.

Cardiovascular disease and air pollution in Scotland: no association or insufficient data and study design?

BackgroundCoronary heart disease and stroke are leading causes of mortality and ill health in Scotland, and clear associations have been found in previous studies between air pollution and cardiovascular disease. This study aimed to use routinely available data to examine whether there is any evidence of an association between short-term exposure to particulate matter (measured as PM10, particles less than 10 micrograms per cubic metre) and hospital admissions due to cardiovascular disease, in the two largest cities in Scotland during the years 2000 to 2006.MethodsThe study utilised an ecological time series design, and the analysis was based on overdispersed Poisson log-linear models.ResultsNo consistent associations were found between PM10 concentrations and cardiovascular hospital admissions in either of the cities studied, as all of the estimated relative risks were close to one, and all but one of the associated 95% confidence intervals contained the null risk of one.ConclusionsThis study suggests that in small cities, where air quality is relatively good, then either PM10 concentrations have no effect on cardiovascular ill health, or that the routinely available data and the corresponding study design are not sufficient to detect an association.

Controlling for unmeasured confounding and spatial misalignment in long-term air pollution and health studies.

The health impact of long‐term exposure to air pollution is now routinely estimated using spatial ecological studies, owing to the recent widespread availability of spatial referenced pollution and disease data. However, this areal unit study design presents a number of statistical challenges, which if ignored have the potential to bias the estimated pollution–health relationship. One such challenge is how to control for the spatial autocorrelation present in the data after accounting for the known covariates, which is caused by unmeasured confounding. A second challenge is how to adjust the functional form of the model to account for the spatial misalignment between the pollution and disease data, which causes within‐area variation in the pollution data. These challenges have largely been ignored in existing long‐term spatial air pollution and health studies, so here we propose a novel Bayesian hierarchical model that addresses both challenges and provide software to allow others to apply our model to their own data. The effectiveness of the proposed model is compared by simulation against a number of state‐of‐the‐art alternatives proposed in the literature and is then used to estimate the impact of nitrogen dioxide and particulate matter concentrations on respiratory hospital admissions in a new epidemiological study in England in 2010 at the local authority level.

An integrated Bayesian model for estimating the long-term health effects of air pollution by fusing modelled and measured pollution data: a case study of nitrogen dioxide concentrations in Scotland

The long-term health effects of air pollution can be estimated using a spatio-temporal ecological study, where the disease data are counts of hospital admissions from populations in small areal units at yearly intervals. Spatially representative pollution concentrations for each areal unit are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over grid level concentrations from an atmospheric dispersion model. We propose a novel fusion model for estimating spatially aggregated pollution concentrations using both the modelled and monitored data, and relate these concentrations to respiratory disease in a new study in Scotland between 2007 and 2011.