Modelling spatio‐temporal variation in exposure to particulate matter: a two‐stage approach

Abstract

SUMMARYStudies investigating associations between air pollution exposure and health outcomes benefit from the estimation of exposures at the individual level, but explicit consideration of the spatio-temporal variation in exposure is relatively new in air pollution epidemiology. We address the problem of estimating spatially and temporally varying particulate matter concentrations (black smoke = BS = PM 4 ) using data routinely collected from 20 monitoring stations in Newcastle-upon-Tyne between 1961 and 1992. We propose a two-stage strategy for modelling BS levels. In the first stage, we use a dynamic linear model to describe the long-term trend and seasonal variation in area-wide average BS levels. In the second stage, we account for the spatio-temporal variation between monitors around the area-wide average in a linear model that incorporates a range of spatio-temporal covariates available throughout the study area, and test for evidence of residual spatio-temporal correlation. We then use the model to assign time-aggregated predictions of BS exposure, with associated prediction variances, to each singleton pregnancy that occurred in the study area during this period, guided by dates of conception and birth and mothers' residential locations. In work to be reported separately, these exposure estimates will be used to investigate relationships between maternal exposure to BS during pregnancy and a range of birth outcomes. Our analysis demonstrates how suitable covariates can be used to explain residual spatio-temporal variation in individual-level exposure, thereby reducing the need to model the residual spatio-temporal correlation explicitly.

Predicting intra‐urban variation in air pollution concentrations with complex spatio‐temporal dependencies

“…It would be straightforward to also calculate a prediction variance at each location, taking a similar approach to Fanshawe et al (2008). We do not pursue this here, however, because separate uncertainty estimates for each location are not helpful if the objective is to use the predicted concentrations to estimate the health effect in an environmental epidemiology study.…”

“…For an overview of techniques for modeling correlated spatio-temporal data, see Banerjee et al (2004). A recent paper by Fanshawe et al (2008) emphasizes the role of carefully chosen covariates in obviating the need to accommodate spatio-temporal correlation in the residuals, but the model in that paper assumes a uniform time trend across locations. Paciorek et al (2008) and Sahu et al (2006) model particulate matter using techniques that allow for more complex spatio-temporal dependencies, however their estimation and prediction procedures are applicable only with relatively well aligned monitoring data.…”

Spatial analysis of health effects of large industrial incinerators in England, 1998–2008: a study using matched case–control areas

“…As this method is only valid when there is no residual spatial correlation, we apply the diagnostic test for residual spatial correlation used by Fanshawe et al, 30 comparing the sample correlation of the distances between LSOA centroids and the squared differences between their residuals to that obtained by repeated random assignment of residuals. We also carry out tests of deviance to compare different models, allowing for overdispersion.…”

A flexible spatio-temporal model for air pollution with spatial and spatio-temporal covariates

“…There are also several methods developed specifically for the modeling of air pollution data (Smith et al, 2003; Sahu et al, 2006; Calder, 2008; Fanshawe et al, 2008; Paciorek et al, 2009; De Iaco and Posa, 2012). However, these methods either require relatively complete observation matrices, or do not allow for sufficiently complex spatio-temporal dependencies.…”