title: Modelling collinear and spatially correlated data.
abstract: In this work we present a statistical approach to distinguish and interpret the complex relationship between several predictors and a response variable at the small area level, in the presence of (i) high correlation between the predictors and (ii) spatial correlation for the response. Covariates which are highly correlated create collinearity problems when used in a standard multiple regression model. Many methods have been proposed in the literature to address this issue. A very common approach is to create an index which aggregates all the highly correlated variables of interest. For example, it is well known that there is a relationship between social deprivation measured through the Multiple Deprivation Index (IMD) and air pollution; this index is then used as a confounder in assessing the effect of air pollution on health outcomes (e.g. respiratory hospital admissions or mortality). However it would be more informative to look specifically at each domain of the IMD and at its relationship with air pollution to better understand its role as a confounder in the epidemiological analyses. In this paper we illustrate how the complex relationships between the domains of IMD and air pollution can be deconstructed and analysed using profile regression, a Bayesian non-parametric model for clustering responses and covariates simultaneously. Moreover, we include an intrinsic spatial conditional autoregressive (ICAR) term to account for the spatial correlation of the response variable.
authors: Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, UK; Medical Research Centre Biostatistics Unit, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, UK; MRC-PHE Centre for Environment and Health, Department of Epidemiology and Biostatistics, Imperial College London, 2 Norfolk Place, London W2 8PG, UK. Electronic address: silvia.liverani@brunel.ac.uk.
authors: Silvia
authors: S
authors: Liverani
authors: Université Lille 3, UFR MIME, Domaine universitaire du Pont de Bois, BP 60149 59653 Villeneuve d'ascq Cedex, France. Electronic address: aurore.lavigne@univ-lille3.fr.
authors: Aurore
authors: A
authors: Lavigne
authors: MRC-PHE Centre for Environment and Health, Department of Epidemiology and Biostatistics, Imperial College London, 2 Norfolk Place, London W2 8PG, UK. Electronic address: m.blangiardo@imperial.ac.uk.
authors: Marta
authors: M
authors: Blangiardo
mesh_terms: D000397:Air Pollution / Q000009:adverse effects / Q000706:statistics & numerical data*; D001499:Bayes Theorem; D015986:Confounding Factors, Epidemiologic; D006801:Humans; D008131:London / Q000453:epidemiology; D008962:Models, Theoretical; D062211:Spatio-Temporal Analysis
keywords: Bayesian clustering; Collinearity; Index of multiple deprivation; Pollution; Profile regression; Spatial modelling