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.
Highlights
In many statistical applications a common challenge arises when trying to assess meaningful relationships between explanatory variables and outcomes through re-S
In its present formulation, profile regression has only been used for studies based on cohorts or surveys where information on the predictors/outcomes is available on each individual; in this paper we extend the method to fit small area studies, commonly used in epidemiological surveillance or in studies where the interest lies on the spatial variability of an outcome (Barcelo et al, 2009) or on cluster detection (Abellan et al, 2008; Li et al, 2012)
Molitor et al (2010) developed methods to process this output to make useful and interpretable inference. Several methods for this are available in the R package PReMiuM but we find the most robust method is to process the similarity matrix using partitioning around medoids (PAM), which is available in the R package cluster
Summary
In many statistical applications a common challenge arises when trying to assess meaningful relationships between explanatory variables and outcomes through re-S. Profile regression is a Bayesian non– parametric method which assesses the link between potentially collinear variables and a response through cluster membership. This allows to formally take into account the correlation between the variables without the need to create a summary score, giving more flexibility to the inferential process. Profile regression has been used on several applications in environmental and social epidemiology and the R package PReMiuM (Liverani et al, 2015) makes it readily available to any applied researcher. Profile regression has been used in environmental epidemiology (Pirani et al, 2015), for studying risk functions associated with multi-dimensional exposure profiles (Hastie et al, 2013; Molitor et al, 2014) as well as for looking for gene–gene interactions (Papathomas et al, 2012)
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