Abstract
BackgroundThe Conditional Autoregressive (CAR) model is widely used in many small-area ecological studies to analyse outcomes measured at an areal level. There has been little evaluation of the influence of different neighbourhood weight matrix structures on the amount of smoothing performed by the CAR model. We examined this issue in detail.MethodsWe created several neighbourhood weight matrices and applied them to a large dataset of births and birth defects in New South Wales (NSW), Australia within 198 Statistical Local Areas. Between the years 1995–2003, there were 17,595 geocoded birth defects and 770,638 geocoded birth records with available data. Spatio-temporal models were developed with data from 1995–2000 and their fit evaluated within the following time period: 2001–2003.ResultsWe were able to create four adjacency-based weight matrices, seven distance-based weight matrices and one matrix based on similarity in terms of a key covariate (i.e. maternal age). In terms of agreement between observed and predicted relative risks, categorised in epidemiologically relevant groups, generally the distance-based matrices performed better than the adjacency-based neighbourhoods. In terms of recovering the underlying risk structure, the weight-7 model (smoothing by maternal-age 'Covariate model') was able to correctly classify 35/47 high-risk areas (sensitivity 74%) with a specificity of 47%, and the 'Gravity' model had sensitivity and specificity values of 74% and 39% respectively.ConclusionWe found considerable differences in the smoothing properties of the CAR model, depending on the type of neighbours specified. This in turn had an effect on the models' ability to recover the observed risk in an area. Prior to risk mapping or ecological modelling, an exploratory analysis of the neighbourhood weight matrix to guide the choice of a suitable weight matrix is recommended. Alternatively, the weight matrix can be chosen a priori based on decision-theoretic considerations including loss, cost and inferential aims.
Highlights
The Conditional Autoregressive (CAR) model is widely used in many small-area ecological studies to analyse outcomes measured at an areal level
The expected count of birth defects in each areal unit at a particular time period was defined as Ei = (Birthsi/Totalbirths)*Totalbirthdefects, where Birthsi refers to total births in the ith Statistical Local Area (SLA), and Totalbirths and Totalbirthdefects refer to the overall number of births and birth defects in the New South Wales (NSW) study region for that particular time-period
The number of birth defects recorded during the time periods 1995–1997, 1998–2000 and 2001–2003 that we used in the analysis were 5924, 6161 and 5510 respectively
Summary
The Conditional Autoregressive (CAR) model is widely used in many small-area ecological studies to analyse outcomes measured at an areal level. There has been little evaluation of the influence of different neighbourhood weight matrix structures on the amount of smoothing performed by the CAR model The Conditional Autoregressive (CAR) model is widely used in small-area ecological studies to map outcomes measured at some areal level and to examine associations with covariates. Most of these applications are in the field of disease mapping (See Elliott for a list of studies [1]). Lawson highlights some of the applications of CAR models in disease mapping studies [3]
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