Evaluating the effect of neighbourhood weight matrices on smoothing properties of Conditional Autoregressive (CAR) models

Arul Earnest¹ , Geoff Morgan¹^,2 , Kerrie Mengersen³ , Louise Ryan⁴ , Richard Summerhayes¹^,5 and John Beard¹^,5^,6

¹Northern Rivers University Department of Rural Health, The University of Sydney, New South Wales, Australia

²Population Health & Planning, North Coast Area Health Service, New South Wales, Australia

³Faculty of Science, Queensland University of Technology, Queensland, Australia

⁴Department of Biostatistics, Harvard School of Public Health, Boston, USA

⁵Graduate Research College, Southern Cross University, New South Wales, Australia

⁶Centre for Urban Epidemiologic Studies. New York Academy of Medicine, New York, USA

author email corresponding author email

International Journal of Health Geographics 2007, 6:54doi:10.1186/1476-072X-6-54


Published:	29 November 2007

Abstract

Background

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. We examined this issue in detail.

Methods

We 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.

Results

We 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.

Conclusion

We 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.