Interpolation between spatial frameworks: An application of process convolution to estimating neighbourhood disease prevalence

Abstract

Health data may be collected across one spatial framework (e.g. health provider agencies), but contrasts in health over another spatial framework (neighbourhoods) may be of policy interest. In the UK, population prevalence totals for chronic diseases are provided for populations served by general practitioner practices, but not for neighbourhoods (small areas of circa 1500 people), raising the question whether data for one framework can be used to provide spatially interpolated estimates of disease prevalence for the other. A discrete process convolution is applied to this end and has advantages when there are a relatively large number of area units in one or other framework. Additionally, the interpolation is modified to take account of the observed neighbourhood indicators (e.g. hospitalisation rates) of neighbourhood disease prevalence. These are reflective indicators of neighbourhood prevalence viewed as a latent construct. An illustrative application is to prevalence of psychosis in northeast London, containing 190 general practitioner practices and 562 neighbourhoods, including an assessment of sensitivity to kernel choice (e.g. normal vs exponential). This application illustrates how a zero-inflated Poisson can be used as the likelihood model for a reflective indicator.

Keywords

Spatial neighbourhood prevalence kernel convolution bayesian

Get full access to this article

View all access options for this article.

References

Department of Health. Quality and outcomes framework: online GP practice results database, 2011, http://www.qof.ic.nhs.uk/.

Office of National Statistics. Neighbourhood statistics: super output areas explained, 2011, http://neighbourhood.statistics.gov.uk/dissemination/Info.do?page=nessgeography/superoutputareasexplained/output-areas-explained.htm.

Lee

Higdon

Calder

. Efficient models for correlated data via convolutions of intrinsic processes. Stat Model 2005; 5: 53–74.

Calder

. Exploring latent structure in spatial temporal processes using process convolutions. PhD Thesis, Duke University: Durham, NC 27708, 2003.

Calder

. Dynamic factor process convolution models for multivariate space–time data with application to air quality assessment. Environ Ecol Stat 2007; 14: 229–247.

Kyriakidis

. A geostatistical framework for area-to-point spatial interpolation. Geograph Anal 2004; 36: 259–289.

Gotway

Young

. A geostatistical approach to linking geographically-aggregated data from different sources. J Comput Graph Stat 2007; 16: 115–135.

Goovaerts

. Geostatistical analysis of disease data: accounting for spatial support and population density in the isopleth mapping of cancer mortality risk using area-to-point Poisson kriging. Int J Health Geogr 2006; 5: 52–52. 2006 Nov 30.

Diamantopoulos

Siguaw

. Formative versus reflective indicators in organizational measure development: a comparison and empirical illustration. Br J Manage 2006; 17: 263–282.

10.

Wang

Wall

. Generalized common spatial factor model. Biostatistics 2003; 4: 569–582.

11.

Higdon

A primer on space–time modeling from a bayesian perspective, chapter 6. In: Finkenstädt

Held

Isham

(eds). Statistical methods for spatio-temporal systems, Boca Raton, FL: Chapman & Hall, 2007, pp. 217–279.

12.

Higdon

Swall

Kern

. Non-stationary spatial modeling. Bayesian statistics 6. Proceedings of the sixth valencia international meeting, Valencia: Spain, 6–10 June 1999, pp. 761–768.

13.

Higdon

. A process-convolution approach to modeling temperatures in the North Atlantic ocean. J Environ Ecol Stat 1998; 5: 173–190.

14.

Freeze

Raschke

. An assessment of formative and reflective constructs in IS research. In: ECIS 2007 proceedings. St. Gallen, 9–7 June 2007, Paper no. 171, http://aisel.aisnet.org/ecis2007/171.

15.

Allardyce

Gilmour

Atkinson

. Social fragmentation, deprivation and urbanicity: relation to first-admission rates for psychoses. Br J Psychiatry 2005; 187: 401–406.

16.

Böhning

Schlattmann

Dietz

Zero-inflated count models and their applications in public health and social science, chapter 32. In: Rost

Langeheine

(eds). Applications of latent trait and latent class models in the social sciences, Münster: Waxmann, 1997, pp. 333–344.

17.

Office of National Statistics. Super output area look-up files, 2011, http://www. neighbourhood.statistics.gov.uk/dissemination/Info.do?page=aboutneighbourhood/geography/superoutputareas/soalookupfiles/soa-constitutions.htm.

18.

Calder

. Efficient posterior inference and prediction of space-time processes using dynamic process convolutions. In: 2004 Conference of the international spatial accuracy research association 2004. Portland, ME, 28 June–1 July 2004, http://www.spatial-accuracy.org/Calder2004accuracy.

19.

Knorr-Held

Rainer

. Projections of lung cancer mortality in West Germany: a case study in Bayesian prediction. Biostatistics 2001; 2: 109–129.

20.

Venables

Ripley

. Modern applied statistics with S, 4th ed. New York: Springer, 2002.

21.

Spiegelhalter

Best

Carlin

. Bayesian measures of model complexity and fit. J Roy Stat Soc B 2002; 64: 583–639.

22.

Hanson

Branscum

Johnson

. Predictive comparison of joint longitudinal-survival modeling: a case study illustrating competing approaches. Lifetime Data Anal 2011; 17: 3–28.

23.

Marshall

Spiegelhalter

. Approximate cross-validatory predictive checks in disease mapping models. Stat Med 2003; 22: 1649–1660.

24.

Gelfand

Model determination using sampling-based methods. In: Gilks

Richardson

Spiegelhalter

(eds). Markov chain Monte Carlo in practice, London: Chapman Hall, 1996, pp. 145–161.

25.

Brooks

Gelman

. General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 1998; 7: 434–455.

26.

Diggle

Ribeiro

Christensen

An introduction to model based geostatistics. In: Möller

(ed). Spatial statistics and computational methods. Lecture notes in Statistics 2003; vol. 173, New York: Springer, pp. 43–86.

27.

Hossain

Lawson

. Cluster detection diagnostics for small area health data. Stat Med 2006; 25: 771–786.

28.

Allardyce

Boydell

. Review: the wider social environment and schizophrenia. Schizophr Bull 2006; 32: 592–598.

29.

Department for Communities and Local Government. The English indices of deprivation 2010. DCLG, London, 2011.

30.

Páez

Scott

. Spatial statistics for urban analysis: a review of techniques with examples. GeoJournal 2004; 61: 53–67.