Spatial Design for GP Consortia?

The government is set to release a bill detailing how it is they expect the proposed GP Consortia to work. GP Consortia, groups of GPs working together, are set to replace the current structure of Primary Care Trusts (PCTs) and Strategic Health Authorities (SHAs) as the mechanism through which primary healthcare is provided to the public, and services are commissioned. Recently, the planned wholesale changes to the NHS have come under a sustained attack from the media, professional bodies and MPs, meanwhile the plans for GP consortia have moved into a trial phase in which different setups are being tested for their effectiveness. The trial consortia demonstrate the extent to which the plans represent a completely new venture, with a broad spectrum of possibilities being tested in terms of consortia templates, from a ‘consortia’ of a mere 3 GP practices, to a vast group of 83 GP practices. There seems little reasoning behind how Consortia are allowed to form at the moment, thus I saw an interesting opportunity to consider the ‘GP Consortia Problem’ as a geographic question. This is most evident in the fact that the NHS is mandated to provide an equitable and universal service, and an unmetered potential for GPs to ‘consort’ may well lead to increasing inequities in healthcare provision.

I see the ‘GP Consortia Problem’ as solvable through a zone-design approach. To do this, I identify contiguity between all English GPs and employ spatially constrained clustering. The following assumptions are made:

  • Distance is important, GP consortia should be space covering without holes or islands, therefore a ‘neighbour’ approach to contiguity is advocated using graphs.
  • As a preliminary test, GPs are considered to be equal, although there is scope in the future to develop measures of dissimilarity and homegeneity which will provide better, or more appropriate solutions to the GP Consortia problem.
  • Based on the trials, I assume that Consortia must consist of at least 35 GPs, the average number of GPs per consortia in the trial phase.

I have used two approaches to creating contiguity amongst the English GP practices, both of them graph theoretical concepts based upon geometric analyses: the delaunay triangulation, and the gabriel graph. I believe that the gabriel graph is a sub graph of the delaunay triangulation, as such it is sparser than the delaunay graph. The two graphs are defined as:

  • Delaunay Triangulation – for a set of nodes (GP practices) the delaunay triangulation is the set of triangles created by drawing a circle with 3 nodes (which define the triangles edges) on the circle’s perimeter, in which the circle does not contain any other points- iterated for all sets of 3-points.
  • Gabriel Graph- 2 nodes are connected if they form the start and end-point of the diameter of a circle, and the circle does not contain any other points – iterated for all pairs of points.

In this sense, both the Delaunay triangulation and the Gabriel graph are nearest proximity measures. Having obtained the graph, the differences can be seen below. Note both graphs have been constrained for the English boundary.

Having created the ‘contiguity’ graphs, I wrote a short python script to extract the realtionships between GPs and write the output as a ‘.gal’ file for use with pySAL. I utilised the pySAL regionalisation module to compute the consortia solutions, I have used this previously in my blog, so I won’t go into detail on it. I paramterised the solution using the contiguity matrices created, assuming equality amongst GP practices, and looking for groups of at least 35 GPs. The regionalisations were then joined to a special areal geography I created for visualisation, this is simply the Voronoi diagram of the English GPs clipped to the English boundary. The results are below:

In these results it is notable that the Gabriel graph gives a cleaner result, the density of the delaunay-based contiguity matrix means that the result is subject to some sliver-like polygons in the regionalisation, and ‘spikier’ regions in general.

Of course, this is just a test, but it does point at the potential to create a rationalised system fo GP Consortia. Naturally, the biggest issue with these maps is that they only establish an areal depiction of consortia, one that is largely irrelevant. This is because the actual service areas of GPs tend to overlap and extend beyond any given GP’s voronoi defined footprint. Therefore the geography of patients requires a subsequent treatment once a geography of COnsortia has been established, and only in the interaction of the two can issues pertaining to equity be understood.