Cliffs and slopes: better ways to deal with spatial auto-correlation

This project, led by Dr Duncan Lee, aims to develop and test statistical methodology which can identify discontinuities (cliffs) in spatial risk surfaces for poor health in small-area epidemiological data. The methods we develop will be used to explore and explain the spatial inequalities in risk for significant public health problems.

Growth in the availability of small-area ecological data, in computing power, and substantive interest in how and why lives vary from place to place has led to an increase in spatial modelling, particularly in epidemiology. The UK has a wealth of small-area ecological datasets, which when modelled, requires the physical relationship between the small-areas to be considered. Following Tobler’s ‘first law of geography’ (TFL), which affirms that “everything is related to everything else, but near things are more related than distant things”, we expect greater similarity in the lives and characteristics of people and places (including their health) that are closer together, than in those which are further apart. We should, in turn, expect spatial correlation in the rates of disease in neighbouring areas, even after the effects of important covariates have been accounted for. Such residual spatial correlation is caused by the presence of unmeasured or unidentified confounders which affect the health outcome in question, and which also have spatial structure. Statistical methods that allow for this residual spatial structure are, in effect, accounting for these unmeasured confounders.

Conventional approaches to analysing spatial data deal with this problem by ‘smoothing’ risk across adjacent areas. That’s OK if the risk surface itself is smooth. However, if the health outcome of interest is heavily influenced by social and economic factors, the risk surface is much less likely to be smooth. Often, adjacent communities have vastly different social, economic and cultural characteristics.

In this project, we will be developing methods which can spot, and then handle, situations in which smoothing a risk surface across adjacent areas is a bad idea. We will develop the techniques, test them and then make them available as R packages, for anyone to use.

This project is funded by the ESRC. Rich Mitchell is the Co-I on this project

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