A flexible class of Bayesian spatio-temporal models for cluster detection, trend estimation and forecasting of disease risk

Maps are a common visual tool for presenting information on the spatial variability in disease rates across a city of country. Such maps are typically created for raw disease rates, and one's eye is generally drawn to areas exhibiting extremely high or low rates. Some of these extreme rates are often found in areas with small numbers of disease cases, and in such situations the rate estimates can be affected by random fluctuations and thus be highly unstable. Therefore statistical modelling of these data is often undertaken, which improves the estimation of these rates. This modelling assumes that areas which are close together have similar disease rates relative to areas which are further apart, and this assumption tends to smooth rates over adjacent areas. Taking into account this spatial autocorrelation is one of the features which makes modelling these data relatively complex, compared to other statistical analyses where the data are assumed to be independent. Separate maps could be produced for each time period, and then compared visually to assess the presence of any change in disease rates over time. Alternatively, models that identify both spatial and temporal patterns in disease rates have been developed, but these approaches currently assume that the shape of the temporal trend is the same in each area. This does not really permit the researcher to model data where the temporal trends in disease rates are different, such as increasing linearly in one area but decreasing non-linearly in another.

The main contribution of this project is the development of a novel class of statistical models for estimating the spatio-temporal pattern in disease rates, which has much greater flexibility than existing methods. For example, in some areas the rates may increase, in others they may decrease first and then increase, and in others they may remain relatively constant. The methodology developed here will enable academic researchers and public health practitioners to investigate these phenomena, which are currently beyond the scope of existing methods. Widespread uptake of these methods will be achieved by the development of well-written, tested and documented software, which will use a freely available software platform and hence provide no hindrance to the use of the models. Such general-purpose software for fitting both existing and novel statistical models used in this field does not yet exist, and its development is one of the key outcomes the project will deliver. Furthermore we plan to run workshops and training events at the conclusion of the project, to demonstrate how the software can be used and how the models can be interpreted.

Having developed the theory and software, we will use three example case studies to illustrate the power and flexibility of this approach. The project benefits from close collaboration with Public Health and Intelligence (PHI),part of NHS Scotland, and these links will enable the use of these models in the analysis of NHS data. The data used in these studies (vaccine uptake, GP consultations and cardiac hospitalisation and mortality) reflect important questions in public health epidemiology, where descriptive maps of raw disease rates have been used previously. The applicability of the methods and software developed in this research is not restricted to these examples however, and almost any problem involving spatio-temporal mapping of spatially aggregated data can be tackled. The project is also a timely one, as a result of a rapid expansion in the public availability of population level data at relatively small geographic areas at regular intervals such as yearly or monthly. Such data are available through the neighbourhood statistics databases, and the models developed will also interest researchers modelling spatio-temporal patterns in non-health data, such as educational attainment or house prices. Thus the successful completion of this project will yield a large impact.

This project will develop novel statistical methodology for modelling spatially and temporally aggregated disease data, which will be implemented in a Bayesian paradigm using Markov chain Monte carlo simulation. The project will extend published research by developing a flexible general class of models, which incorporate spatio-temporal autocorrelation and flexible temporal trends. Binomial, Gaussian and Poisson likelihood models will be developed, with the linear predictor depending on covariates, spatial random effects and a flexible temporal trend component. The novel aspect of this methodology is the latter, which allows the disease rates in each area to be modelled by a mixture of temporal trends. These include smooth functions, regular parametric polynomials or sinusoidal curves, piecewise linear trends and autoregressive models, and as the parameters controlling these trends can vary spatially, they are not constrained to exhibit the same underlying shape unlike existing research. The likely spatio-temporal autocorrelation in these trends will be modelled with smooth spatially and temporally varying parameters, utilising univariate and multivariate conditional autoregressive models. Within this Bayesian modelling framework short term prediction of the rates is a relatively straightforward procedure together with appropriate prediction intervals. Software will be produced to allow others to implement this model class, which will encompass some previously published models as special cases. This will permit greater flexibility in model fitting, model testing and selection. No general purpose software currently exists to allow others to implement a range of disease mapping models without substantial programming effort, and its development in this project will be a major novel aspect. The models will then be applied to undertake substantive analyses of data concerning GP consultations, vaccine uptake, and coronary heart disease hospitalisation and mortality.

This project has the potential for substantial academic and non-academic impact. It will impact upon UK science as a whole by increasing scientific knowledge in the area of spatio-temporal statistical modelling. This increased knowledge will be the theoretical underpinning to a new class of spatio-temporal models that can be used to analyse spatially aggregated data, which in a health mapping context will add value to the current method of visually interpreting maps of raw disease rates. This research will thus put the UK at the forefront of this important research area. The development of the software will impact both methodological and applied researchers in the UK and internationally, whose interests are in modelling the spatio-temporal patterns in spatially aggregated data. These researchers could be in public health, science or social science, and will benefit by being given software tools to enable them to analyse their own data using the cutting-edge statistical methods that have been developed. This project thus gives applied statisticians, epidemiologists and other researchers the statistical tools to analyse data and answer substantive research questions across both science and social science. The uptake of these tools will be encouraged by the training workshops that we will run, for practitioners from both academic and non-academic disciplines.

Another impact of the project will be the development of a highly skilled research fellow, which will benefit the individual concerned through vastly enhancing their career development prospects. This will also benefit UK science as a whole, because highly trained statisticians with interdisciplinary epidemiology skills are rare. As a result the research fellow will have the potential to become a future research leader in statistical epidemiology.

The collaboration with Public Health and Intelligence (PHI),within NHS Scotland will ensure that the research has a non-academic impact. The Scottish and UK governments will benefit from the project through advanced statistical analyses of data from PHI concerning GP consultations, vaccine uptake, and coronary heart disease hospitalisation and mortality. These analyses will lead to improved public health understanding and dissemination of spatial health data within NHS Scotland. PHI also has close links with Public Health England (PHE), and this will enable the statistical analyses to impact on public health in England via PHE as well as in Scotland. In addition, the CoI Lawson is an advisor to the World Health Organisation (WHO), so through his influence there is potential for a global health impact.

This research also has the potential to impact the general public in the long-term, as a result of improved detection of disease epidemics. This impact would arise if/when the spatially aggregated surveillance systems that will be developed detected a disease outbreak, which would not have been noticed as quickly through the use of current methods based upon spatially disaggregated data. However, we acknowledge that this is a potential impact, as we have no way of knowing how common this may be. However, the simulation studies we will conduct will provide evidence of the likely magnitude of the impact given a simulated epidemic. A side effect to improving public health is reduced costs to government of hospital treatment and stays, so this project has the potential to impact on health costs in the long-term.