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

地图是一种常见的可视化工具，用于显示全国城市发病率的空间变异性信息。这类地图通常是为原始发病率创建的，人们的眼睛通常被吸引到发病率极高或极低的地区。其中一些极端比率经常出现在疾病病例数量较少的地区，在这种情况下，比率估计可能会受到随机波动的影响，因此非常不稳定。因此，经常对这些数据进行统计建模，从而改进对这些比率的估计。该模型假设距离较近的地区与相距较远的地区的发病率相似，而这一假设往往会使相邻地区的发病率趋于平稳。与假设数据是独立的其他统计分析相比，考虑到这种空间自相关性是使这些数据建模相对复杂的特征之一。可以为每个时间段制作单独的地图，然后进行可视比较，以评估随着时间的推移发病率是否有任何变化。或者，已经开发了识别发病率的空间和时间模式的模型，但这些方法目前假设每个地区的时间趋势的形状是相同的。这实际上不允许研究人员对发病率的时间趋势不同的数据进行建模，例如一个地区呈线性增加，而另一个地区呈非线性下降。该项目的主要贡献是开发了一类新的统计模型，用于估计发病率的时空模式，比现有方法具有更大的灵活性。例如，有些地区的税率可能增加，有些地区的税率可能先降后升，有些地区的税率可能保持相对不变。这里开发的方法将使学术研究人员和公共卫生从业者能够调查这些现象，这些现象目前超出了现有方法的范围。将通过开发编写良好、经过测试和记录良好的软件来实现对这些方法的广泛采用，这些软件将使用免费提供的软件平台，因此不会对模型的使用构成障碍。这种适用于该领域现有和新的统计模型的通用软件尚不存在，其开发是该项目将取得的关键成果之一。此外，我们计划在项目结束时举办研讨会和培训活动，以演示如何使用软件以及如何解释模型。在开发了理论和软件之后，我们将使用三个示例案例研究来说明这种方法的能力和灵活性。该项目得益于与苏格兰国民健康保险制度下属的公共卫生和情报机构(PHI)的密切合作，这些联系将使这些模型能够用于分析国民健康保险制度的数据。这些研究中使用的数据(疫苗接种量、全科医生会诊和心脏住院和死亡率)反映了公共卫生流行病学中的重要问题，以前曾使用过原始发病率的描述性地图。然而，本研究中开发的方法和软件的适用性并不局限于这些例子，几乎任何涉及空间聚集数据的时空映射的问题都可以解决。该项目也是一个及时的项目，因为在相对较小的地理区域，以每年或每月的定期间隔向公众提供人口水平数据的情况迅速扩大。这样的数据可以通过社区统计数据库获得，开发的模型也将引起研究人员的兴趣，他们在非健康数据中模拟时空模式，如教育程度或房价。因此，这一项目的顺利完成将产生很大的影响。

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.