The analysis of case-control point pattern data is an important problem in spatial epidemiology. The spatial variation of cases if often compared to that of a set of controls to assess spatial risk variation as well as the detection of risk factors and exposure to putative pollution sources using spatial regression models. The intensities of the point patterns of cases and controls are estimated using log-Gaussian Cox models, so that fixed and spatial random effects can be included. Bayesian inference is conducted via the integrated Nested Laplace approximation (INLA) method using the inlabru R package. In this way, potential risk factors can be assessed by including them as fixed effects while residual spatial variation is considered as a Gaussian process with Mat\'ern covariance. In addition, exposure to pollution sources is modeled using different smooth terms. The proposed methods have been applied to the Chorley-Ribble dataset, that records the locations of lung and larynx cancer cases as well as the location of an disused old incinerator in the area of Lancashire (England, United Kingdom). Taking the locations of lung cancer as controls, the spatial variation of both types of cases has been estimated and the increase of larynx cases in the vicinity of the incinerator has been assessed. The results are similar to those found in the literature. In a nutshell, a framework for Bayesian analysis of multivariate case-control point patterns within an epidemiological framework has been presented. Models to assess spatial variation and the effect of risk factors and pollution sources can be fit with ease with the inlabru R package.

翻译：病例-对照点模式数据的分析是空间流行病学中的一个重要问题。通常将病例的空间变异与一组对照的空间变异进行比较，以评估空间风险变异，并利用空间回归模型检测风险因素及对假定污染源的暴露情况。病例与对照点模式的强度使用对数高斯考克斯模型进行估计，从而可以纳入固定效应和空间随机效应。贝叶斯推断通过集成嵌套拉普拉斯近似（INLA）方法，使用 inlabru R 包进行。通过这种方式，潜在风险因素可以作为固定效应纳入模型进行评估，而残余空间变异则被视为具有 Matérn 协方差的高斯过程。此外，对污染源的暴露使用不同的平滑项进行建模。所提出的方法已应用于 Chorley-Ribble 数据集，该数据集记录了 Lancashire（英国英格兰）地区肺癌和喉癌病例的位置以及一个废弃旧焚化炉的位置。以肺癌病例的位置作为对照，估计了两种类型病例的空间变异，并评估了焚化炉附近喉癌病例的增加情况。结果与文献中的发现相似。简而言之，本文提出了一个在流行病学框架内进行多变量病例-对照点模式贝叶斯分析的框架。使用 inlabru R 包可以轻松拟合评估空间变异以及风险因素和污染源影响的模型。