Inference for complex epidemiological problems: censoring, mismeasurement, and high-dimensional problems

该项目将开发新的统计模型和相关的推断方法，以解决全球卫生、新出现的传染病和环境卫生方面的最新研究浪潮所遇到的复杂的流行病学问题。这个项目由三个研究流派组成。首先，发展了时空过程方差矩阵的新形式。其次，将为将每日空气质量与人口水平的健康结果联系起来的分层模型创建基于部分似然和后验近似的推理方法。第三，发展用血清调查研究新冠肺炎的方法。这项研究将对项目团队将参与的三个应用研究项目产生直接影响。这些项目包括：与加拿大卫生部合作建立新的空气质量预警系统；利用抗体-C研究评估新冠肺炎在加拿大的流行情况和影响；以及作为全球卫生研究中心的一部分，了解影响全球死亡率的因素。-时空：在Brown和Stafford(2021)的基础上，时空协方差函数的频谱表示将被用来在高空间分辨率下为大数据集建立推理算法。这些近似值将用于聚集空间点过程的模型，例如公开报告的健康结果。-病例交叉模型：这些模型是量化空气污染短期影响的一种方便有效的方法，其中每例死亡与前几周的“控制天数”分组。继Stringer，Brown和Stafford(2021A)和Zhang等人(2021)之后，病例交叉模型将被扩展到包括过度分散和层级非线性效应。-贝叶斯计算：所开发的模型都需要在重要方面偏离传统的“条件独立”和“潜在高斯”规范，这使得推理具有挑战性。Stringer等人(2021b)的近似将通过使用多元倾斜正态密度来改进，而不是当前正态分布的混合。通过使用EMS算法，将改进多次执行的内部优化步骤。-传染病：报告的病例只涵盖一小部分感染者，CGHR进行了一项纵向干血现场调查，以衡量血清阳性率，以更准确地了解加拿大疾病的性质。测试的灵敏度远不是完美的，在情况下的不确定性必须加以调整。除了方法论研究论文外，这项工作还将产生开源统计软件，作为R包分发，供更广泛的研究界使用。

This project will develop new statistical models and associated inference methods to address the complex epidemiological problems being encountered by the latest wave of research in global health, emerging infectious diseases, and environmental health. Three streams of research comprise this project. First, new for variance matrices of spatio-temporal processes will be developed. Second, inferential methods based on partial likelihoods and posterior approximations will be created for hierarchical models relating daily air quality to population-level health outcomes. Third, methods for studying COVID-19 with serosurveys will be developed. The research will have an immediate impact on three applied research programs which the project team will be embedded in. These projects include: building a new air quality warning system with Health Canada; estimating the prevalence and impact of COVID-19 in Canada with the Ab-C study; and understanding the factors influencing global mortality as part of the Centre for Global Health Research (CGHR). - Space-time: Building on Brown and Stafford (2021), spectral representations of spatio-temporal covariance functions will be leveraged to build inferential algorithms for large datasets at high spatial resolutions. These approximations will be used with models for aggregated spatial point processes, such as publicly reported health outcomes. - Case-crossover models: These models are a convenient and effective way of quantifying short-term effects of air pollution, where each death is grouped with a number of `control days' on previous weeks. Following on from Stringer, Brown and Stafford (2021a) and Zhang et al. (2021), case-crossover models will be extended to incorporate overdispersion and hierarchical non-linear effects. - Bayesian computation: The models developed will all need to deviate from the conventional `conditionally-independent' and `latent-Gaussian' specification in important ways, which makes inference challenging. Approximations from Stringer et al (2021b) will be improved through the use of multivariate skew-Normal densities, in place of the current mixture of Normals. An inner optimization step which is performed multiple times will be improved with the use of an EMS algorithm. - Infectious diseases: Reported cases cover only a fraction of infected individuals, and a longitudinal dried blood spot survey measuring seroprevalence has been undertaken by CGHR to obtain a more accurate picture of the nature of the disease in Canada. Test sensitivity is far from perfect and uncertainty in case ascertainment must be adjusted for. In addition to methodological research papers, the work will result in open-source statistical software distributed as R packages for use by the wider research community.