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

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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.