A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health

In the United Kingdom, air pollution is linked to around 40000 premature deaths each year, but estimating its health effects is challenging in a spatio-temporal study. The challenges include spatial misalignment between the pollution and disease data; uncertainty in the estimated pollution surface; and complex residual spatio-temporal autocorrelation in the disease data. This article develops a two-stage model that addresses these issues. The first stage is a spatio-temporal fusion model linking modeled and measured pollution data, while the second stage links these predictions to the disease data. The methodology is motivated by a new five-year study investigating the effects of multiple pollutants on respiratory hospitalizations in England between 2007 and 2011, using pollution and disease data relating to local and unitary authorities on a monthly time scale

Multimodal Data Fusion and Quantitative Analysis for Medical Applications

Medical big data is not only enormous in its size, but also heterogeneous and complex in its data structure, which makes conventional systems or algorithms difficult to process. These heterogeneous medical data include imaging data (e.g., Positron Emission Tomography (PET), Computerized Tomography (CT), Magnetic Resonance Imaging (MRI)), and non-imaging data (e.g., laboratory biomarkers, electronic medical records, and hand-written doctor notes). Multimodal data fusion is an emerging vital field to address this urgent challenge, aiming to process and analyze the complex, diverse and heterogeneous multimodal data. The fusion algorithms bring great potential in medical data analysis, by 1) taking advantage of complementary information from different sources (such as functional-structural complementarity of PET/CT images) and 2) exploiting consensus information that reflects the intrinsic essence (such as the genetic essence underlying medical imaging and clinical symptoms). Thus, multimodal data fusion benefits a wide range of quantitative medical applications, including personalized patient care, more optimal medical operation plan, and preventive public health. Though there has been extensive research on computational approaches for multimodal fusion, there are three major challenges of multimodal data fusion in quantitative medical applications, which are summarized as feature-level fusion, information-level fusion and knowledge-level fusion: • Feature-level fusion. The first challenge is to mine multimodal biomarkers from high-dimensional small-sample multimodal medical datasets, which hinders the effective discovery of informative multimodal biomarkers. Specifically, efficient dimension reduction algorithms are required to alleviate "curse of dimensionality" problem and address the criteria for discovering interpretable, relevant, non-redundant and generalizable multimodal biomarkers. • Information-level fusion. The second challenge is to exploit and interpret inter-modal and intra-modal information for precise clinical decisions. Although radiomics and multi-branch deep learning have been used for implicit information fusion guided with supervision of the labels, there is a lack of methods to explicitly explore inter-modal relationships in medical applications. Unsupervised multimodal learning is able to mine inter-modal relationship as well as reduce the usage of labor-intensive data and explore potential undiscovered biomarkers; however, mining discriminative information without label supervision is an upcoming challenge. Furthermore, the interpretation of complex non-linear cross-modal associations, especially in deep multimodal learning, is another critical challenge in information-level fusion, which hinders the exploration of multimodal interaction in disease mechanism. • Knowledge-level fusion. The third challenge is quantitative knowledge distillation from multi-focus regions on medical imaging. Although characterizing imaging features from single lesions using either feature engineering or deep learning methods have been investigated in recent years, both methods neglect the importance of inter-region spatial relationships. Thus, a topological profiling tool for multi-focus regions is in high demand, which is yet missing in current feature engineering and deep learning methods. Furthermore, incorporating domain knowledge with distilled knowledge from multi-focus regions is another challenge in knowledge-level fusion. To address the three challenges in multimodal data fusion, this thesis provides a multi-level fusion framework for multimodal biomarker mining, multimodal deep learning, and knowledge distillation from multi-focus regions. Specifically, our major contributions in this thesis include: • To address the challenges in feature-level fusion, we propose an Integrative Multimodal Biomarker Mining framework to select interpretable, relevant, non-redundant and generalizable multimodal biomarkers from high-dimensional small-sample imaging and non-imaging data for diagnostic and prognostic applications. The feature selection criteria including representativeness, robustness, discriminability, and non-redundancy are exploited by consensus clustering, Wilcoxon filter, sequential forward selection, and correlation analysis, respectively. SHapley Additive exPlanations (SHAP) method and nomogram are employed to further enhance feature interpretability in machine learning models. • To address the challenges in information-level fusion, we propose an Interpretable Deep Correlational Fusion framework, based on canonical correlation analysis (CCA) for 1) cohesive multimodal fusion of medical imaging and non-imaging data, and 2) interpretation of complex non-linear cross-modal associations. Specifically, two novel loss functions are proposed to optimize the discovery of informative multimodal representations in both supervised and unsupervised deep learning, by jointly learning inter-modal consensus and intra-modal discriminative information. An interpretation module is proposed to decipher the complex non-linear cross-modal association by leveraging interpretation methods in both deep learning and multimodal consensus learning. • To address the challenges in knowledge-level fusion, we proposed a Dynamic Topological Analysis framework, based on persistent homology, for knowledge distillation from inter-connected multi-focus regions in medical imaging and incorporation of domain knowledge. Different from conventional feature engineering and deep learning, our DTA framework is able to explicitly quantify inter-region topological relationships, including global-level geometric structure and community-level clusters. K-simplex Community Graph is proposed to construct the dynamic community graph for representing community-level multi-scale graph structure. The constructed dynamic graph is subsequently tracked with a novel Decomposed Persistence algorithm. Domain knowledge is incorporated into the Adaptive Community Profile, summarizing the tracked multi-scale community topology with additional customizable clinically important factors