Grant: Discovery Launch Supplement

Developing innovative statistical methods tailored to the complexities of modern massive and complex data, is the objective of the proposed research. Collection of vast amounts of data in many fields is underway on an unprecedented scale. Such large data resources complicate a number of diverse methodological questions, which can impede effective knowledge extraction. I am particularly interested in addressing these methodological gaps in three key areas: (1) learning association patterns, (2) building causal models, and (3) integrating diverse data sources. The complex data type I aim to tackle, in the context of learning association patterns, is sequencing-derived DNA methylation data. Such data often manifest data errors, exhibit dispersion tendencies, and are impacted by high-dimensional (HD) genetic variants. Existing HD methods, optimized for low measurement error and strict parametric adherence, may not fully align with the nature of this data. To address this gap, I will develop novel HD methods that accommodate mis-measured multivariate outcomes, and allow for varying levels of variability compared to what would be expected based on a parametric model. These developments will enable accurate inference for flexible association patterns across different study designs. Beyond learning patterns of association, drawing causal conclusions is vital to discern the real impact of variables. Capitalizing on the increasing availability of summary-level genetic association data, Mendelian randomization (MR) has emerged as a rapid and affordable way to evaluating causal questions. However, existing MR methods often underuse available data, for example, by restricting themselves to uncorrelated instrumental variables (IVs), screening for strong IVs, or focusing solely on distinct datasets for exposure and outcome. By relaxing these assumptions, I aim to improve causal estimates in summary-data MR. The novel estimators will maintain strong theoretical properties while making more efficient use of the data. The complexity of integrating multi-source data arises from their potentially diverse underlying distributions. Thus, it's vital to develop methods that can perform well when the data-generating distribution is perturbed. To address this, my goal is to develop a novel framework that explicitly handles distributional shifts and non-equivalent predictor spaces, thus enhancing robustness across various integrative scenarios. In summary, the proposed research addresses urgent challenges in the analysis of complex data. These comprehensive endeavours have the potential to enrich our understanding of various health-related phenomena, ultimately contributing to an improved quality of life in Canada. Moreover, the rich training experience acquired during the implementation of the program will equip the students for success in various statistical or data science-related career paths.