Statistical methods for longitudinal integrated mechanistic modeling of multiview data

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Abstract In longitudinal neuroimaging studies, modeling within-subject variation across time offers insights about time- dependent effects and causal relationships in brain changes related to neurodevelopment, neurodegeneration, or disease progression. Uncovering and quantifying the multi-way relationship across modalities, including environ- mental, *omics, imaging, and neurocognitive data, will help better understand the mechanisms behind complex diseases, such as the impact of substance abuse on neurodevelopment and Alzheimer's Disease. Considering genetic, demographic, and phenotypic traits, it is crucial to characterize disease heterogeneity, such as sex- related differences, for precision medicine. Though methods to perform longitudinal and path analysis of univari- ate data can be applied to individual data elements, limited methods are available directly for data with structured constraints and integrated analysis of large datasets. The long-term goal of this proposal is to develop novel statistical methodologies to analyze longitudinal high-dimensional data with mathematical constraints and novel generalized path analysis methodologies to integrate complex data collected from multiple sources, with appli- cation to the study of neurodevelopment/neurodegeneration and related mental disorders. The overall objective is to elucidate longitudinal effects on brain structure and function, to characterize population heterogeneity, to understand the role of different modalities and mechanisms, and to provide guidance on personalized early prevention/intervention strategies. The challenges of longitudinal integrated mechanistic modeling of multiview data include (i) longitudinal modeling of variables with complex structure (e.g. positive definite matrices), (ii) high dimensionality and heterogeneity, (iii) delineation of multiple pathways, and (iv) development of large-scale and computationally efficient algorithms. To address these, three specific aims are proposed: (1) develop novel regression frameworks for multiple longitudinal, high-dimensional covariance matrix outcomes with predictors across modalities; (2) develop big-data path analysis with longitudinal, high-dimensional, complex variables; (3) develop statistical methodologies to characterize individual growth trajectories of complex variables. Aim 1 introduces longitudinal models with covariance matrices as the outcome to investigate changes in data struc- ture and/or characteristics at a network level. Aim 2 innovates path regularization and integrated optimization criteria for high-dimensional structured data to identify markers and search for causal pathways under longitudi- nal settings. Aim 3 develops methodologies to guide personalized prevention/intervention strategies. To foster dissemination, repeatability, reproducibility, and replicability of scientific findings, open-source software will be developed. The proposed research is innovative because it proposes methodologies to perform longitudinal and path analysis for high-dimensional data with complex and specific structures collected from multiple domains. The proposed research is significant because it will enrich the understanding of the human brain and guide practitioners to promote well-being in adolescent and elderly populations.