Functional Analysis of Sparse Longitudinal Data

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Project Abstractproposal: 0406430PI: Jane-Ling Wang Functional Regression Analysis of Sparse Longitudinal DataRecent advances in modern technology have facilitated the collection ofrepeated measurements over a period of time on the same subject. Such dataare common in nearly all fields including the biological, medical, neural,physical and social sciences, but are termed differently, with"longitudinal data" being the preferred term in health and social sciencesand "functional data" being the preferred term in engineering and physicalsciences. Statistical approaches to analyze such data are alsointrinsically different in the longitudinal and functional data researchcommunities. Parametric approaches such as GEE and GLMM arepredominantly used methods to analyze longitudinal data, whilenonparametric approaches play the analogous role for functionaldata. Due to the limitations of each approach, semiparametric modelscombining longitudinal and functional data analysis methods emerge as apromising alternative, which can bring out and combine the best aspects ofthe two approaches. Longitudinal or functional data are intrinsicallycomplex owing to irregularity of observational times, dependence ofobservations within subjects, sparsity and size of the data. They posechallenges both on the computational and theoretical fronts. Thisproposal aims at bringing together methodology from various areas instatistics, including nonparametric smoothing, multivariate statistics,random and mixed effects models, dimension reduction and robustness, toaddress several challenging issues and to provide flexible modeling andefficient implementation for longitudinal/functional data. The proposedmethods range from extension of traditional linear models to newsemiparametric and nonparametric models, and focus particularly onhandling sparse longitudinal data with or without measurement error. Anew version of functional principal components (PCA) analysis wasdeveloped recently by the PI and collaborators, where the functionalprincipal component scores are framed as conditional expectations. Thisextends the applicability of functional PCA to typical situations inlongitudinal data analysis, where only few repeated measurements areavailable per subject. This approach is known as Principal ComponentsAnalysis through Conditional Expectation (PACE) for longitudinal data.With PACE serving as the backbone, the proposal includes three projects:(1) Modeling covariate effects, (2) Semi-parametric dimension reductionapproaches, and (3) Robust covariance estimation and functional PCA.In addition to new methodology, statistical theory will be a major focusto establish formal inference procedures. So far, theoretical resultsfor functional data are scattered and this proposal aims to fill the gaps.The proposed research is motivated by ongoing interdisciplinary researchcollaborations of the PI with biologists and physicians. The newapproaches are applied to data generated from these ongoing and futurecollaborations. The proposed research helps to better understand therelationship between reproductive activity and longevity and willcontribute to the growing fields of aging research and biodemography. Asthe procedures developed will be applicable to general longitudinal orfunctional data from other disciplines, they will provide much neededmodern statistical tools to analyze such data, which in turn willfacilitate the advancement of many scientific fields. Moreover, with thefast rising trend towards the collection of such large and complex datasets, there is a shortage of Ph.D. statisticians trained to handle suchdata. The research assistantship provides a trainingopportunity to address this need. The PI is engaged inundergraduate research training, and continues this activity inaddition to the dissemination of the new research findings throughteaching, training, and the web.