Functional Analysis of Sparse Longitudinal Data

University Of California-Davis, Davis CA

Investigators

Abstract

Project Abstract proposal: 0406430 PI: Jane-Ling Wang Functional Regression Analysis of Sparse Longitudinal Data Recent advances in modern technology have facilitated the collection of repeated measurements over a period of time on the same subject. Such data are 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 sciences and "functional data" being the preferred term in engineering and physical sciences. Statistical approaches to analyze such data are also intrinsically different in the longitudinal and functional data research communities. Parametric approaches such as GEE and GLMM are predominantly used methods to analyze longitudinal data, while nonparametric approaches play the analogous role for functional data. Due to the limitations of each approach, semiparametric models combining longitudinal and functional data analysis methods emerge as a promising alternative, which can bring out and combine the best aspects of the two approaches. Longitudinal or functional data are intrinsically complex owing to irregularity of observational times, dependence of observations within subjects, sparsity and size of the data. They pose challenges both on the computational and theoretical fronts. This proposal aims at bringing together methodology from various areas in statistics, including nonparametric smoothing, multivariate statistics, random and mixed effects models, dimension reduction and robustness, to address several challenging issues and to provide flexible modeling and efficient implementation for longitudinal/functional data. The proposed methods range from extension of traditional linear models to new semiparametric and nonparametric models, and focus particularly on handling sparse longitudinal data with or without measurement error. A new version of functional principal components (PCA) analysis was developed recently by the PI and collaborators, where the functional principal component scores are framed as conditional expectations. This extends the applicability of functional PCA to typical situations in longitudinal data analysis, where only few repeated measurements are available per subject. This approach is known as Principal Components Analysis 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 reduction approaches, and (3) Robust covariance estimation and functional PCA. In addition to new methodology, statistical theory will be a major focus to establish formal inference procedures. So far, theoretical results for functional data are scattered and this proposal aims to fill the gaps. The proposed research is motivated by ongoing interdisciplinary research collaborations of the PI with biologists and physicians. The new approaches are applied to data generated from these ongoing and future collaborations. The proposed research helps to better understand the relationship between reproductive activity and longevity and will contribute to the growing fields of aging research and biodemography. As the procedures developed will be applicable to general longitudinal or functional data from other disciplines, they will provide much needed modern statistical tools to analyze such data, which in turn will facilitate the advancement of many scientific fields. Moreover, with the fast rising trend towards the collection of such large and complex data sets, there is a shortage of Ph.D. statisticians trained to handle such data. The research assistantship provides a training opportunity to address this need. The PI is engaged in undergraduate research training, and continues this activity in addition to the dissemination of the new research findings through teaching, training, and the web.