An ever-increasing number of biomedical studies yield functional data, in which the ideal units of observation are curves. The goal of this research program is to develop new Bayesian methodology that provides a unifying framework for performing nonparametric estimation and inference for samples of curves. These methods will be flexible enough to model functions obtained from a variety of experimental designs, provide answers to a broad range of research questions, and will be sufficiently adaptive to apply to functional data from a wide range of applications. We will apply these methods to model functional data from a series of cancer-related biomedical studies that have motivated our methodological thinking. The methods we propose are appropriate for functional data characterized by numerous local features like peaks since we employ adaptive regularization procedures which denoise the functions with minimal attenuation of the dominant local features.
The specific aims of this research are: 1. Introduce a unified functional mixed model framework for modeling samples of curves. Develop a wavelet-based method to fit this model and obtain adaptively regularized nonparametric estimates and Bayesian inference for fixed and random effect functions as well as covariance parameters. 2. Develop methodology to perform formal Bayesian inference and model selection in functional mixed models. Applications of this method include testing functional hypotheses on fixed/random effects, comparing models with different covariance structures, determining the number of basis functions, testing for correlation among different functional responses, and identifying appropriate piecewise constant compartment models. 3. Develop methods to perform wavelet-regularized functional principal component analysis. Extend our wavelet-based functional mixed model methods developed in Specific Aims 1 and 2 to other basis functions, including wavelet-regularized eigen functions and splines. 4. Apply the methods we develop in Specific Aims 1, 2, and 3 to a series of biomedical applications involving functional data, including colon carcinogenesis studies, a Planet Health children's activity study, an animal study investigating acute renal failure, and medical studies involving proteomics. 5. Produce publicly available statistical software for implementing the methods developed in this proposal.

Agency
National Institute of Health (NIH)
Institute
National Cancer Institute (NCI)
Type
Research Project (R01)
Project #
1R01CA107304-01
Application #
6760523
Study Section
Biostatistical Methods and Research Design Study Section (BMRD)
Program Officer
Tiwari, Ram C
Project Start
2004-03-01
Project End
2007-02-28
Budget Start
2004-03-01
Budget End
2005-02-28
Support Year
1
Fiscal Year
2004
Total Cost
$225,696
Indirect Cost
Name
University of Texas MD Anderson Cancer Center
Department
Biostatistics & Other Math Sci
Type
Other Domestic Higher Education
DUNS #
800772139
City
Houston
State
TX
Country
United States
Zip Code
77030
Zhu, Hongxiao; Caspers, Philip; Morris, Jeffrey S et al. (2018) A Unified Analysis of Structured Sonar-terrain Data using Bayesian Functional Mixed Models. Technometrics 60:112-123
Zhu, Hongxiao; Morris, Jeffrey S; Wei, Fengrong et al. (2017) Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study. Comput Stat Data Anal 111:88-101
Morris, Jeffrey S (2017) Comparison and Contrast of Two General Functional Regression Modeling Frameworks. Stat Modelling 17:59-85
Lee, Wonyul; Morris, Jeffrey S (2016) Identification of differentially methylated loci using wavelet-based functional mixed models. Bioinformatics 32:664-72
Morris, Jeffrey S; Gutstein, Howard B (2016) Detection and Quantification of Protein Spots by Pinnacle. Methods Mol Biol 1384:185-201
Zhang, Lin; Baladandayuthapani, Veerabhadran; Zhu, Hongxiao et al. (2016) Functional CAR models for large spatially correlated functional datasets. J Am Stat Assoc 111:772-786
Meyer, Mark J; Coull, Brent A; Versace, Francesco et al. (2015) Bayesian function-on-function regression for multilevel functional data. Biometrics 71:563-74
Lancia, Leonardo; Rausch, Philip; Morris, Jeffrey S (2015) Automatic quantitative analysis of ultrasound tongue contours via wavelet-based functional mixed models. J Acoust Soc Am 137:EL178-83
Fazio, Massimo A; Grytz, Rafael; Morris, Jeffrey S et al. (2014) Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci 55:7189-98
Fazio, Massimo A; Grytz, Rafael; Morris, Jeffrey S et al. (2014) Age-related changes in human peripapillary scleral strain. Biomech Model Mechanobiol 13:551-63

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