Accelerometer monitoring has been heralded as an objective, unobtrusive tool to provide around the clock observation of physical activity in free-living situations. These devices have been adopted and deployed in a large number of studies already, with goals ranging from identifying activity determinants of childhood to under- standing age-related declines in mobility in elderly populations. Despite the richness inherent to accelerometer monitoring, which provides minute-by-minute activity counts spanning multiple days, analyses often simplify the observed data to single summary measures like the total activity count; these analyses thereby implicitly assuming that timing, intensity and duration of activity are unimportant aside from the contribution to the total. Our proposal develops functional data approaches to accelerometer data. Because functional data techniques incorporate temporal structure as a fundamental part of the analysis, we seek to identify daily activity patterns and understand associations between covariates and complete activity time courses. These tools are critically important to understanding etiologies of childhood obesity, a key interest in our motivating dataset, as well as to the many other studies currently using accelerometry for physical activity quantification. Consequently, new findings using the proposed techniques are essential for designing effective interventions to promote physical activity. In this proposal we develop a collection of tools for generalized, multilevel functional data: these data are generalized in that they do not follow a Gaussian distribution, multilevel in that several days are observed for each subject, and functional in that activity is monitored nearly continuously within each day. Currently, there is little or no existing work for data of thi type.
Our aims are to develop unique functional principal components analysis and to introduce statistically novel function-on-scalar regression models approaches for data of this type. Throughout, we use a Bayesian approach that jointly models all parameters of interest and develop fast approximate algorithms to ensure rapid computation and scalability. All new methods will be implemented in robust, publicly available software, be validated on simulated datasets designed to mimic real-data scenarios, and be deployed on the motivating dataset to generate insights into the mechanisms behind childhood obesity. 1

Public Health Relevance

We propose to develop statistical methods for estimation and inference in generalized, multilevel function-on- scalar regression models. Additionally, we develop a principal components analysis for generalized, multilevel functional data. Our work is motivated by accelerometer data, in which activity counts are recorded in one- minute intervals for each subject over multiple days. Our methods address a gap in the statistical literature and improve on existing approaches to accelerometer analysis, which typically reduce several days' data to a single summary. Once methods have been developed and validated they will be applied to the motivating dataset, and will further be broadly useful in a range of functional data applications with public health relevance. 1

National Institute of Health (NIH)
National Institute of Biomedical Imaging and Bioengineering (NIBIB)
Exploratory/Developmental Grants (R21)
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Biostatistical Methods and Research Design Study Section (BMRD)
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Pai, Vinay Manjunath
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Columbia University (N.Y.)
Biostatistics & Other Math Sci
Schools of Public Health
New York
United States
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Gertheiss, Jan; Goldsmith, Jeff; Staicu, Ana-Maria (2017) A note on modeling sparse exponential-family functional response curves. Comput Stat Data Anal 105:46-52
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Reiss, Philip T; Goldsmith, Jeff; Shang, Han Lin et al. (2017) Methods for scalar-on-function regression. Int Stat Rev 85:228-249
Chen, Yakuan; Goldsmith, Jeff; Ogden, Todd (2016) Variable Selection in Function-on-Scalar Regression. Stat (Int Stat Inst) 5:88-101
Wrobel, Julia; Park, So Young; Staicu, Ana Maria et al. (2016) Interactive graphics for functional data analyses. Stat (Int Stat Inst) 5:108-118
Goldsmith, Jeff; Kitago, Tomoko (2016) Assessing systematic effects of stroke on motorcontrol by using hierarchical function-on-scalar regression. J R Stat Soc Ser C Appl Stat 65:215-236
Goldsmith, Jeff; Liu, Xinyue; Jacobson, Judith S et al. (2016) New Insights into Activity Patterns in Children, Found Using Functional Data Analyses. Med Sci Sports Exerc 48:1723-9