title: Methods to assess an exercise intervention trial based on 3-level functional data.
abstract: Motivated by data recording the effects of an exercise intervention on subjects' physical activity over time, we develop a model to assess the effects of a treatment when the data are functional with 3 levels (subjects, weeks and days in our application) and possibly incomplete. We develop a model with 3-level mean structure effects, all stratified by treatment and subject random effects, including a general subject effect and nested effects for the 3 levels. The mean and random structures are specified as smooth curves measured at various time points. The association structure of the 3-level data is induced through the random curves, which are summarized using a few important principal components. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed effects model framework for model fitting, prediction and inference. We develop an algorithm to fit the model iteratively with the Expectation/Conditional Maximization Either (ECME) version of the EM algorithm and eigenvalue decompositions. Selection of the number of principal components and handling incomplete data issues are incorporated into the algorithm. The performance of the Wald-type hypothesis test is also discussed. The method is applied to the physical activity data and evaluated empirically by a simulation study.
authors.affiliation: Departments of Oncology and Community Health Sciences, University of Calgary, Calgary, AB, T2N 4N2, Canada haocheng.li@ucalgary.ca.
authors.forename: Haocheng
authors.initials: H
authors.lastname: Li
authors.affiliation: Nutritional Epidemiology Branch, National Cancer Institute, 9609 Medical Center Drive, Bethesda, MD 20892, USA.
authors.forename: Sarah
authors.initials: S
authors.lastname: Kozey Keadle
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305, USA.
authors.forename: John
authors.initials: J
authors.lastname: Staudenmayer
authors.affiliation: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA.
authors.forename: Houssein
authors.initials: H
authors.lastname: Assaad
authors.affiliation: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA.
authors.forename: Jianhua Z
authors.initials: JZ
authors.lastname: Huang
authors.affiliation: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA and Department of Mathematics and Statistics, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia.
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
mesh_terms: D000465:Algorithms; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D005081:Exercise Therapy / Q000706:statistics & numerical data*; D006801:Humans; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data*; D012107:Research Design / Q000706:statistics & numerical data*
keywords: Longitudinal data; Mixed-effects model; Penalized splines; Physical activity measurement; Principal components