1
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Long AS, Reich BJ, Staicu AM, Meitzen J. A nonparametric test of group distributional differences for hierarchically clustered functional data. Biometrics 2023; 79:3778-3791. [PMID: 36805970 PMCID: PMC10695330 DOI: 10.1111/biom.13846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 02/03/2023] [Indexed: 02/22/2023]
Abstract
Biological sex and gender are critical variables in biomedical research, but are complicated by the presence of sex-specific natural hormone cycles, such as the estrous cycle in female rodents, typically divided into phases. A common feature of these cycles are fluctuating hormone levels that induce sex differences in many behaviors controlled by the electrophysiology of neurons, such as neuronal membrane potential in response to electrical stimulus, typically summarized using a priori defined metrics. In this paper, we propose a method to test for differences in the electrophysiological properties across estrous cycle phase without first defining a metric of interest. We do this by modeling membrane potential data in the frequency domain as realizations of a bivariate process, also depending on the electrical stimulus, by adopting existing methods for longitudinal functional data. We are then able to extract the main features of the bivariate signals through a set of basis function coefficients. We use these coefficients for testing, adapting methods for multivariate data to account for an induced hierarchical structure that is a product of the experimental design. We illustrate the performance of the proposed approach in simulations and then apply the method to experimental data.
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Affiliation(s)
- Alexander S Long
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A
| | - Brian J Reich
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A
| | - John Meitzen
- Department of Biological Sciences, North Carolina State University, Raleigh, North Carolina, U.S.A
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2
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Ghosal R, Matabuena M, Zhang J. Functional proportional hazards mixture cure model with applications in cancer mortality in NHANES and post ICU recovery. Stat Methods Med Res 2023; 32:2254-2269. [PMID: 37855203 DOI: 10.1177/09622802231206472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2023]
Abstract
We develop a functional proportional hazards mixture cure model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the expectation-maximization algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze (i) minute-by-minute physical activity data from the National Health And Nutrition Examination Survey 2003-2006 to study the association between diurnal patterns of physical activity at baseline and all cancer mortality through 2019 while adjusting for other biological factors; (ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post intensive care unit recovery and mortality event. Our findings provide novel epidemiological insights into the association between daily patterns of physical activity and cancer mortality. Software implementation and illustration of the proposed estimation method are provided in R.
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Affiliation(s)
- Rahul Ghosal
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA
| | - Marcos Matabuena
- Department of Biostatistics, Harvard University T. H. Chan School of Public Health, Boston, MA, USA
| | - Jiajia Zhang
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA
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3
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Pini A, Sørensen H, Tolver A, Vantini S. Local inference for functional linear mixed models. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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4
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Abramowicz K, Pini A, Schelin L, de Luna SS, Stamm A, Vantini S. Domain selection and family-wise error rate for functional data: a unified framework. Biometrics 2022. [PMID: 35352337 DOI: 10.1111/biom.13669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 03/23/2022] [Indexed: 11/26/2022]
Abstract
Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as component-wise inference for multivariate data naturally performs feature selection, subset-wise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p-values of hypothesis tests performed on point-wise evaluations of functional data are suitably adjusted for providing a control of the family-wise error rate (FWER) over a family of subsets of the domain. We show that several state-of-the-art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined threshold-wise testing, in which the family of subsets is instead built in a data-driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a-priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples, and compare their performance with other existing methods. This article is protected by copyright. All rights reserved.
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Affiliation(s)
- Konrad Abramowicz
- Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden
| | - Alessia Pini
- Department of Statistical Sciences, Università Cattolica del Sacro Cuore, Milan, Italy
| | - Lina Schelin
- Department of Statistics, Umeå School of Business, Economics and Statistics, UmeåUniversity, Umeå, Sweden
| | - Sara Sjöstedt de Luna
- Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden
| | - Aymeric Stamm
- Department of Mathematics Jean Leray, UMR CNRS 6629, Nantes University, Nantes, France
| | - Simone Vantini
- MOX - Modelling and Scientific Computing Laboratory, Department of Mathematics, Politecnico di Milano, Milan, Italy
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5
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Harris T, Li B, Steiger NJ, Smerdon JE, Narisetty N, Tucker JD. Evaluating Proxy Influence in Assimilated Paleoclimate Reconstructions—Testing the Exchangeability of Two Ensembles of Spatial Processes. J Am Stat Assoc 2021. [DOI: 10.1080/01621459.2020.1799810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Trevor Harris
- Department of Statistics, University of Illinois at Urbana-Champaign , Champaign , IL
| | - Bo Li
- Department of Statistics, University of Illinois at Urbana-Champaign , Champaign , IL
| | - Nathan J. Steiger
- Department of Oceanography, Lamont-Doherty Earth Observatory , Palisades , NY
| | - Jason E. Smerdon
- Department of Oceanography, Lamont-Doherty Earth Observatory , Palisades , NY
| | - Naveen Narisetty
- Department of Statistics, University of Illinois at Urbana-Champaign , Champaign , IL
| | - J. Derek Tucker
- Department of Statistical Sciences, Sandia National Laboratories , Albuquerque , NM
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6
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Qiu Z, Chen J, Zhang JT. Two-sample tests for multivariate functional data with applications. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2020.107160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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7
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Wang Q. Two-sample inference for sparse functional data. Electron J Stat 2021. [DOI: 10.1214/21-ejs1802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Qiyao Wang
- Department of Statistics, University of Pittsburgh, 1826 Wesley W. Posvar Hall, Pittsburgh, PA 15260
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8
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Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections. MATHEMATICS 2020. [DOI: 10.3390/math9010044] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Sign, Wilcoxon and Mann-Whitney tests are nonparametric methods in one or two-sample problems. The nonparametric methods are alternatives used for testing hypothesis when the standard methods based on the Gaussianity assumption are not suitable to be applied. Recently, the functional data analysis (FDA) has gained relevance in statistical modeling. In FDA, each observation is a curve or function which usually is a realization of a stochastic process. In the literature of FDA, several methods have been proposed for testing hypothesis with samples coming from Gaussian processes. However, when this assumption is not realistic, it is necessary to utilize other approaches. Clustering and regression methods, among others, for non-Gaussian functional data have been proposed recently. In this paper, we propose extensions of the sign, Wilcoxon and Mann-Whitney tests to the functional data context as methods for testing hypothesis when we have one or two samples of non-Gaussian functional data. We use random projections to transform the functional problem into a scalar one, and then we proceed as in the standard case. Based on a simulation study, we show that the proposed tests have a good performance. We illustrate the methodology by applying it to a real data set.
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10
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Causeur D, Sheu CF, Perthame E, Rufini F. A functional generalized F-test for signal detection with applications to event-related potentials significance analysis. Biometrics 2019; 76:246-256. [PMID: 31301147 DOI: 10.1111/biom.13118] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2018] [Accepted: 07/02/2019] [Indexed: 11/28/2022]
Abstract
Motivated by the analysis of complex dependent functional data such as event-related brain potentials (ERP), this paper considers a time-varying coefficient multivariate regression model with fixed-time covariates for testing global hypotheses about population mean curves. Based on a reduced-rank modeling of the time correlation of the stochastic process of pointwise test statistics, a functional generalized F-test is proposed and its asymptotic null distribution is derived. Our analytical results show that the proposed test is more powerful than functional analysis of variance testing methods and competing signal detection procedures for dependent data. Simulation studies confirm such power gain for data with patterns of dependence similar to those observed in ERPs. The new testing procedure is illustrated with an analysis of the ERP data from a study of neural correlates of impulse control.
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Affiliation(s)
- David Causeur
- IRMAR UMR CNRS 6625, Agrocampus Ouest, Rennes Cedex, France
| | - Ching-Fan Sheu
- Institute of Education, National Cheng Kung University, Tainan, Taiwan
| | - Emeline Perthame
- Bioinformatique et Biostatistique, Bioinformatics and Biostatistics Hub C3BI, USR 3756 IP CNRS, Institut Pasteur, Paris, France
| | - Flavia Rufini
- Department of Statistics and Computer Science, Agrocampus Ouest, Rennes Cedex, France
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11
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Li Y, Huang C, Härdle WK. Spatial functional principal component analysis with applications to brain image data. J MULTIVARIATE ANAL 2019. [DOI: 10.1016/j.jmva.2018.11.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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12
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Pini A, Spreafico L, Vantini S, Vietti A. Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles. J MULTIVARIATE ANAL 2019. [DOI: 10.1016/j.jmva.2018.11.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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13
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Xu P, Lee Y, Shi JQ, Eyre J. Automatic detection of significant areas for functional data with directional error control. Stat Med 2019; 38:376-397. [PMID: 30225994 DOI: 10.1002/sim.7968] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2017] [Revised: 07/30/2018] [Accepted: 08/22/2018] [Indexed: 11/11/2022]
Abstract
In this paper, we propose a large-scale multiple testing procedure to find the significant sub-areas between two samples of curves automatically. The procedure is optimal in that it controls the directional false discovery rate at any specified level on a continuum asymptotically. By introducing a nonparametric Gaussian process regression model for the two-sided multiple test, the procedure is computationally inexpensive. It can cope with problems with multidimensional covariates and accommodate different sampling designs across the samples. We further propose the significant curve/surface, giving an insight on dynamic significant differences between two curves. Simulation studies demonstrate that the proposed procedure enjoys superior performance with strong power and good directional error control. The procedure is also illustrated with the application to two executive function studies in hemiplegia.
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Affiliation(s)
- Peirong Xu
- College of Mathematics and Sciences, Shanghai Normal University, Shanghai, China
| | - Youngjo Lee
- Department of Statistics, Seoul National University, Seoul, Korea
| | - Jian Qing Shi
- School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, UK
| | - Janet Eyre
- Institute of Neuroscience, Newcastle University, Newcastle upon Tyne, UK
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14
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15
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Sharghi Ghale-Joogh H, Hosseini-Nasab SME. A two-sample test for mean functions with increasing number of projections. STATISTICS-ABINGDON 2018. [DOI: 10.1080/02331888.2018.1472599] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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16
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Chen J, Ohlssen D, Zhou Y. Functional Mixed Effects Model for the Analysis of Dose-Titration Studies. Stat Biopharm Res 2018. [DOI: 10.1080/19466315.2018.1458649] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Ji Chen
- Department of Statistics and Actuarial Sciences, East China Normal University, Shanghai, P. R. China
| | - David Ohlssen
- Novartis Pharmaceuticals Corporation, East Hanover, NJ
| | - Yingchun Zhou
- Department of Statistics and Actuarial Sciences, East China Normal University, Shanghai, P. R. China
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17
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Abramowicz K, Häger CK, Pini A, Schelin L, Sjöstedt de Luna S, Vantini S. Nonparametric inference for functional-on-scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament. Scand Stat Theory Appl 2018. [DOI: 10.1111/sjos.12333] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Konrad Abramowicz
- Department of Mathematics and Mathematical Statistics; Umeå University; Umeå Sweden
| | - Charlotte K. Häger
- Department of Community Medicine and Rehabilitation; Umeå University; Umeå Sweden
| | - Alessia Pini
- Department of Statistics, Umeå School of Business, Economics and Statistics; Umeå University; Umeå Sweden
- Department of Statistical Sciences; Università Cattolica del Sacro Cuore; Milan Italy
| | - Lina Schelin
- Department of Community Medicine and Rehabilitation; Umeå University; Umeå Sweden
- Department of Statistics, Umeå School of Business, Economics and Statistics; Umeå University; Umeå Sweden
| | | | - Simone Vantini
- MOX - Modelling and Scientific Computing Laboratory, Department of Mathematics; Politecnico di Milano; Milan Italy
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18
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Park SY, Staicu AM, Xiao L, Crainiceanu CM. Simple fixed-effects inference for complex functional models. Biostatistics 2018; 19:137-152. [PMID: 29036541 PMCID: PMC5862370 DOI: 10.1093/biostatistics/kxx026] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2016] [Revised: 04/09/2017] [Accepted: 05/07/2017] [Indexed: 11/14/2022] Open
Abstract
We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g. subjects) to conduct inference on the fixed effects parameters. Simulations show excellent coverage probability of the confidence intervals and size of tests for the fixed effects model parameters. Methods are motivated by and applied to the Baltimore Longitudinal Study of Aging, though they are applicable to other studies that collect correlated functional data.
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Affiliation(s)
- So Young Park
- Department of Statistics, North Carolina State University, Raleigh, NC, USA
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, NC, USA
| | - Luo Xiao
- Department of Statistics, North Carolina State University, Raleigh, NC, USA
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19
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Laber EB, Staicu AM. Functional feature construction for individualized treatment regimes. J Am Stat Assoc 2017; 113:1219-1227. [PMID: 30416232 PMCID: PMC6223315 DOI: 10.1080/01621459.2017.1321545] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2015] [Revised: 01/01/2017] [Indexed: 10/19/2022]
Abstract
Evidence-based personalized medicine formalizes treatment selection as an individualized treatment regime that maps up-to-date patient information into the space of possible treatments. Available patient information may include static features such race, gender, family history, genetic and genomic information, as well as longitudinal information including the emergence of comorbidities, waxing and waning of symptoms, side-effect burden, and adherence. Dynamic information measured at multiple time points before treatment assignment should be included as input to the treatment regime. However, subject longitudinal measurements are typically sparse, irregularly spaced, noisy, and vary in number across subjects. Existing estimators for treatment regimes require equal information be measured on each subject and thus standard practice is to summarize longitudinal subject information into a scalar, ad hoc summary during data pre-processing. This reduction of the longitudinal information to a scalar feature precedes estimation of a treatment regime and is therefore not informed by subject outcomes, treatments, or covariates. Furthermore, we show that this reduction requires more stringent causal assumptions for consistent estimation than are necessary. We propose a data-driven method for constructing maximally prescriptive yet interpretable features that can be used with standard methods for estimating optimal treatment regimes. In our proposed framework, we treat the subject longitudinal information as a realization of a stochastic process observed with error at discrete time points. Functionals of this latent process are then combined with outcome models to estimate an optimal treatment regime. The proposed methodology requires weaker causal assumptions than Q-learning with an ad hoc scalar summary and is consistent for the optimal treatment regime.
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Affiliation(s)
- Eric B Laber
- Department of Statistics, North Carolina State University, Raleigh, NC, 27695, U.S.A
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, NC, 27695, U.S.A
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20
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Affiliation(s)
- A. Pini
- MOX – Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - S. Vantini
- MOX – Department of Mathematics, Politecnico di Milano, Milan, Italy
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21
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Abstract
Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for ‘generalized’ functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases—particularly splines and functional principal components—and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost , respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.
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Affiliation(s)
- Sonja Greven
- Department of Statistics, Ludwig-Maximilians-Universität München, Germany
| | - Fabian Scheipl
- Department of Statistics, Ludwig-Maximilians-Universität München, Germany
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22
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Gruen ME, Alfaro-Córdoba M, Thomson AE, Worth AC, Staicu AM, Lascelles BDX. The Use of Functional Data Analysis to Evaluate Activity in a Spontaneous Model of Degenerative Joint Disease Associated Pain in Cats. PLoS One 2017; 12:e0169576. [PMID: 28099449 PMCID: PMC5242440 DOI: 10.1371/journal.pone.0169576] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2016] [Accepted: 12/19/2016] [Indexed: 11/22/2022] Open
Abstract
Introduction and objectives Accelerometry is used as an objective measure of physical activity in humans and veterinary species. In cats, one important use of accelerometry is in the study of therapeutics designed to treat degenerative joint disease (DJD) associated pain, where it serves as the most widely applied objective outcome measure. These analyses have commonly used summary measures, calculating the mean activity per-minute over days and comparing between treatment periods. While this technique has been effective, information about the pattern of activity in cats is lost. In this study, functional data analysis was applied to activity data from client-owned cats with (n = 83) and without (n = 15) DJD. Functional data analysis retains information about the pattern of activity over the 24-hour day, providing insight into activity over time. We hypothesized that 1) cats without DJD would have higher activity counts and intensity of activity than cats with DJD; 2) that activity counts and intensity of activity in cats with DJD would be inversely correlated with total radiographic DJD burden and total orthopedic pain score; and 3) that activity counts and intensity would have a different pattern on weekends versus weekdays. Results and conclusions Results showed marked inter-cat variability in activity. Cats exhibited a bimodal pattern of activity with a sharp peak in the morning and broader peak in the evening. Results further showed that this pattern was different on weekends than weekdays, with the morning peak being shifted to the right (later). Cats with DJD showed different patterns of activity from cats without DJD, though activity and intensity were not always lower; instead both the peaks and troughs of activity were less extreme than those of the cats without DJD. Functional data analysis provides insight into the pattern of activity in cats, and an alternative method for analyzing accelerometry data that incorporates fluctuations in activity across the day.
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Affiliation(s)
- Margaret E. Gruen
- Comparative Pain Research Program, Department of Clinical Sciences, College of Veterinary Medicine, North Carolina State University, Raleigh, North Carolina, United States of America
- Comparative Medicine Institute, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Marcela Alfaro-Córdoba
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Andrea E. Thomson
- Comparative Pain Research Program, Department of Clinical Sciences, College of Veterinary Medicine, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Alicia C. Worth
- Comparative Pain Research Program, Department of Clinical Sciences, College of Veterinary Medicine, North Carolina State University, Raleigh, North Carolina, United States of America
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, United States of America
- * E-mail:
| | - B. Duncan X. Lascelles
- Comparative Pain Research Program, Department of Clinical Sciences, College of Veterinary Medicine, North Carolina State University, Raleigh, North Carolina, United States of America
- Comparative Medicine Institute, North Carolina State University, Raleigh, North Carolina, United States of America
- Center for Pain Research and Innovation, University of North Carolina School of Dentistry, Chapel Hill, North Carolina, United States of America
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24
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Pini A, Vantini S. The interval testing procedure: A general framework for inference in functional data analysis. Biometrics 2016; 72:835-45. [PMID: 26811864 DOI: 10.1111/biom.12476] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2015] [Revised: 12/01/2015] [Accepted: 12/01/2015] [Indexed: 11/28/2022]
Abstract
We introduce in this work the Interval Testing Procedure (ITP), a novel inferential technique for functional data. The procedure can be used to test different functional hypotheses, e.g., distributional equality between two or more functional populations, equality of mean function of a functional population to a reference. ITP involves three steps: (i) the representation of data on a (possibly high-dimensional) functional basis; (ii) the test of each possible set of consecutive basis coefficients; (iii) the computation of the adjusted p-values associated to each basis component, by means of a new strategy here proposed. We define a new type of error control, the interval-wise control of the family wise error rate, particularly suited for functional data. We show that ITP is provided with such a control. A simulation study comparing ITP with other testing procedures is reported. ITP is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology. ITP is implemented in the fdatest R package.
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Affiliation(s)
- Alessia Pini
- MOX-Department of Mathematics, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy.
| | - Simone Vantini
- MOX-Department of Mathematics, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy.
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25
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Pomann GM, Staicu AM, Ghosh S. A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis. J R Stat Soc Ser C Appl Stat 2016; 65:395-414. [PMID: 27041772 DOI: 10.1111/rssc.12130] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Motivated by an imaging study, this paper develops a nonparametric testing procedure for testing the null hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. The objective is to formally compare white matter tract profiles between healthy individuals and multiple sclerosis patients, as assessed by conventional diffusion tensor imaging measures. We propose to decompose the curves using functional principal component analysis of a mixture process, which we refer to as marginal functional principal component analysis. This approach reduces the dimension of the testing problem in a way that enables the use of traditional nonparametric univariate testing procedures. The procedure is computationally efficient and accommodates different sampling designs. Numerical studies are presented to validate the size and power properties of the test in many realistic scenarios. In these cases, the proposed test has been found to be more powerful than its primary competitor. Application to the diffusion tensor imaging data reveals that all the tracts studied are associated with multiple sclerosis and the choice of the diffusion tensor image measurement is important when assessing axonal disruption.
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Affiliation(s)
| | | | - Sujit Ghosh
- North Carolina State University, Raleigh and Statistical and Applied Mathematical Sciences Institute, RTP, NC. USA
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26
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Affiliation(s)
| | - Xiang‐Nan Feng
- Department of Statistics The Chinese University of Hong Kong
| | - Min Chen
- Academy of Mathematics System Science Chinese Academy of Sciences
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27
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Staicu AM, Lahiri SN, Carroll RJ. Significance tests for functional data with complex dependence structure. J Stat Plan Inference 2015; 156:1-13. [PMID: 26023253 DOI: 10.1016/j.jspi.2014.08.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
We propose an L2-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups-clusters or subjects-units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients. The asymptotic null distribution of the test statistic is developed, under mild regularity conditions. To our knowledge this is the first work that studies hypothesis testing, when data have such complex multilevel functional and spatial structure. Two small-sample alternatives, including a novel block bootstrap for functional data, are proposed, and their performance is examined in simulation studies. The paper concludes with an illustration of a motivating experiment.
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Affiliation(s)
- Ana-Maria Staicu
- Department of Statistics, North Carolina State University, United States
| | - Soumen N Lahiri
- Department of Statistics, North Carolina State University, United States
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