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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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Zhu C, Wang JL. Testing homogeneity: the trouble with sparse functional data. J R Stat Soc Series B Stat Methodol 2023; 85:705-731. [PMID: 37521166 PMCID: PMC10376451 DOI: 10.1093/jrsssb/qkad021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2022] [Revised: 12/06/2022] [Accepted: 02/25/2023] [Indexed: 08/01/2023]
Abstract
Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.
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Affiliation(s)
- Changbo Zhu
- Address for correspondence: Changbo Zhu, Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA.
| | - Jane-Ling Wang
- Department of Statistics, University of California, Davis, Davis, United States
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3
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Wang Q, Guo S, Yao F, Zou C. Thresholding mean test for functional data with power enhancement. Stat (Int Stat Inst) 2022. [DOI: 10.1002/sta4.509] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Qingsong Wang
- Institute of Statistics and Big Data Renmin University of China Beijing China
| | - Shaojun Guo
- Institute of Statistics and Big Data Renmin University of China Beijing China
| | - Fang Yao
- School of Mathematical Sciences, Center for Statistical Science Peking University Beijing China
| | - Changliang Zou
- School of Statistics and Data Science LPMC, KLMDASR and LEBPS, Nankai University Tianjin China
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4
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Li M, Wang K, Maity A, Staicu AM. Inference in Functional Linear Quantile Regression. J MULTIVARIATE ANAL 2022; 190:104985. [PMID: 35370319 PMCID: PMC8975129 DOI: 10.1016/j.jmva.2022.104985] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the R code is published online at https://github.com/xylimeng/fQR-testing.
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Affiliation(s)
- Meng Li
- Department of Statistics, Rice University, Houston, TX
| | | | - Arnab Maity
- Department of Statistics, North Carolina State University, Raleigh, NC
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, NC
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5
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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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6
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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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Li T, Li T, Zhu Z, Zhu H. Regression Analysis of Asynchronous Longitudinal Functional and Scalar Data. J Am Stat Assoc 2020. [DOI: 10.1080/01621459.2020.1844211] [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)
- Ting Li
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Tengfei Li
- Department of Radiology and Biomedical Research Imaging Center (BRIC), University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Zhongyi Zhu
- Department of Statistics, Fudan University, Shanghai, China
| | - Hongtu Zhu
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC
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García‐Portugués E, Álvarez‐Liébana J, Álvarez‐Pérez G, González‐Manteiga W. A goodness‐of‐fit test for the functional linear model with functional response. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12486] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eduardo García‐Portugués
- Department of Statistics Carlos III University of Madrid, Spain
- UC3M‐Santander Big Data Institute Carlos III University of Madrid, Spain
| | - Javier Álvarez‐Liébana
- Department of Statistics and Operations Research and Mathematics Didactics University of Oviedo, Spain
| | | | - Wenceslao González‐Manteiga
- Department of Statistics, Mathematical Analysis and Optimization University of Santiago de Compostela, Spain
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Hu M, Crainiceanu C, Schindler MK, Dewey B, Reich DS, Shinohara RT, Eloyan A. Matrix decomposition for modeling lesion development processes in multiple sclerosis. Biostatistics 2020; 23:83-100. [PMID: 32318692 DOI: 10.1093/biostatistics/kxaa016] [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: 07/01/2019] [Revised: 03/11/2019] [Accepted: 03/12/2020] [Indexed: 11/14/2022] Open
Abstract
Our main goal is to study and quantify the evolution of multiple sclerosis lesions observed longitudinally over many years in multi-sequence structural magnetic resonance imaging (sMRI). To achieve that, we propose a class of functional models for capturing the temporal dynamics and spatial distribution of the voxel-specific intensity trajectories in all sMRI sequences. To accommodate the hierarchical data structure (observations nested within voxels, which are nested within lesions, which, in turn, are nested within study participants), we use structured functional principal component analysis. We propose and evaluate the finite sample properties of hypothesis tests of therapeutic intervention effects on lesion evolution while accounting for the multilevel structure of the data. Using this novel testing strategy, we found statistically significant differences in lesion evolution between treatment groups.
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Affiliation(s)
- Menghan Hu
- Department of Biostatistics, Brown University, Providence, RI 02903, USA
| | - Ciprian Crainiceanu
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA
| | - Matthew K Schindler
- Translational Neuroradiology Section, Division of Neuroimmunology and Neurovirology, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892, USA
| | - Blake Dewey
- Translational Neuroradiology Section, Division of Neuroimmunology and Neurovirology, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892, USA and Department of Electrical and Computer Engineering, Johns Hopkins Whiting School of Engineering, Baltimore, MD 21218, USA
| | - Daniel S Reich
- Translational Neuroradiology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892, USA
| | - Russell T Shinohara
- Department of Biostatistics, Epidemiology, and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA and Department of Radiology, Center for Biomedical Image Computing and Analytics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ani Eloyan
- Department of Biostatistics, Brown University, Providence, RI 02903, USA
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Zhu H, Chen K, Luo X, Yuan Y, Wang JL. FMEM: Functional Mixed Effects Models for Longitudinal Functional Responses. Stat Sin 2019; 29:2007-2033. [PMID: 31745381 DOI: 10.5705/ss.202017.0505] [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] [Indexed: 11/06/2022]
Abstract
The aim of this paper is to conduct a systematic and theoretical analysis of estimation and inference for a class of functional mixed effects models (FMEM). Such FMEMs consist of fixed effects that characterize the association between longitudinal functional responses and covariates of interest and random effects that capture the spatial-temporal correlations of longitudinal functional responses. We propose local linear estimates of refined fixed effect functions and establish their weak convergence along with a simultaneous confidence band for each fixed-effect function. We propose a global test for the linear hypotheses of varying coefficient functions and derive the associated asymptotic distribution under the null hypothesis and the asymptotic power under the alternative hypothesis are derived. We also establish the convergence rates of the estimated spatial-temporal covariance operators and their associated eigenvalues and eigenfunctions. We conduct extensive simulations and apply our method to a white-matter fiber data set from a national database for autism research to examine the finite-sample performance of the proposed estimation and inference procedures.
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Affiliation(s)
- Hongtu Zhu
- The University of Texas MD Anderson Cancer Center
| | | | | | - Ying Yuan
- The University of Texas MD Anderson Cancer Center.,University of Pittsburgh.,Statistics & Decision Sciences.,University of California at Davis
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Pilavakis D, Paparoditis E, Sapatinas T. Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem. BERNOULLI 2019. [DOI: 10.3150/18-bej1099] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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12
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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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13
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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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15
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Testing Gait with Ankle-Foot Orthoses in Children with Cerebral Palsy by Using Functional Mixed-Effects Analysis of Variance. Sci Rep 2017; 7:11081. [PMID: 28894132 PMCID: PMC5594035 DOI: 10.1038/s41598-017-11282-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2017] [Accepted: 08/17/2017] [Indexed: 11/25/2022] Open
Abstract
Existing statistical methods extract insufficient information from 3-dimensional gait data, rendering clinical interpretation of impaired movement patterns sub-optimal. We propose an alternative approach based on functional data analysis that may be worthy of exploration. We apply this to gait data analysis using repeated-measurements data from children with cerebral palsy who had been prescribed fixed ankle-foot orthoses as an example. We analyze entire gait curves by means of a new functional F test with comparison to multiple pointwise F tests and also to the traditional method - univariate repeated-measurements analysis of variance of joint angle minima and maxima. The new test maintains the nominal significance level and can be adapted to test hypotheses for specific phases of the gait cycle. The main findings indicate that ankle-foot orthoses exert significant effects on coronal and sagittal plane ankle rotation; and both sagittal and horizontal plane foot rotation. The functional F test provided further information for the stance and swing phases. Differences between the results of the different statistical approaches are discussed, concluding that the novel method has potential utility and is worthy of validation through larger scale patient and clinician engagement to determine whether it is preferable to the traditional approach.
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16
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Bai J, Ivanescu A, Crainiceanu CM. Discussion of the paper ‘A general framework for functional regression modelling’. STAT MODEL 2017. [DOI: 10.1177/1471082x16681335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This discussion provides our reaction to the article by Greven and Scheipl. It contains an overview of their article and a description of the many areas of research that remain open and could benefit from further methodological and computational development.
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Affiliation(s)
- Jiawei Bai
- Department of Biostatistics, Johns Hopkins University, Baltimore, MD, USA
| | - Andrada Ivanescu
- Department of Mathematical Sciences, Montclair State University, Montclair, NJ, USA
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17
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