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Zoh RS, Luan Y, Xue L, Allison DB, Tekwe CD. A Bayesian semi-parametric scalar-on-function regression with measurement error using instrumental variables. Stat Med 2024; 43:4043-4054. [PMID: 38978160 DOI: 10.1002/sim.10165] [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: 08/02/2022] [Revised: 03/26/2024] [Accepted: 06/17/2024] [Indexed: 07/10/2024]
Abstract
Wearable devices such as the ActiGraph are now commonly used in research to monitor or track physical activity. This trend corresponds with the growing need to assess the relationships between physical activity and health outcomes, such as obesity, accurately. Device-based physical activity measures are best treated as functions when assessing their associations with scalar-valued outcomes such as body mass index. Scalar-on-function regression (SoFR) is a suitable regression model in this setting. Most estimation approaches in SoFR assume that the measurement error in functional covariates is white noise. Violating this assumption can lead to underestimating model parameters. There are limited approaches to correcting measurement errors for frequentist methods and none for Bayesian methods in this area. We present a non-parametric Bayesian measurement error-corrected SoFR model that relaxes all the constraining assumptions often involved with these models. Our estimation relies on an instrumental variable allowing a time-varying biasing factor, a significant departure from the current generalized method of moment (GMM) approach. Our proposed method also permits model-based grouping of the functional covariate following measurement error correction. This grouping of the measurement error-corrected functional covariate allows additional ease of interpretation of how the different groups differ. Our method is easy to implement, and we demonstrate its finite sample properties in extensive simulations. Finally, we applied our method to data from the National Health and Examination Survey to assess the relationship between wearable device-based measures of physical activity and body mass index in adults in the United States.
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Affiliation(s)
- Roger S Zoh
- Department of Epidemiology and Biostatistics, School of Public Health, Indiana University, Bloomington, Indiana
| | - Yuanyuan Luan
- Department of Epidemiology and Biostatistics, School of Public Health, Indiana University, Bloomington, Indiana
| | - Lan Xue
- Department of Statistics, Oregon State University, Corvallis, Oregon
| | - David B Allison
- Department of Epidemiology and Biostatistics, School of Public Health, Indiana University, Bloomington, Indiana
| | - Carmen D Tekwe
- Department of Epidemiology and Biostatistics, School of Public Health, Indiana University, Bloomington, Indiana
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2
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Yang Q, Jiang M, Li C, Luo S, Crowley MJ, Shaw RJ. Predicting health outcomes with intensive longitudinal data collected by mobile health devices: a functional principal component regression approach. BMC Med Res Methodol 2024; 24:69. [PMID: 38494505 PMCID: PMC10944610 DOI: 10.1186/s12874-024-02193-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 03/01/2024] [Indexed: 03/19/2024] Open
Abstract
BACKGROUND Intensive longitudinal data (ILD) collected in near real time by mobile health devices provide a new opportunity for monitoring chronic diseases, early disease risk prediction, and disease prevention in health research. Functional data analysis, specifically functional principal component analysis, has great potential to abstract trends in ILD but has not been used extensively in mobile health research. OBJECTIVE To introduce functional principal component analysis (fPCA) and demonstrate its potential applicability in estimating trends in ILD collected by mobile heath devices, assessing longitudinal association between ILD and health outcomes, and predicting health outcomes. METHODS fPCA and scalar-to-function regression models were reviewed. A case study was used to illustrate the process of abstracting trends in intensively self-measured blood glucose using functional principal component analysis and then predicting future HbA1c values in patients with type 2 diabetes using a scalar-to-function regression model. RESULTS Based on the scalar-to-function regression model results, there was a slightly increasing trend between daily blood glucose measures and HbA1c. 61% of variation in HbA1c could be predicted by the three preceding months' blood glucose values measured before breakfast (P < 0.0001, [Formula: see text]). CONCLUSIONS Functional data analysis, specifically fPCA, offers a unique tool to capture patterns in ILD collected by mobile health devices. It is particularly useful in assessing longitudinal dynamic association between repeated measures and outcomes, and can be easily integrated in prediction models to improve prediction precision.
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Affiliation(s)
- Qing Yang
- School of Nursing, Duke University, Durham, USA.
| | | | - Cai Li
- Department of Biostatistics, St. Jude Children's Research Hospital, Memphis, TN, USA
| | - Sheng Luo
- Biostatistics & Bioinformatics, Duke University, Durham, USA
| | - Matthew J Crowley
- Center of Innovation to Accelerate Discovery and Practice Transformation, Durham Veterans Affairs Medical Center, Durham, NC, USA
- Division of Endocrinology, Diabetes and Metabolism, Duke University School of Medicine, Durham, NC, USA
| | - Ryan J Shaw
- School of Nursing, Duke University, Durham, USA
- Center of Innovation to Accelerate Discovery and Practice Transformation, Durham Veterans Affairs Medical Center, Durham, NC, USA
- Center for Applied Genomics & Precision Medicine, School of Medicine, Duke University, Durham, NC, USA
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3
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Xie S, Ogden RT. Functional support vector machine. Biostatistics 2024:kxae007. [PMID: 38476094 DOI: 10.1093/biostatistics/kxae007] [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] [Received: 04/03/2023] [Revised: 12/26/2023] [Accepted: 02/13/2024] [Indexed: 03/14/2024] Open
Abstract
Linear and generalized linear scalar-on-function modeling have been commonly used to understand the relationship between a scalar response variable (e.g. continuous, binary outcomes) and functional predictors. Such techniques are sensitive to model misspecification when the relationship between the response variable and the functional predictors is complex. On the other hand, support vector machines (SVMs) are among the most robust prediction models but do not take account of the high correlations between repeated measurements and cannot be used for irregular data. In this work, we propose a novel method to integrate functional principal component analysis with SVM techniques for classification and regression to account for the continuous nature of functional data and the nonlinear relationship between the scalar response variable and the functional predictors. We demonstrate the performance of our method through extensive simulation experiments and two real data applications: the classification of alcoholics using electroencephalography signals and the prediction of glucobrassicin concentration using near-infrared reflectance spectroscopy. Our methods especially have more advantages when the measurement errors in functional predictors are relatively large.
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Affiliation(s)
- Shanghong Xie
- School of Statistics, Southwestern University of Finance and Economics, Chengdu, China
- Department of Biostatistics, Columbia University, New York, NY, United States
| | - R Todd Ogden
- Department of Biostatistics, Columbia University, New York, NY, United States
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Godbole S, Leroux A, Brooks-Russell A, Subramanian PS, Kosnett MJ, Wrobel J. A Study of Pupil Response to Light as a Digital Biomarker of Recent Cannabis Use. Digit Biomark 2024; 8:83-92. [PMID: 38682092 PMCID: PMC11052563 DOI: 10.1159/000538561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 03/23/2024] [Indexed: 05/01/2024] Open
Abstract
Introduction Given the traffic safety and occupational injury prevention implications associated with cannabis impairment, there is a need for objective and validated measures of recent cannabis use. Pupillary light response may offer an approach for detection. Method Eighty-four participants (mean age: 32, 42% female) with daily, occasional, and no-use cannabis use histories participated in pupillary light response tests before and after smoking cannabis ad libitum or relaxing for 15 min (no use). The impact of recent cannabis consumption on trajectories of the pupillary light response was modeled using functional data analysis tools. Logistic regression models for detecting recent cannabis use were compared, and average pupil trajectories across cannabis use groups and times since light test administration were estimated. Results Models revealed small, significant differences in pupil response to light after cannabis use comparing the occasional use group to the no-use control group, and similar statistically significant differences in pupil response patterns comparing the daily use group to the no-use comparison group. Trajectories of pupillary light response estimated using functional data analysis found that acute cannabis smoking was associated with less initial and sustained pupil constriction compared to no cannabis smoking. Conclusion These analyses show the promise of pairing pupillary light response and functional data analysis methods to assess recent cannabis use.
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Affiliation(s)
- Suneeta Godbole
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
| | - Andrew Leroux
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
| | - Ashley Brooks-Russell
- Injury and Violence Prevention Center, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
| | - Prem S. Subramanian
- Departments of Ophthalmology, Neurology, and Neurosurgery, Sue Anschutz-Rodgers Eye Center, CU School of Medicine, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
- Department of Surgery, Uniformed Services University of the Health Sciences, Bethesda, MD, USA
| | - Michael J. Kosnett
- Department of Medicine, University of Colorado School of Medicine, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
- Department of Environmental and Occupational Health, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
| | - Julia Wrobel
- Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA, USA
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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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Yi M, Zhan T, Peck AR, Hooke JA, Kovatich AJ, Shriver CD, Hu H, Sun Y, Rui H, Chervoneva I. Quantile Index Biomarkers Based on Single-Cell Expression Data. J Transl Med 2023; 103:100158. [PMID: 37088463 PMCID: PMC10524910 DOI: 10.1016/j.labinv.2023.100158] [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: 01/30/2023] [Revised: 04/06/2023] [Accepted: 04/15/2023] [Indexed: 04/25/2023] Open
Abstract
Current histocytometry methods enable single-cell quantification of biomolecules in tumor tissue sections by multiple detection technologies, including multiplex fluorescence-based immunohistochemistry or in situ hybridization. Quantitative pathology platforms can provide distributions of cellular signal intensity (CSI) levels of biomolecules across the entire cell populations of interest within the sampled tumor tissue. However, the heterogeneity of CSI levels is usually ignored, and the simple mean signal intensity value is considered a cancer biomarker. Here we consider the entire distribution of CSI expression levels of a given biomolecule in the cancer cell population as a predictor of clinical outcome. The proposed quantile index (QI) biomarker is defined as the weighted average of CSI distribution quantiles in individual tumors. The weight for each quantile is determined by fitting a functional regression model for a clinical outcome. That is, the weights are optimized so that the resulting QI has the highest power to predict a relevant clinical outcome. The proposed QI biomarkers were derived for proteins expressed in cancer cells of malignant breast tumors and demonstrated improved prognostic value compared with the standard mean signal intensity predictors. The R package Qindex implementing QI biomarkers has been developed. The proposed approach is not limited to immunohistochemistry data and can be based on any cell-level expressions of proteins or nucleic acids.
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Affiliation(s)
- Misung Yi
- Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Sidney Kimmel Medical College, Thomas Jefferson University, Philadelphia, Pennsylvania.
| | - Tingting Zhan
- Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Sidney Kimmel Medical College, Thomas Jefferson University, Philadelphia, Pennsylvania
| | - Amy R Peck
- Department of Pathology, Medical College of Wisconsin, Milwaukee, Wisconsin
| | - Jeffrey A Hooke
- John P. Murtha Cancer Center, Uniformed Services University and Walter Reed National Military Medical Center, Bethesda, Maryland
| | - Albert J Kovatich
- John P. Murtha Cancer Center, Uniformed Services University and Walter Reed National Military Medical Center, Bethesda, Maryland
| | - Craig D Shriver
- John P. Murtha Cancer Center, Uniformed Services University and Walter Reed National Military Medical Center, Bethesda, Maryland
| | - Hai Hu
- Chan Soon-Shiong Institute of Molecular Medicine at Windber, Windber, Pennsylvania
| | - Yunguang Sun
- Department of Pathology, Medical College of Wisconsin, Milwaukee, Wisconsin
| | - Hallgeir Rui
- Department of Pathology, Medical College of Wisconsin, Milwaukee, Wisconsin
| | - Inna Chervoneva
- Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Sidney Kimmel Medical College, Thomas Jefferson University, Philadelphia, Pennsylvania.
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7
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Ghosal R, Varma VR, Volfson D, Hillel I, Urbanek J, Hausdorff JM, Watts A, Zipunnikov V. Distributional data analysis via quantile functions and its application to modeling digital biomarkers of gait in Alzheimer's Disease. Biostatistics 2023; 24:539-561. [PMID: 36519565 PMCID: PMC10544806 DOI: 10.1093/biostatistics/kxab041] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 09/10/2021] [Accepted: 10/19/2021] [Indexed: 07/20/2023] Open
Abstract
With the advent of continuous health monitoring with wearable devices, users now generate their unique streams of continuous data such as minute-level step counts or heartbeats. Summarizing these streams via scalar summaries often ignores the distributional nature of wearable data and almost unavoidably leads to the loss of critical information. We propose to capture the distributional nature of wearable data via user-specific quantile functions (QF) and use these QFs as predictors in scalar-on-quantile-function-regression (SOQFR). As an alternative approach, we also propose to represent QFs via user-specific L-moments, robust rank-based analogs of traditional moments, and use L-moments as predictors in SOQFR (SOQFR-L). These two approaches provide two mutually consistent interpretations: in terms of quantile levels by SOQFR and in terms of L-moments by SOQFR-L. We also demonstrate how to deal with multi-modal distributional data via Joint and Individual Variation Explained using L-moments. The proposed methods are illustrated in a study of association of digital gait biomarkers with cognitive function in Alzheimers disease. Our analysis shows that the proposed methods demonstrate higher predictive performance and attain much stronger associations with clinical cognitive scales compared to simple distributional summaries.
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Affiliation(s)
- Rahul Ghosal
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
| | - Vijay R Varma
- National Institute on Aging (NIA), National Institutes of Health (NIH), Baltimore, MD, USA
| | - Dmitri Volfson
- Neuroscience Analytics, Computational Biology, Takeda, Cambridge, MA, USA
| | - Inbar Hillel
- Center for the Study of Movement, Cognition and Mobility, Neurological Institute, Tel Aviv Sourasky Medical Center, Tel Aviv, Israel
| | - Jacek Urbanek
- Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Jeffrey M Hausdorff
- Center for the Study of Movement, Cognition and Mobility, Neurological Institute, Tel Aviv Sourasky Medical Center, Tel Aviv, Israel, Department of Physical Therapy, Sackler Faculty of Medicine, and Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel, and Rush Alzheimer’s Disease Center and Department of Orthopedic Surgery, Rush University Medical Center, Chicago, IL, USA
| | - Amber Watts
- Department of Psychology, University of Kansas, Lawrence, KS, USA
| | - Vadim Zipunnikov
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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8
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Beyaztas U, Tez M, Lin Shang H. Robust scalar-on-function partial quantile regression. J Appl Stat 2023; 51:1359-1377. [PMID: 38835823 PMCID: PMC11146266 DOI: 10.1080/02664763.2023.2202464] [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: 12/16/2022] [Accepted: 04/08/2023] [Indexed: 06/06/2024]
Abstract
Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded in the response variable but unbounded in the predictor space. The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. This study proposes a robust procedure to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. We propose a weighted partial quantile covariance to obtain functional partial quantile components of the scalar-on-function quantile regression model. After the decomposition, the model parameters are estimated via a weighted loss function, where the robustness is obtained by iteratively reweighting the partial quantile components. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.
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Affiliation(s)
- Ufuk Beyaztas
- Department of Statistics, Marmara University, Kadikoy-Istanbul, Turkey
| | - Mujgan Tez
- Department of Statistics, Marmara University, Kadikoy-Istanbul, Turkey
| | - Han Lin Shang
- Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia
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9
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Ding H, Yao M, Zhang R. A new estimation in functional linear concurrent model with covariate dependent and noise contamination. METRIKA 2023. [DOI: 10.1007/s00184-023-00900-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
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10
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Circulating microvesicles correlate with radiation proctitis complication after radiotherapy. Sci Rep 2023; 13:2033. [PMID: 36739457 PMCID: PMC9899237 DOI: 10.1038/s41598-022-21726-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 09/30/2022] [Indexed: 02/05/2023] Open
Abstract
In a large retrospective study, we assessed the putative use of circulating microvesicles (MVs), as innovative biomarkers of radiation toxicity in a cohort of 208 patients with prostate adenocarcinoma overexposed to radiation. The level of platelet (P)-, monocyte (M)- and endothelial (E)-derived MVs were assessed by flow cytometry. Rectal bleeding toxicity scores were collected at the time of blood sampling and during the routine follow-up and were tested for association with MVs using a multivariate logistic regression. MVs dosimetric correlation was investigated using dose volume histograms information available for a subset of 36 patients. The number of PMVs was significantly increased in patients with highest toxicity grades compared to lower grades. Risk prediction analysis revealed that increased numbers of PMVs, and an increased amount of MMVs relative to EMVs, were associated with worst rectal bleeding grade compared to the time of blood sampling. Moreover, a significant correlation was found between PMV and MMV numbers, with the range of doses up to the median exposure (40 Gy) of bladder/rectum and anterior rectal wall, respectively. MVs could be considered as new biomarkers to improve the identification of patients with high toxicity grade and may be instrumental for the prognosis of radiation therapy complications.
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11
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Shape-constrained estimation in functional regression with Bernstein polynomials. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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12
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Rao AR, Reimherr M. Non-linear Functional Modeling using Neural Networks. J Comput Graph Stat 2023. [DOI: 10.1080/10618600.2023.2165498] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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13
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Tang B, Zhao Y, Venkataraman A, Tsapkini K, Lindquist MA, Pekar J, Caffo B. Differences in functional connectivity distribution after transcranial direct-current stimulation: A connectivity density point of view. Hum Brain Mapp 2022; 44:170-185. [PMID: 36371779 PMCID: PMC9783448 DOI: 10.1002/hbm.26112] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Revised: 09/09/2022] [Accepted: 10/02/2022] [Indexed: 11/14/2022] Open
Abstract
In this manuscript, we consider the problem of relating functional connectivity measurements viewed as statistical distributions to outcomes. We demonstrate the utility of using the distribution of connectivity on a study of resting-state functional magnetic resonance imaging association with an intervention. The method uses the estimated density of connectivity between nodes of interest as a functional covariate. Moreover, we demonstrate the utility of the procedure in an instance where connectivity is naturally considered an outcome by reversing the predictor/response relationship using case/control methodology. The method utilizes the density quantile, the density evaluated at empirical quantiles, instead of the empirical density directly. This improved the performance of the method by highlighting tail behavior, though we emphasize that by being flexible and non-parametric, the technique can detect effects related to the central portion of the density. To demonstrate the method in an application, we consider 47 primary progressive aphasia patients with various levels of language abilities. These patients were randomly assigned to two treatment arms, transcranial direct-current stimulation and language therapy versus sham (language therapy only), in a clinical trial. We use the method to analyze the effect of direct stimulation on functional connectivity. As such, we estimate the density of correlations among the regions of interest and study the difference in the density post-intervention between treatment arms. We discover that it is the tail of the density, rather than the mean or lower order moments of the distribution, that demonstrates a significant impact in the classification. The new approach has several benefits. Among them, it drastically reduces the number of multiple comparisons compared with edge-wise analysis. In addition, it allows for the investigation of the impact of functional connectivity on the outcomes where the connectivity is not geometrically localized.
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Affiliation(s)
- Bohao Tang
- Department of BiostatisticsJohns Hopkins UniversityBaltimoreMarylandUSA
| | - Yi Zhao
- Department of Biostatistics and Health Data ScienceIndiana University School of MedicineIndianapolisIndianaUSA
| | - Archana Venkataraman
- Department of Electrical and Computer EngineeringJohns Hopkins UniversityBaltimoreMarylandUSA
| | - Kyrana Tsapkini
- Department of NeurologyJohns Hopkins MedicineBaltimoreMarylandUSA,Department of Cognitive ScienceJohns Hopkins MedicineBaltimoreMarylandUSA
| | | | - James Pekar
- F.M. Kirby Research Center for Functional Brain ImagingKennedy Krieger InstituteBaltimoreMarylandUSA,Department of Radiology and Radiological ScienceJohns Hopkins University MedicineBaltimoreMarylandUSA
| | - Brian Caffo
- Department of BiostatisticsJohns Hopkins UniversityBaltimoreMarylandUSA
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Jadhav S, Tekwe CD, Luan Y. A function-based approach to model the measurement error in wearable devices. Stat Med 2022; 41:4886-4902. [PMID: 36036429 PMCID: PMC9804207 DOI: 10.1002/sim.9542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Revised: 06/22/2022] [Accepted: 07/21/2022] [Indexed: 01/05/2023]
Abstract
Physical activity (PA) is an important risk factor for many health outcomes. Wearable-devices such as accelerometers are increasingly used in biomedical studies to understand the associations between PA and health outcomes. Statistical analyses involving accelerometer data are challenging due to the following three characteristics: (i) high-dimensionality, (ii) temporal dependence, and (iii) measurement error. To address these challenges we treat accelerometer-based measures of PA as a single function-valued covariate prone to measurement error. Specifically, in order to determine the relationship between PA and a health outcome of interest, we propose a regression model with a functional covariate that accounts for measurement error. Using regression calibration, we develop a two-step estimation method for the model parameters and establish their consistency. A test is also proposed to test the significance of the estimated model parameters. Simulation studies are conducted to compare the proposed methods with existing alternative approaches under varying scenarios. Finally, the developed methods are used to assess the relationship between PA intensity and BMI obtained from the National Health and Nutrition Examination Survey data.
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Affiliation(s)
- Sneha Jadhav
- Department of Mathematics and StatisticsWake Forest UniversityWinston‐SalemNorth Carolina
| | - Carmen D. Tekwe
- Department of Epidemiology and BiostatisticsIndiana UniversityBloomingtonIndiana
| | - Yuanyuan Luan
- Department of Epidemiology and BiostatisticsIndiana UniversityBloomingtonIndiana
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15
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Jiang Z, Huang Z, Zhang J. Functional single-index composite quantile regression. METRIKA 2022. [DOI: 10.1007/s00184-022-00887-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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16
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Park Y, Li B, Li Y. Crop Yield Prediction Using Bayesian Spatially Varying Coefficient Models with Functional Predictors. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2123333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Yeonjoo Park
- Management Science and Statistics, University of Texas at San Antonio
| | - Bo Li
- Department of Statistics, University of Illinois at Urbana-Champaign
| | - Yehua Li
- Department of Statistics, University of California at Riverside
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17
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Kalogridis I, Van Aelst S. Robust penalized estimators for functional linear regression. J MULTIVARIATE ANAL 2022. [DOI: 10.1016/j.jmva.2022.105104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Representation Theorem and Functional CLT for RKHS-Based Function-on-Function Regressions. MATHEMATICS 2022. [DOI: 10.3390/math10142507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
We investigate a nonparametric, varying coefficient regression approach for modeling and estimating the regression effects caused by two functionally correlated datasets. Due to modern biomedical technology to measure multiple patient features during a time interval or intermittently at several discrete time points to review underlying biological mechanisms, statistical models that do not properly incorporate interventions and their dynamic responses may lead to biased estimates of the intervention effects. We propose a shared parameter change point function-on-function regression model to evaluate the pre- and post-intervention time trends and develop a likelihood-based method for estimating the intervention effects and other parameters. We also propose new methods for estimating and hypothesis testing regression parameters for functional data via reproducing kernel Hilbert space. The estimators of regression parameters are closed-form without computation of the inverse of a large matrix, and hence are less computationally demanding and more applicable. By establishing a representation theorem and a functional central limit theorem, the asymptotic properties of the proposed estimators are obtained, and the corresponding hypothesis tests are proposed. Application and the statistical properties of our method are demonstrated through an immunotherapy clinical trial of advanced myeloma and simulation studies.
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Yu W, Wade S, Bondell HD, Azizi L. Non-stationary Gaussian process discriminant analysis with variable selection for high-dimensional functional data. J Comput Graph Stat 2022. [DOI: 10.1080/10618600.2022.2098136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Weichang Yu
- Melbourne Centre for Data Science, University of Melbourne
| | - Sara Wade
- School of Mathematics, University of Edinburgh
| | | | - Lamiae Azizi
- School of Mathematics and Statistics, University of Sydney
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20
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Ghosal R, Varma VR, Volfson D, Urbanek J, Hausdorff JM, Watts A, Zipunnikov V. Scalar on time-by-distribution regression and its application for modelling associations between daily-living physical activity and cognitive functions in Alzheimer's Disease. Sci Rep 2022; 12:11558. [PMID: 35798763 PMCID: PMC9263176 DOI: 10.1038/s41598-022-15528-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Accepted: 06/24/2022] [Indexed: 11/26/2022] Open
Abstract
Wearable data is a rich source of information that can provide a deeper understanding of links between human behaviors and human health. Existing modelling approaches use wearable data summarized at subject level via scalar summaries in regression, temporal (time-of-day) curves in functional data analysis (FDA), and distributions in distributional data analysis (DDA). We propose to capture temporally local distributional information in wearable data using subject-specific time-by-distribution (TD) data objects. Specifically, we develop scalar on time-by-distribution regression (SOTDR) to model associations between scalar response of interest such as health outcomes or disease status and TD predictors. Additionally, we show that TD data objects can be parsimoniously represented via a collection of time-varying L-moments that capture distributional changes over the time-of-day. The proposed method is applied to the accelerometry study of mild Alzheimer's disease (AD). We found that mild AD is significantly associated with reduced upper quantile levels of physical activity, particularly during morning hours. In-sample cross validation demonstrated that TD predictors attain much stronger associations with clinical cognitive scales of attention, verbal memory, and executive function when compared to predictors summarized via scalar total activity counts, temporal functional curves, and quantile functions. Taken together, the present results suggest that SOTDR analysis provides novel insights into cognitive function and AD.
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Affiliation(s)
- Rahul Ghosal
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA.
| | - Vijay R Varma
- National Institute on Aging (NIA), National Institutes of Health (NIH), Baltimore, MD, USA
| | - Dmitri Volfson
- Neuroscience Analytics, Computational Biology, Takeda, Cambridge, MA, USA
| | - Jacek Urbanek
- Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Jeffrey M Hausdorff
- Center for the Study of Movement, Cognition and Mobility, Neurological Institute, Tel Aviv Sourasky Medical Center, Tel Aviv, Israel
- Department of Physical Therapy, Sackler Faculty of Medicine, and Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
- Rush Alzheimer's Disease Center and Department of Orthopedic Surgery, Rush University Medical Center, Chicago, IL, USA
| | - Amber Watts
- Department of Psychology, University of Kansas, Lawrence, KS, USA
| | - Vadim Zipunnikov
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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21
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Di Brisco AM, Bongiorno EG, Goia A, Migliorati S. Bayesian flexible beta regression model with functional covariate. Comput Stat 2022. [DOI: 10.1007/s00180-022-01240-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
AbstractStandard parametric regression models are unsuitable when the aim is to predict a bounded continuous response, such as a proportion/percentage or a rate. A possible solution is the flexible beta regression model which is based on a special mixture of betas designed to cope with (though not limited to) bimodality, heavy tails, and outlying observations. This work introduces such a model in the case of a functional covariate, motivated by a spectrometric analysis on milk specimens. Estimation issues are dealt with through a combination of standard basis expansion and Markov chains Monte Carlo techniques. Specifically, the selection of the most significant coefficients of the expansion is done through Bayesian variable selection methods that take advantage of shrinkage priors. The effectiveness of the proposal is illustrated with simulation studies and the application on spectrometric data.
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22
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Mutis M, Beyaztas U, Simsek GG, Shang HL. A robust scalar-on-function logistic regression for classification. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2065018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Muge Mutis
- Graduate School of Natural and Applied Sciences, Yildiz Technical University
| | | | | | - Han Lin Shang
- Department of Actuarial Studies and Business Analytics, Macquarie University
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23
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Hesamian G, Akbari MG. A fuzzy functional linear regression model with functional predictors and fuzzy responses. Soft comput 2022. [DOI: 10.1007/s00500-021-06435-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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24
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Wang Z, Dong H, Ma P, Wang Y. Estimation and model selection for nonparametric function-on-function regression. J Comput Graph Stat 2022; 31:835-845. [PMID: 36594047 PMCID: PMC9802009 DOI: 10.1080/10618600.2022.2037434] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Regression models with a functional response and functional covariate have received significant attention recently. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. In this article, we develop a unified framework for estimation and model selection in nonparametric function-on-function regression. We propose a general nonparametric functional regression model with the model space constructed through smoothing spline analysis of variance (SS ANOVA). The proposed model reduces to some of the existing models when selected components in the SS ANOVA decomposition are eliminated. We propose new estimation procedures under either L 1 or L 2 penalty and show that the combination of the SS ANOVA decomposition and L 1 penalty provides powerful tools for model selection and diagnostics. We establish consistency and convergence rates for estimates of the regression function and each component in its decomposition under both the L 1 and L 2 penalties. Simulation studies and real examples show that the proposed methods perform well. Technical details and additional simulation results are available in online supplementary materials.
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Affiliation(s)
- Zhanfeng Wang
- International Institute of Finance, The School of Management, University of Science and Technology of China
| | - Hao Dong
- Department of Statistics and Applied Probability, University of California, Santa Barbara
| | - Ping Ma
- Department of Statistics, University of Georgia
| | - Yuedong Wang
- Department of Statistics and Applied Probability, University of California, Santa Barbara
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25
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Zou H, Li K, Zeng D, Luo S. Bayesian inference and dynamic prediction of multivariate joint model with functional data: An application to Alzheimer's disease. Stat Med 2021; 40:6855-6872. [PMID: 34649301 PMCID: PMC8671252 DOI: 10.1002/sim.9214] [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: 11/24/2020] [Revised: 08/03/2021] [Accepted: 09/20/2021] [Indexed: 01/01/2023]
Abstract
Alzheimer's disease (AD) is a severe neurodegenerative disorder impairing multiple domains, for example, cognition and behavior. Assessing the risk of AD progression and initiating timely interventions at early stages are critical to improve the quality of life for AD patients. Due to the heterogeneous nature and complex mechanisms of AD, one single longitudinal outcome is insufficient to assess AD severity and disease progression. Therefore, AD studies collect multiple longitudinal outcomes, including cognitive and behavioral measurements, as well as structural brain images such as magnetic resonance imaging (MRI). How to utilize the multivariate longitudinal outcomes and MRI data to make efficient statistical inference and prediction is an open question. In this article, we propose a multivariate joint model with functional data (MJM-FD) framework that relates multiple correlated longitudinal outcomes to a survival outcome, and use the scalar-on-function regression method to include voxel-based whole-brain MRI data as functional predictors in both longitudinal and survival models. We adopt a Bayesian paradigm to make statistical inference and develop a dynamic prediction framework to predict an individual's future longitudinal outcomes and risk of a survival event. We validate the MJM-FD framework through extensive simulation studies and apply it to the motivating Alzheimer's Disease Neuroimaging Initiative (ADNI) study.
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Affiliation(s)
- Haotian Zou
- Gillings School of Global Public Health, Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599, USA
| | - Kan Li
- Merck Research Lab, Merck & Co, North Wales, Pennsylvania
| | - Donglin Zeng
- Department of Biostatistics, Gillings School of Global Public Health, CB#7420, University of North Carolina at Chapel Hill, NC 27599, USA
| | - Sheng Luo
- Corresponding author: Sheng Luo, Department of Biostatistics and Informatics, Duke University, 2424 Erwin Rd, Durham, NC 27705, USA ()
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26
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Soares MLM, Guimarães NGM, Bonfada D. [Trend, spatialization and circumstances associated with violence against vulnerable populations in Brazil, between 2009 and 2017]. CIENCIA & SAUDE COLETIVA 2021; 26:5751-5763. [PMID: 34852106 DOI: 10.1590/1413-812320212611.25242020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 09/10/2020] [Indexed: 11/22/2022] Open
Abstract
The scope of this study was to analyze the trend, spatialization and circumstances associated with violence against vulnerable populations in Brazil between 2009 and 2017. Descriptive analysis, spatialization and polynomial regression were used. A total of 1,116,331 cases of violence were notified, with an increase of 667.5% over the period. In all populations under research there was a predominance of physical violence against women with low levels of schooling, perpetrated by men in residences. Sexual and psychological violence was highlighted in female and LGBT populations. Negligence, however, was significant among people with disabilities, children/adolescents, and the elderly. At least 65% of the notifications of violence in Brazil were characterized as indiscriminate regarding the motivation behind the act. Tendency analysis showed a rise of interpersonal violence against women (+8.5%), disabled people (+7.1%), elderly individuals (+55.4%), natives (+99.4%), LGBT people (+3.4%) and racial violence (+30.2%), except for violence against underaged individuals, which showed a decrease (-11.4%). In North and Northwest regions violence against women and underaged individuals prevailed, while in Midwest, South and Southeast regions the LGBT, disabled and elderly populations were most subject to abuse.
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Affiliation(s)
- Marcelo Luiz Medeiros Soares
- Escola Multicampi de Ciências Médicas, Universidade Federal do Rio Grande do Norte. Av. Cel. Martiniano 541. 59300-000 Caicó RN Brasil.
| | - Natália Guedes Miguel Guimarães
- Escola Multicampi de Ciências Médicas, Universidade Federal do Rio Grande do Norte. Av. Cel. Martiniano 541. 59300-000 Caicó RN Brasil.
| | - Diego Bonfada
- Escola Multicampi de Ciências Médicas, Universidade Federal do Rio Grande do Norte. Av. Cel. Martiniano 541. 59300-000 Caicó RN Brasil.
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27
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Mehrotra S, Maity A. Simultaneous variable selection, clustering, and smoothing in function‐on‐scalar regression. CAN J STAT 2021. [DOI: 10.1002/cjs.11668] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Suchit Mehrotra
- Department of Statistics North Carolina State University Raleigh NC U.S.A
| | - Arnab Maity
- Department of Statistics North Carolina State University Raleigh NC U.S.A
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28
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29
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Zhang X, Xue W, Wang Q. Covariate balancing functional propensity score for functional treatments in cross-sectional observational studies. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2021.107303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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30
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Zemplenyi M, Meyer MJ, Cardenas A, Hivert MF, Rifas-Shiman SL, Gibson H, Kloog I, Schwartz J, Oken E, DeMeo DL, Gold DR, Coull BA. Function-on-function regression for the identification of epigenetic regions exhibiting windows of susceptibility to environmental exposures. Ann Appl Stat 2021; 15:1366-1385. [DOI: 10.1214/20-aoas1425] [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)
- Michele Zemplenyi
- Department of Biostatistics, Harvard T. H. Chan School of Public Health
| | - Mark J. Meyer
- Department of Mathematics and Statistics, Georgetown University
| | - Andres Cardenas
- Division of Environmental Health Sciences, University of California, Berkeley
| | | | | | - Heike Gibson
- Department of Environmental Health, Harvard T. H. Chan School of Public Health
| | - Itai Kloog
- Department of Geography and Environmental Development, Ben-Gurion University
| | - Joel Schwartz
- Department of Environmental Health, Harvard T. H. Chan School of Public Health
| | - Emily Oken
- Department of Population Medicine, Harvard Medical School
| | - Dawn L. DeMeo
- Center for Chest Diseases, Brigham and Women’s Hospital
| | - Diane R. Gold
- Department of Environmental Health, Harvard T. H. Chan School of Public Health
| | - Brent A. Coull
- Department of Biostatistics, Harvard T. H. Chan School of Public Health
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31
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Moreno-Oyervides A, Aguilera-Morillo MC, de la Cruz Fernández MJ, Pascual EL, Jiménez LL, Krozer V, Acedo P. Clinical assessment of W-band spectroscopy for non-invasive detection and monitoring of sustained hyperglycemia. BIOMEDICAL OPTICS EXPRESS 2021; 12:5008-5022. [PMID: 34513239 PMCID: PMC8407808 DOI: 10.1364/boe.428524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Revised: 07/09/2021] [Accepted: 07/11/2021] [Indexed: 06/13/2023]
Abstract
HbA1c is the gold standard test for monitoring medium/long term glycemia conditions in diabetes care, which is a critical factor in reducing the risk of chronic diabetes complications. Current technologies for measuring HbA1c concentration are invasive and adequate assays are still limited to laboratory-based methods that are not widely available worldwide. The development of a non-invasive diagnostic tool for HbA1c concentration can lead to the decrease of the rate of undiagnosed cases and facilitate early detection in diabetes care. We present a preliminary validation diagnostic study of W-band spectroscopy for detection and monitoring of sustained hyperglycemia, using the HbA1c concentration as reference. A group of 20 patients with type 1 diabetes mellitus and 10 healthy subjects were non-invasively assessed at three different visits over a period of 7 months by a millimeter-wave spectrometer (transmission mode) operating across the full W-band. The relationship between the W-band spectral profile and the HbA1c concentration is studied using longitudinal and non-longitudinal functional data analysis methods. A potential blind discrimination between patients with or without diabetes is obtained, and more importantly, an excellent relation (R-squared = 0.97) between the non-invasive assessment and the HbA1c measure is achieved. Such results support that W-band spectroscopy has great potential for developing a non-invasive diagnostic tool for in-vivo HbA1c concentration monitoring in humans.
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Affiliation(s)
- Aldo Moreno-Oyervides
- Department of Electronic Technology, Universidad Carlos III de Madrid, Leganés, 28911 Madrid, Spain
- Instituto de Investigación Sanitaria Fundación Jiménez Díaz (IIS-FJD), Madrid, Spain
| | - M. Carmen Aguilera-Morillo
- Department of Applied Statistics and Operational Research, and Quality, Universitat Politècnica de València, 46022 Valencia, Spain
| | | | | | - Lucía Llanos Jiménez
- Instituto de Investigación Sanitaria Fundación Jiménez Díaz (IIS-FJD), Madrid, Spain
| | - Viktor Krozer
- Physics Institute, Goethe University Frankfurt am Main, Frankfurt am Main 60438, Germany
| | - Pablo Acedo
- Department of Electronic Technology, Universidad Carlos III de Madrid, Leganés, 28911 Madrid, Spain
- Instituto de Investigación Sanitaria Fundación Jiménez Díaz (IIS-FJD), Madrid, Spain
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32
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Ma W, Xiao L, Liu B. A functional mixed model for scalar on function regression with application to a functional MRI study. Biostatistics 2021; 22:439-454. [PMID: 31631222 PMCID: PMC8286587 DOI: 10.1093/biostatistics/kxz046] [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: 11/10/2018] [Revised: 09/23/2019] [Accepted: 09/25/2019] [Indexed: 11/12/2022] Open
Abstract
Motivated by a functional magnetic resonance imaging (fMRI) study, we propose a new functional mixed model for scalar on function regression. The model extends the standard scalar on function regression for repeated outcomes by incorporating subject-specific random functional effects. Using functional principal component analysis, the new model can be reformulated as a mixed effects model and thus easily fit. A test is also proposed to assess the existence of the subject-specific random functional effects. We evaluate the performance of the model and test via a simulation study, as well as on data from the motivating fMRI study of thermal pain. The data application indicates significant subject-specific effects of the human brain hemodynamics related to pain and provides insights on how the effects might differ across subjects.
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Affiliation(s)
- Wanying Ma
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27606, USA
| | - Luo Xiao
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27606, USA
| | - Bowen Liu
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27606, USA
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33
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Shang HL. Double bootstrapping for visualizing the distribution of descriptive statistics of functional data. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1885670] [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]
Affiliation(s)
- Han Lin Shang
- Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW, Australia
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34
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Alfini A, Albert M, Faria AV, Soldan A, Pettigrew C, Wanigatunga S, Zipunnikov V, Spira AP. Associations of actigraphic sleep and circadian rest/activity rhythms with cognition in the early phase of Alzheimer's disease. ACTA ACUST UNITED AC 2021; 2:zpab007. [PMID: 34095836 PMCID: PMC8168567 DOI: 10.1093/sleepadvances/zpab007] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Indexed: 11/20/2022]
Abstract
Study Objectives To compare sleep and circadian rest/activity rhythms (RARs), quantified by standard and novel actigraphic metrics, between controls and participants with mild cognitive impairment (MCI), and to examine the cross-sectional relationships between these measures and cognition. Methods Actigraphy data were collected in 179 older individuals (mean age = 72.6 years) with normal cognition (n = 153) and MCI (n = 26). Sleep parameters (e.g. sleep efficiency), and standard nonparametric RARs (e.g. interdaily stability) were generated. Functional principal component analysis (fPCA) was used to generate three novel RAR metrics (fPC1, fPC2, and fPC3). Cognitive composite scores reflecting episodic memory and executive function were derived using factor analysis. Regression models compared sleep and RAR parameters between diagnostic groups and their association with cognitive performance. Results Compared to controls, the MCI group exhibited lower levels of the standard RAR parameter: relative amplitude and fPC3—a novel RAR whereby lower scores reflected a lower rhythm peak, as well as greater nighttime activity and less activity in the morning. Across groups, several standard RAR parameters (e.g. interdaily stability) and fPC3 were associated with better episodic memory and executive function performance. Additionally, several standard RAR measures (e.g. relative amplitude) and the novel RAR measure fPC1 (reflecting the total volume of activity and rhythm strength) were associated with better executive function performance. Conclusions Individuals with MCI have altered circadian RARs compared to controls, including the novel RAR metric fPC3, reflecting greater nighttime activity and less activity in the morning compared to mean values. Additionally, these measures are significantly associated with cognitive performance.
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Affiliation(s)
- Alfonso Alfini
- Department of Neurology, Johns Hopkins School of Medicine, Baltimore, MD
| | - Marilyn Albert
- Department of Neurology, Johns Hopkins School of Medicine, Baltimore, MD
| | - Andreia V Faria
- Department of Radiology and Radiological Science, Johns Hopkins School of Medicine, Baltimore, MD
| | - Anja Soldan
- Department of Neurology, Johns Hopkins School of Medicine, Baltimore, MD
| | - Corinne Pettigrew
- Department of Neurology, Johns Hopkins School of Medicine, Baltimore, MD
| | - Sarah Wanigatunga
- Department of Mental Health, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD
| | - Vadim Zipunnikov
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD
| | - Adam P Spira
- Department of Mental Health, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD
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35
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Tan CW, Bergmeir C, Petitjean F, Webb GI. Time series extrinsic regression: Predicting numeric values from time series data. Data Min Knowl Discov 2021; 35:1032-1060. [PMID: 33727888 PMCID: PMC7951134 DOI: 10.1007/s10618-021-00745-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 02/17/2021] [Indexed: 12/02/2022]
Abstract
This paper studies time series extrinsic regression (TSER): a regression task of which the aim is to learn the relationship between a time series and a continuous scalar variable; a task closely related to time series classification (TSC), which aims to learn the relationship between a time series and a categorical class label. This task generalizes time series forecasting, relaxing the requirement that the value predicted be a future value of the input series or primarily depend on more recent values. In this paper, we motivate and study this task, and benchmark existing solutions and adaptations of TSC algorithms on a novel archive of 19 TSER datasets which we have assembled. Our results show that the state-of-the-art TSC algorithm Rocket, when adapted for regression, achieves the highest overall accuracy compared to adaptations of other TSC algorithms and state-of-the-art machine learning (ML) algorithms such as XGBoost, Random Forest and Support Vector Regression. More importantly, we show that much research is needed in this field to improve the accuracy of ML models. We also find evidence that further research has excellent prospects of improving upon these straightforward baselines.
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Affiliation(s)
- Chang Wei Tan
- Faculty of Information Technology, Monash University, 25 Exhibition Walk, Melbourne, VIC 3800 Australia
| | - Christoph Bergmeir
- Faculty of Information Technology, Monash University, 25 Exhibition Walk, Melbourne, VIC 3800 Australia
| | - François Petitjean
- Faculty of Information Technology, Monash University, 25 Exhibition Walk, Melbourne, VIC 3800 Australia
| | - Geoffrey I Webb
- Faculty of Information Technology, Monash University, 25 Exhibition Walk, Melbourne, VIC 3800 Australia
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Wrobel J, Muschelli J, Leroux A. Diurnal Physical Activity Patterns across Ages in a Large UK Based Cohort: The UK Biobank Study. SENSORS (BASEL, SWITZERLAND) 2021; 21:1545. [PMID: 33672201 PMCID: PMC7927049 DOI: 10.3390/s21041545] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Revised: 02/10/2021] [Accepted: 02/18/2021] [Indexed: 11/18/2022]
Abstract
The ability of individuals to engage in physical activity is a critical component of overall health and quality of life. However, there is a natural decline in physical activity associated with the aging process. Establishing normative trends of physical activity in aging populations is essential to developing public health guidelines and informing clinical perspectives regarding individuals' levels of physical activity. Beyond overall quantity of physical activity, patterns regarding the timing of activity provide additional insights into latent health status. Wearable accelerometers, paired with statistical methods from functional data analysis, provide the means to estimate diurnal patterns in physical activity. To date, these methods have been only applied to study aging trends in populations based in the United States. Here, we apply curve registration and functional regression to 24 h activity profiles for 88,793 men (N = 39,255) and women (N = 49,538) ages 42-78 from the UK Biobank accelerometer study to understand how physical activity patterns vary across ages and by gender. Our analysis finds that daily patterns in both the volume of physical activity and probability of being active change with age, and that there are marked gender differences in these trends. This work represents the largest-ever population analyzed using tools of this kind, and suggest that aging trends in physical activity are reproducible in different populations across countries.
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Affiliation(s)
- Julia Wrobel
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, USA;
| | - John Muschelli
- Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD 21218, USA;
| | - Andrew Leroux
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, USA;
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37
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Hörmann S, Jammoul F, Kuenzer T, Stadlober E. Separating the impact of gradual lockdown measures on air pollutants from seasonal variability. ATMOSPHERIC POLLUTION RESEARCH 2021; 12:84-92. [PMID: 33162774 PMCID: PMC7605804 DOI: 10.1016/j.apr.2020.10.011] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2020] [Revised: 10/13/2020] [Accepted: 10/13/2020] [Indexed: 05/30/2023]
Abstract
Analysis of near-surface measurements at several measuring points in Graz, Austria, reveals the impact of restrictive measures during the COVID-19 pandemic on the emission of atmospheric pollutants. We quantify the effects at traffic hotspots, industrial and residential areas. Using historical data collected over several years, we are able to account for meteorological and seasonal confounders. Our analysis is based on daily means as well as intraday pollution level curves. Nitrogen dioxide (NO2) has decreased drastically while the levels of particulate matter PM10 and carbon monoxide (CO) mostly exhibit little change. Traffic data shows that the decrease in traffic frequency is parallel to the decline in the levels of NO2 and NO.
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Affiliation(s)
- Siegfried Hörmann
- Institute of Statistics, Graz University of Technology, Kopernikusgasse 24/III, 8010, Graz, Austria
| | - Fatima Jammoul
- Institute of Statistics, Graz University of Technology, Kopernikusgasse 24/III, 8010, Graz, Austria
| | - Thomas Kuenzer
- Institute of Statistics, Graz University of Technology, Kopernikusgasse 24/III, 8010, Graz, Austria
| | - Ernst Stadlober
- Institute of Statistics, Graz University of Technology, Kopernikusgasse 24/III, 8010, Graz, Austria
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38
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Tarpey T, Petkova E, Ciarleglio A, Ogden RT. Extracting scalar measures from functional data with applications to placebo response. STATISTICS AND ITS INTERFACE 2021; 14:255-265. [PMID: 34316322 PMCID: PMC8313021 DOI: 10.4310/20-sii633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In controlled and observational studies, outcome measures are often observed longitudinally. Such data are difficult to compare among units directly because there is no natural ordering of curves. This is relevant not only in clinical trials, where typically the goal is to evaluate the relative efficacy of treatments on average, but also in the growing and increasingly important area of personalized medicine, where treatment decisions are optimized with respect to a relevant patient outcome. In personalized medicine, there are no methods for optimizing treatment decision rules using longitudinal outcomes, e.g., symptom trajectories, because of the lack of a natural ordering of curves. A typical practice is to summarize the longitudinal response by a scalar outcome that can then be compared across patients, treatments, etc. We describe some of the summaries that are in common use, especially in clinical trials. We consider a general summary measure (weighted average tangent slope) with weights that can be chosen to optimize specific inference depending on the application. We illustrate the methodology on a study of depression treatment, in which it is difficult to separate placebo effects from the specific effects of the antidepressant. We argue that this approach provides a better summary for estimating the benefits of an active treatment than traditional non-weighted averages.
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Affiliation(s)
- Thaddeus Tarpey
- Department of Population Health, New York University, 180 Madison Ave, 5nd Floor, Room 4-53, New York, NY, 10016, USA
| | - Eva Petkova
- Department of Population Health, New York University, 180 Madison Ave, 2th Floor, Room 2-55, New York, NY, 10016, USA
| | - Adam Ciarleglio
- Department of Biostatistics and Bioinformatics, Milken Institute School of Public Health, George Washington University, 950 New Hampshire Avenue, Room 517, Washington, DC, 20052, USA
| | - Robert Todd Ogden
- Department of Biostatistics, Columbia University, 722 W. 168th Street, 6th Floor, New York, NY 10032, USA
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Xu W, Ding H, Zhang R, Liang H. Estimation and inference in partially functional linear regression with multiple functional covariates. J Stat Plan Inference 2020. [DOI: 10.1016/j.jspi.2020.02.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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40
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On the Number of Independent Pieces of Information in a Functional Linear Model with a Scalar Response. STATS 2020. [DOI: 10.3390/stats3040032] [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] Open
Abstract
In a functional linear model (FLM) with scalar response, the parameter curve quantifies the relationship between a functional explanatory variable and a scalar response. While these models can be ill-posed, a penalized regression spline approach may be used to obtain an estimate of the parameter curve. The penalized regression spline estimate will be dependent on the value of a smoothing parameter. However, the ability to obtain a reasonable parameter curve estimate is reliant on how much information is present in the covariate functions for estimating the parameter curve. We propose to quantify the information present in the covariate functions to estimate the parameter curve. In addition, we examine the influence of this information on the stability of the parameter curve estimator and on the performance of smoothing parameter selection methods in a FLM with a scalar response.
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41
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Regression models using shapes of functions as predictors. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2020.107017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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42
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Palma M, Tavakoli S, Brettschneider J, Nichols TE. Quantifying uncertainty in brain-predicted age using scalar-on-image quantile regression. Neuroimage 2020; 219:116938. [PMID: 32502669 PMCID: PMC7443707 DOI: 10.1016/j.neuroimage.2020.116938] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 05/07/2020] [Accepted: 05/08/2020] [Indexed: 12/12/2022] Open
Abstract
Prediction of subject age from brain anatomical MRI has the potential to provide a sensitive summary of brain changes, indicative of different neurodegenerative diseases. However, existing studies typically neglect the uncertainty of these predictions. In this work we take into account this uncertainty by applying methods of functional data analysis. We propose a penalised functional quantile regression model of age on brain structure with cognitively normal (CN) subjects in the Alzheimer's Disease Neuroimaging Initiative (ADNI), and use it to predict brain age in Mild Cognitive Impairment (MCI) and Alzheimer's Disease (AD) subjects. Unlike the machine learning approaches available in the literature of brain age prediction, which provide only point predictions, the outcome of our model is a prediction interval for each subject.
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Affiliation(s)
- Marco Palma
- Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom.
| | - Shahin Tavakoli
- Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom
| | - Julia Brettschneider
- Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom; The Alan Turing Institute, London, NW1 2DB, United Kingdom
| | - Thomas E Nichols
- Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom; Oxford Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, Nuffield Department of Population Health, University of Oxford, Oxford, OX3 7LF, United Kingdom; Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, OX3 9DU, United Kingdom
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43
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Luo R, Qi X. Functional Regression for Densely Observed Data With Novel Regularization. J Comput Graph Stat 2020. [DOI: 10.1080/10618600.2020.1807994] [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)
- Ruiyan Luo
- Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA
| | - Xin Qi
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA
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Agniel D, Parast L. Evaluation of longitudinal surrogate markers. Biometrics 2020; 77:477-489. [PMID: 32506496 DOI: 10.1111/biom.13310] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Accepted: 05/05/2020] [Indexed: 11/27/2022]
Abstract
The use of surrogate markers to examine the effectiveness of a treatment has the potential to decrease study length and identify effective treatments more quickly. Most available methods to investigate the usefulness of a surrogate marker involve restrictive parametric assumptions and tend to focus on settings where the surrogate is measured at a single point in time. However, in many clinical settings, the potential surrogate marker is often measured repeatedly over time, and thus, the surrogate marker information is a trajectory of measurements. In addition, it is often difficult in practice to correctly specify the relationship between a treatment, primary outcome, and surrogate marker trajectory. In this paper, we propose a model-free definition for the proportion of the treatment effect on the primary outcome that is explained by the treatment effect on the longitudinal surrogate markers. We propose three novel flexible methods to estimate this proportion, develop the asymptotic properties of our estimators, and investigate the robustness of the estimators under multiple settings via a simulation study. We apply our proposed procedures to an AIDS clinical trial dataset to examine a trajectory of CD4 counts as a potential surrogate.
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Abstract
AbstractIn this article, we focus on the estimation of varying-coefficient mixed effects models for longitudinal and sparse functional response data, by using the generalized least squares method coupling a modified local kernel smoothing technique. This approach provides a useful framework that simultaneously takes into account the within-subject covariance and all observation information in the estimation to improve efficiency. We establish both uniform consistency and pointwise asymptotic normality for the proposed estimators of varying-coefficient functions. Numerical studies are carried out to illustrate the finite sample performance of the proposed procedure. An application to the white matter tract dataset obtained from Alzheimer’s Disease Neuroimaging Initiative study is also provided.
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Liebl D, Rameseder S, Rust C. Improving Estimation in Functional Linear Regression With Points of Impact: Insights Into Google AdWords. J Comput Graph Stat 2020. [DOI: 10.1080/10618600.2020.1754224] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Dominik Liebl
- Institute of Finance and Statistics, University of Bonn, Bonn, Germany
- Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany
| | - Stefan Rameseder
- Department of Econometrics, University of Regensburg, Regensburg, Germany
| | - Christoph Rust
- Department of Econometrics, University of Regensburg, Regensburg, Germany
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47
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Zhang X, Zhong Q, Wang JL. A new approach to varying-coefficient additive models with longitudinal covariates. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2020.106912] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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48
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Shah DA, Paul PA, De Wolf ED, Madden LV. Predicting plant disease epidemics from functionally represented weather series. Philos Trans R Soc Lond B Biol Sci 2020; 374:20180273. [PMID: 31056045 DOI: 10.1098/rstb.2018.0273] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Epidemics are often triggered by specific weather patterns favouring the pathogen on susceptible hosts. For plant diseases, models predicting epidemics have therefore often emphasized the identification of early season weather patterns that are correlated with a disease outcome at some later point. Toward that end, window-pane analysis is an exhaustive search algorithm traditionally used in plant pathology for mining correlations in a weather series with respect to a disease endpoint. Here we show, with reference to Fusarium head blight (FHB) of wheat, that a functional approach is a more principled analytical method for understanding the relationship between disease epidemics and environmental conditions over an extended time series. We used scalar-on-function regression to model a binary outcome (FHB epidemic or non-epidemic) relative to weather time series spanning 140 days relative to flowering (when FHB infection primarily occurs). The functional models overall fit the data better than previously described standard logistic regression (lr) models. Periods much earlier than heretofore realized were associated with FHB epidemics. The findings were used to create novel weather summary variables which, when incorporated into lr models, yielded a new set of models that performed as well as existing lr models for real-time predictions of disease risk. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.
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Affiliation(s)
- D A Shah
- 1 Department of Plant Pathology, Kansas State University , 4024 Throckmorton PSC, Manhattan, KS 66506 , USA
| | - P A Paul
- 2 Department of Plant Pathology, The Ohio State University , 1680 Madison Avenue, Wooster, OH 44691 , USA
| | - E D De Wolf
- 1 Department of Plant Pathology, Kansas State University , 4024 Throckmorton PSC, Manhattan, KS 66506 , USA
| | - L V Madden
- 2 Department of Plant Pathology, The Ohio State University , 1680 Madison Avenue, Wooster, OH 44691 , USA
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Shan G, Hou Y, Liu B. Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions. Comput Stat 2020. [DOI: 10.1007/s00180-020-00975-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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50
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Shang HL. Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density. J Appl Stat 2020; 48:583-604. [PMID: 35706989 PMCID: PMC9041737 DOI: 10.1080/02664763.2020.1736527] [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: 05/24/2019] [Accepted: 02/23/2020] [Indexed: 10/24/2022]
Abstract
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.
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Affiliation(s)
- Han Lin Shang
- Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, Australia
- Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia
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