Smoothing spline analysis of variance models: A new tool for the analysis of cyclic biomechanical data

Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical differences between experimental conditions and/or subject populations. A common approach to analyzing cyclic biomechanical data involves averaging...

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Published in:	Journal of biomechanics Vol. 49; no. 14; pp. 3216 - 3222
Main Authors:	Helwig, Nathaniel E., Shorter, K. Alex, Ma, Ping, Hsiao-Wecksler, Elizabeth T.
Format:	Journal Article
Language:	English
Published:	United States Elsevier Ltd 03.10.2016 Elsevier Limited
Subjects:	Analysis of Variance Ankle Biomechanical engineering Biomechanical Phenomena Biomechanics Confidence intervals Cyclic data Functional data analysis Gait analysis Humans Male Mathematical models Mechanical Phenomena Models, Statistical Physical Medicine and Rehabilitation Physiology Populations Smoothing Smoothing spline Splines Statistics as Topic - methods Studies Time series Variance analysis Young Adult Cyclic data Gait analysis Functional data analysis Smoothing spline
ISSN:	0021-9290, 1873-2380
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Abstract	Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical differences between experimental conditions and/or subject populations. A common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications, and then comparing mean differences at specific points of the cycle. This pointwise analysis approach ignores the functional nature of the data, which can hinder one׳s ability to find subtle differences between experimental conditions and/or subject populations. To overcome this limitation, we propose using mixed-effects smoothing spline analysis of variance (SSANOVA) to analyze differences in cyclic biomechanical data. The SSANOVA framework makes it possible to decompose the estimated function into the portion that is common across groups (i.e., the average cycle, AC) and the portion that differs across groups (i.e., the contrast cycle, CC). By partitioning the signal in such a manner, we can obtain estimates of the CC differences (CCDs), which are the functions directly describing group differences in the cyclic biomechanical data. Using both simulated and experimental data, we illustrate the benefits of using SSANOVA models to analyze differences in noisy biomechanical (gait) signals collected from multiple locations (joints) of subjects participating in different experimental conditions. Using Bayesian confidence intervals, the SSANOVA results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and/or subject populations.
AbstractList	Abstract Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical differences between experimental conditions and/or subject populations. A common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications, and then comparing mean differences at specific points of the cycle. This pointwise analysis approach ignores the functional nature of the data, which can hinder one׳s ability to find subtle differences between experimental conditions and/or subject populations. To overcome this limitation, we propose using mixed-effects smoothing spline analysis of variance (SSANOVA) to analyze differences in cyclic biomechanical data. The SSANOVA framework makes it possible to decompose the estimated function into the portion that is common across groups (i.e., the average cycle, AC) and the portion that differs across groups (i.e., the contrast cycle, CC). By partitioning the signal in such a manner, we can obtain estimates of the CC differences (CCDs), which are the functions directly describing group differences in the cyclic biomechanical data. Using both simulated and experimental data, we illustrate the benefits of using SSANOVA models to analyze differences in noisy biomechanical (gait) signals collected from multiple locations (joints) of subjects participating in different experimental conditions. Using Bayesian confidence intervals, the SSANOVA results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and/or subject populations. Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical differences between experimental conditions and/or subject populations. A common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications, and then comparing mean differences at specific points of the cycle. This pointwise analysis approach ignores the functional nature of the data, which can hinder one׳s ability to find subtle differences between experimental conditions and/or subject populations. To overcome this limitation, we propose using mixed-effects smoothing spline analysis of variance (SSANOVA) to analyze differences in cyclic biomechanical data. The SSANOVA framework makes it possible to decompose the estimated function into the portion that is common across groups (i.e., the average cycle, AC) and the portion that differs across groups (i.e., the contrast cycle, CC). By partitioning the signal in such a manner, we can obtain estimates of the CC differences (CCDs), which are the functions directly describing group differences in the cyclic biomechanical data. Using both simulated and experimental data, we illustrate the benefits of using SSANOVA models to analyze differences in noisy biomechanical (gait) signals collected from multiple locations (joints) of subjects participating in different experimental conditions. Using Bayesian confidence intervals, the SSANOVA results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and/or subject populations. Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical differences between experimental conditions and/or subject populations. A common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications, and then comparing mean differences at specific points of the cycle. This pointwise analysis approach ignores the functional nature of the data, which can hinder one's ability to find subtle differences between experimental conditions and/or subject populations. To overcome this limitation, we propose using mixed-effects smoothing spline analysis of variance (SSANOVA) to analyze differences in cyclic biomechanical data. The SSANOVA framework makes it possible to decompose the estimated function into the portion that is common across groups (i.e., the average cycle, AC) and the portion that differs across groups (i.e., the contrast cycle, CC). By partitioning the signal in such a manner, we can obtain estimates of the CC differences (CCDs), which are the functions directly describing group differences in the cyclic biomechanical data. Using both simulated and experimental data, we illustrate the benefits of using SSANOVA models to analyze differences in noisy biomechanical (gait) signals collected from multiple locations (joints) of subjects participating in different experimental conditions. Using Bayesian confidence intervals, the SSANOVA results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and/or subject populations.
Author	Shorter, K. Alex Helwig, Nathaniel E. Hsiao-Wecksler, Elizabeth T. Ma, Ping
Author_xml	– sequence: 1 givenname: Nathaniel E. surname: Helwig fullname: Helwig, Nathaniel E. email: helwig@umn.edu organization: Department of Psychology, University of Minnesota, Minneapolis, MN 55455-0366, United States – sequence: 2 givenname: K. Alex surname: Shorter fullname: Shorter, K. Alex email: kshorter@umich.edu organization: Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109-2125, United States – sequence: 3 givenname: Ping surname: Ma fullname: Ma, Ping email: pingma@uga.edu organization: Department of Statistics, University of Georgia, Athens, GA 30602-5029, United States – sequence: 4 givenname: Elizabeth T. surname: Hsiao-Wecksler fullname: Hsiao-Wecksler, Elizabeth T. email: ethw@illinois.edu organization: Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801-2906, United States
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Keywords	Cyclic data Gait analysis Functional data analysis Smoothing spline
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Snippet	Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical... Abstract Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare...
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SubjectTerms	Analysis of Variance Ankle Biomechanical engineering Biomechanical Phenomena Biomechanics Confidence intervals Cyclic data Functional data analysis Gait analysis Humans Male Mathematical models Mechanical Phenomena Models, Statistical Physical Medicine and Rehabilitation Physiology Populations Smoothing Smoothing spline Splines Statistics as Topic - methods Studies Time series Variance analysis Young Adult
Title	Smoothing spline analysis of variance models: A new tool for the analysis of cyclic biomechanical data
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