Using Simultaneous Confidence Bands to Calculate the Margin of Error in Estimating Typical Biomechanical Waveforms

in Journal of Applied Biomechanics
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  • 1 Department of Orthopaedic Surgery, University of Pittsburgh, Pittsburgh, PA, USA
  • | 2 School of Medicine, University of Pittsburgh, Pittsburgh, PA, USA
  • | 3 Department of Biostatistics, University of Pittsburgh, Pittsburgh, PA, USA
  • | 4 Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA
  • | 5 Foot and Ankle Injury Research (F.A.I.R.) Group, Pittsburgh, PA, USA
  • | 6 Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA, USA
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Studies of human movement usually collect data from multiple repetitions of a task and use the average of all movement trials to approximate the typical kinematics or kinetics pattern for each individual. Few studies report the expected accuracy of these estimated mean kinematics or kinetics waveforms for each individual. The purpose of this study is to demonstrate how simultaneous confidence bands, which is an approach to quantify uncertainty across an entire waveform based on limited data, can be used to calculate margin of error (MOE) for waveforms. Bilateral plantar pressure data were collected from 70 participants as they walked over 4 surfaces for an average of at least 300 steps per surface. The relationship between MOE and the number of steps included in the analysis was calculated using simultaneous confidence bands, and 3 methods commonly used for pointwise estimates: intraclass correlation, sequential averaging, and T-based MOE. The conventional pointwise approaches underestimated the number of trials required to estimate biomechanical waveforms within a desired MOE. Simultaneous confidence bands are an objective approach to more accurately estimate the relationship between the number of trials collected and the MOE in estimating typical biomechanical waveforms.

Anderst (anderst@pitt.edu) is corresponding author.

  • 1.

    Stergiou N, Harbourne R, Cavanaugh J. Optimal movement variability: a new theoretical perspective for neurologic physical therapy. J Neurol Phys Ther. 2006;30(3):120129. PubMed ID: 17029655 doi:10.1097/01.NPT.0000281949.48193.d9

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 2.

    Hamill J, McNiven L. Reliability of selected ground reaction force parameters during walking. Hum Mov Sci. 1990;9(2):117131. doi:10.1016/0167-9457(90)90023-7

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 3.

    DeVita P, Bates B. Intraday reliability of ground reaction force data. Hum Mov Sci. 1988;7(1):7385. doi:10.1016/0167-9457(88)90005-X

  • 4.

    James CR, Herman JA, Dufek JS, Bates BT. Number of trials necessary to achieve performance stability of selected ground reaction force variables during landing. J Sports Sci Med. 2007;6(1):126134. PubMed ID: 24149234

    • Search Google Scholar
    • Export Citation
  • 5.

    Racic V, Pavic A, Brownjohn JM. Number of successive cycles necessary to achieve stability of selected ground reaction force variables during continuous jumping. J Sports Sci Med. 2009;8(4):639647. PubMed ID: 24149607

    • Search Google Scholar
    • Export Citation
  • 6.

    Hafer JF, Lenhoff MW, Song J, Jordan JM, Hannan MT, Hillstrom HJ. Reliability of plantar pressure platforms. Gait Posture. 2013;38(3):544548. PubMed ID: 23454044 doi:10.1016/j.gaitpost.2013.01.028

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 7.

    Kernozek TW, LaMott EE, Dancisak MJ. Reliability of an in-shoe pressure measurement system during treadmill walking. Foot Ankle Int. 1996;17(4):204209. PubMed ID: 8696496 doi:10.1177/107110079601700404

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 8.

    Hughes J, Pratt L, Linge K, Clark P, Klenerman L. Reliability of pressure measurements: the EM ED F system. Clin Biomech. 1991;6(1):1418. PubMed ID: 23916339 doi:10.1016/0268-0033(91)90036-P

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 9.

    Gore SJ, Marshall BM, Franklyn-Miller AD, Falvey EC, Moran KA. The number of trials required to obtain a representative movement pattern during a hurdle hop exercise. J Appl Biomech. 2016;32(3):295300. PubMed ID: 26667614 doi:10.1123/jab.2015-0121

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 10.

    Helwig NE, Shorter KA, Ma P, Hsiao-Wecksler ET. Smoothing spline analysis of variance models: a new tool for the analysis of cyclic biomechanical data. J Biomech. 2016;49(14):32163222. PubMed ID: 27553848 doi:10.1016/j.jbiomech.2016.07.035

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 11.

    Lenhoff MW, Santner TJ, Otis JC, Peterson MG, Williams BJ, Backus SI. Bootstrap prediction and confidence bands: a superior statistical method for analysis of gait data. Gait Posture. 1999;9(1):1017. PubMed ID: 10575065 doi:10.1016/S0966-6362(98)00043-5

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 12.

    Pataky TC. Generalized n-dimensional biomechanical field analysis using statistical parametric mapping. J Biomech. 2010;43(10):19761982. PubMed ID: 20434726 doi:10.1016/j.jbiomech.2010.03.008

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 13.

    Degras D. Simultaneous confidence bands for the mean of functional data. WIREs Comput Stat. 2017;9(3):e1397. doi:10.1002/wics.1397

  • 14.

    Block JA. The reproducibility crisis and statistical review of clinical and translational studies. Osteoarthritis Cartilage. 2021;29(7):937938. doi:10.1016/j.joca.2021.04.008

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15.

    Cao G. Simultaneous confidence bands for derivatives of dependent functional data. Elec J Stat. 2014;8(2):26392663. doi:10.1214/14-EJS967

  • 16.

    Cao G, Yang L, Todem D. Simultaneous inference for the mean function based on dense functional data. J Nonparametr Stat. 2012;24(2):359377. PubMed ID: 22665964 doi:10.1080/10485252.2011.638071

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 17.

    Ma S, Yang L, Carroll RJ. A simultaneous confidence band for sparse longitudinal regression. Stat Sin. 2012;22:95122. PubMed ID: 23459083

  • 18.

    Zheng S, Yang L, Hardel W. A smooth simultaneous confidence corridor for the mean of sparse functional data. J Am Stat Assoc. 2014;109(506):661873. doi:10.1080/01621459.2013.866899

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 19.

    Goldsmith J, Greven S, Crainiceanu C. Corrected confidence bands for functional data using principal components. Biometrics. 2013;69(1):4151. PubMed ID: 23003003 doi:10.1111/j.1541-0420.2012.01808.x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 20.

    Choi H, Reimherr M. A geometric approach to confidence regions and bands for functional parameters. J R Stat Soc Series B Stat Methodol. 2018;80(1):239260. doi:10.1111/rssb.12239

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21.

    Baker M. 1,500 scientists lift the lid on reproducibility. Nature. 2016;533(7604):452454. PubMed ID: 27225100 doi:10.1038/533452a

  • 22.

    Knudson D. Confidence crisis of results in biomechanics research. Sports Biomech. 2017;16(4):425433. PubMed ID: 28632059 doi:10.1080/14763141.2016.1246603

    • Crossref
    • Search Google Scholar
    • Export Citation
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