Latent Class and Functional Data Analyses for the Investigation of Stiffness in Low Back Pain

• Author / Creator

  Casciaro, Yolanda

• Low back pain (LBP) is known to be a prevalent, debilitating and costly condition, not to mention the difficulty clinicians have treating it. But progress has been made, as it has recently been shown that instrumented L3 indentation generates force-displacement (F-D) data that is associated with patient-reported measures of disability. This is the first quantitative measure positively linked with a specific patient outcome. As such, F-D curves may be key in successfully sorting patients to appropriate treatments for LBP. Unfortunately, only single value representations of the complex biomechanical response described by these plots (e.g. terminal stiffness, regional stiffness) have been analyzed to date. A more thorough understanding of F-D data may improve success rates for treatment of LBP in a similar way that a thorough understanding of other biomechanical responses, such as an ECG, have allowed clinicians to identify patients at risk of disease or disability. As such, two specific functional statistical analysis techniques, functional data analysis (FDA) and latent class analysis (LCA) will be applied in an attempt to analyze and classify F-D curves in their entirety. Specifically, the three hypotheses that follow were tested in three separate experiments, each comprising a chapter in this thesis:

  1. Functional data analysis (FDA) and a latent class analysis (LCA) will be able to cluster simulated functional data equally well. Since this is a novel application of LCA, a comparative application to a known technique is important.
  2. FDA and LCA will perform at least as well as traditional statistics to cluster experimental F-D curves with a large effect size. Knowledge of FDA and LCA performance with respect to traditional statistics will guide interpretation of results when analyzing true clinical patient data.
  3. FDA and LCA will perform at least as well as traditional statistics to identify clinical patient F-D curves after successful application of a LBP intervention. The findings developed and analyzed here would inform further work to enhance interpretations of stiffness with respect to patient outcomes. The results of the first experiment served to identify that LCA emphasizes end values and overall curve proximity ahead of distinctive features of curve shape, while FDA emphasizes rates of change. In the second experiment, the FDA method performed as expected and grouped F-D curves by salient features of shape, though this did not associate with any specific patient identifiers. The dimensionality of the data did not maintain sufficient degrees of freedom for effective investigation by LCA. The third and final investigation did not perform as well as anticipated, since a small effect size diminished the overall performance of fPCA. Again, dimensionality of the F-D data limited LCA analysis to only two clusters, neither of which were meaningful. While outcomes of the second and third experiments were not as definitive as anticipated, valuable information with respect to F-D curve analysis was gleaned. Specifically, regional and terminal stiffness do not discard relevant biomechanical data in the case of post-hoc identification of responders and non-responders to a specific treatment.
     As identifying the salient features of F-D curves could streamline and expedite the process of assigning appropriate treatment to LBP patients, thereby saving clinical cost, time and reducing frustration for patients, a thorough understanding of the stiffness phenomenon holds promise, since it has already been definitively linked to patient-reported recovery. Based on this work, some specific recommendations for data collection and analysis have emerged. Explicitly, a lack of correlation to measured demographics data may signal a need to collect different data, and it is therefore recommended that a comprehensive list of LBP risk factors be assembled and reviewed to ensure data collection is thorough. In terms of analysis, FDA requires a secondary step. This work employs a k-means clustering algorithm, but hierarchical clustering methods have been applied to biomechanics with success, and it may also be of interest to apply the LCA method in the secondary analysis. In addition, a time-based bivariate analysis, F-D phase-plane plots, or a piecewise curve analysis approach may emphasize information that is otherwise not apparent. Future work would ideally link quantitative stiffness measures to other clinical assessments including MRI, experimental biomechanics of functional spinal units, and theoretical biomechanical modelling to develop a full understanding of the stiffness phenomenon and the component motions comprising a bulk measurement of force and displacement.

• Subjects / Keywords

  • Classification
  • Functional Statistics
  • Low Back Pain
  • Latent Class Analysis
  • Spinal Stiffness
  • Functional Data Analysis

• Graduation date

  Fall 2018

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3W37MB6F

• License

  Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.