Not straightforward: modelling non-linearity in training load and injury research
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  • Published on:
    Response to “Important Nuances for Non-Linear Modeling”
    • Lena K Bache-Mathiesen, PhD Candidate Oslo Sports Trauma Research Centre, Department of Sports Medicine, Norwegian School of Sports Sciences
    • Other Contributors:
      • Thor Einar Andersen, Professor
      • Torstein Dalen-Lorentsen, PhD Candidate
      • Benjamin Clarsen, Associate Professor
      • Morten W Fagerland, Associate Professor

    We thank Shrier et al. for a thoughtful expansion on the topic of non-linearity.1 The comments from the authors provide valuable insights and detail to both the handling and the interpretation of fractional polynomials and splines, and may interest readers who seek more information than the short introduction in Bache-Mathiesen, et al. 2.

    We are especially grateful for elaborating on the interpretation of restricted cubic splines, and the solution of adding a small constant (i.e. 0.1) to all values to handle the value “0” when using fractional polynomials. These topics could not be sufficiently addressed within the limited wordcount of the original article, and we encourage readers to consider these comments.

    Conflict of Interest:
    None declared.

    1. Shrier I, Wang C, Stokes T, et al. Important Nuances for Non-Linear Modeling. BMJ Open Sport & Exercise Medicine 2021
    2. Bache-Mathiesen LK, Andersen TE, Dalen-Lorentsen T, et al. Not straightforward: modelling non-linearity in training load and injury research. BMJ Open Sport & Exercise Medicine 2021;7(3):e001119. doi: 10.1136/bmjsem-2021-001119

    Conflict of Interest:
    None declared.
  • Published on:
    Important Nuances for Non-Linear Modeling
    • Ian Shrier, Investigator, primary care sport medicine physician Lady Davis Institute, McGill University
    • Other Contributors:
      • Chinchin Wang, PhD candidate
      • Tyrel Stokes, PhD candidate
      • Jorge Trejo Vargas, PhD candidate
      • Russell Steele, Associate Professor

    We would like to thank Bache-Matiesen et al.(1) for their thoughtful article on non-linear modelling in sport medicine. Our own study on the non-linear relationship between acute: chronic workload ratio (ACWR) and injury risk in children was published as a preprint (2) and recently accepted by the American Journal of Epidemiology.(3) Below, we highlight some additional underlying principles in non-linear modelling that readers should understand.

    Models are based on information, which includes both data and assumptions. Simple linear models are more prone to bias because they assume a data generating process that is likely incorrect. The flexibility of non-linear models leads to less risk of bias, but also less precision. The optimal choice between bias and uncertainty depends on the context.(4)

    Bache-Matiesen describe three non-linear modelling options: quadratic modelling, fractional polynomials (FP), and restricted cubic splines (RCS, where knots are determined by either data driven or a priori methods). These all fall under generalized additive models (GAMs), or generalized additive mixed models (GAMMs; if one uses “random effects” to adjust for repeated measures on participants).

    FP methods use a single polynomial function over the entire range of exposures to predict the outcome. Quadratic models are special cases of FP (with exponents of 0, 1 and 2) and are too restrictive to be generally recommended. RCS separate data i...

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    Conflict of Interest:
    None declared.