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Hierarchical process using Brier Score Metrics for lower leg injury risk curves in vertical impact
  1. Nicholas DeVogel1,
  2. N Yoganandan2,
  3. A Banerjee1 and
  4. F A Pintar3
  1. 1 Division of Biostatistics, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
  2. 2 Department of Neurosurgery, Center for Neuro-Trauma Research, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
  3. 3 Joint Department of Biomedical Engineering, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
  1. Correspondence to Professor N Yoganandan, Department of Neurosurgery, Medical College of Wisconsin, Milwaukee, WI 53226, USA; yoga{at}


Introduction Parametric survival models are used to develop injury risk curves (IRCs) from impact tests using postmortem human surrogates (PMHS). Through the consideration of different output variables, input parameters and censoring, different IRCs could be created. The purpose of this study was to demonstrate the feasibility of the Brier Score Metric (BSM) to determine the optimal IRCs and derive them from lower leg impact tests.

Methods Two series of tests of axial impacts to PMHS foot–ankle complex were used in the study. The first series used the metrics of force, time and rate, and covariates of age, posture, stature, device and presence of a boot. Also demonstrated were different censoring schemes: right and exact/uncensored (RC-UC) or right and uncensored/left (RC-UC-LC). The second series involved only one metric, force, and covariates age, sex and weight. It contained interval censored (IC) data demonstrating different censoring schemes: RC-IC-UC, RC-IC-LC and RC-IC-UC-LC.

Results For each test set combination, optimal IRCs were chosen based on metric–covariate combination that had the lowest BSM value. These optimal IRCs are shown along with 95% CIs and other measures of interval quality. Forces were greater for UC than LC data sets, at the same risk levels (10% used in North Atlantic Treaty Organisation (NATO)). All data and IRCs are presented.

Conclusions This study demonstrates a novel approach to examining which metrics and covariates create the best parametric survival analysis-based IRCs to describe human tolerance, the first step in describing lower leg injury criteria under axial loading to the plantar surface of the foot.

  • trauma
  • injury
  • fractures
  • injury risk curves
  • survival analysis
  • impact biomechanics

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  • Contributors NY and FAP conducted the experiments and obtained the biomechanical data. NDV and AB developed the theory. NDV performed the computations. FAP and AB reviewed the manuscript initially prepared by NY and NDV. All authors were involved in the approval of the manuscript.

  • Funding This material is the result of work supported by the US Department of Defense, Medical Research and Materiel Command, Grant W81XWH-16-1-0010, and Contract #N00024-13-D-6400. Any views expressed in this article are those of the authors and not necessarily representative of the funding organisations.

  • Competing interests None declared.

  • Patient consent for publication Not required.

  • Ethics approval The study used already published data that are available for this analysis-based paper.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Author note Narayan Yoganandan and Frank Pintar are part-time employees of the VA Medical Center, Milwaukee, Wisconsin.