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J Biomech. 2015 Sep 18;48(12):3059-65. doi: 10.1016/j.jbiomech.2015.07.026. Epub 2015 Aug 6.

Accounting for sampling variability, injury under-reporting, and sensor error in concussion injury risk curves.

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Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI 48109, United States; Survey Methodology Program, Institute for Social Research, University of Michigan, Ann Arbor, MI 48109, United States.
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, United States.
Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, United States.
Center for Injury Research and Prevention, Children's Hospital of Philadelphia, Department of Pediatrics, University of Pennsylvania, 34th and Civic, Center Blvd, Suite 1150, Philadelphia, PA 19104, United States. Electronic address:


There has been recent dramatic increase in the use of sensors affixed to the heads or helmets of athletes to measure the biomechanics of head impacts that lead to concussion. The relationship between injury and linear or rotational head acceleration measured by such sensors can be quantified with an injury risk curve. The utility of the injury risk curve relies on the accuracy of both the clinical diagnosis and the biomechanical measure. The focus of our analysis was to demonstrate the influence of three sources of error on the shape and interpretation of concussion injury risk curves: sampling variability associated with a rare event, concussion under-reporting, and sensor measurement error. We utilized Bayesian statistical methods to generate synthetic data from previously published concussion injury risk curves developed using data from helmet-based sensors on collegiate football players and assessed the effect of the three sources of error on the risk relationship. Accounting for sampling variability adds uncertainty or width to the injury risk curve. Assuming a variety of rates of unreported concussions in the non-concussed group, we found that accounting for under-reporting lowers the rotational acceleration required for a given concussion risk. Lastly, after accounting for sensor error, we find strengthened relationships between rotational acceleration and injury risk, further lowering the magnitude of rotational acceleration needed for a given risk of concussion. As more accurate sensors are designed and more sensitive and specific clinical diagnostic tools are introduced, our analysis provides guidance for the future development of comprehensive concussion risk curves.


Injury risk; Sensor error; Traumatic brain injury

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