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Data Censoring and Parametric Distribution Assignment in the Development of Injury Risk Functions from Biochemical Data
ISSN: 0148-7191, e-ISSN: 2688-3627
Published March 08, 2004 by SAE International in United States
Annotation ability available
Biomechanical data are often assumed to be doubly censored. In this paper, this assumption is evaluated critically for several previously published sets of data. Injury risk functions are compared using simple logistic regression and using survival analysis with 1) the assumption of doubly censored data and 2) the assumption of right-censored (uninjured specimens) and uncensored (injured) data. It is shown that the injury risk functions that result from these differing assumptions are not similar and that some experiments will require a preliminary assessment of data censoring prior to finalizing the experimental design. Some types of data are obviously doubly censored (e.g., chest deflection as a predictor of rib fracture risk), but many types are not left censored since injury is a force-limiting phenomenon (e.g., axial force as a predictor of tibia fracture). Guidelines for determining the censoring for various types of experiment are presented.
This paper also develops injury risk functions using parametric models having four distributions: Weibull, logistic, log-normal, and normal. The goodness of fit for each of these distributions is assessed using the adjusted Anderson-Darling statistic and by comparing the shape of the risk curve to the non-parametric Consistent-Threshold model. We show that none of the parametric distributions is consistently more appropriate than any other for the datasets considered here and that the parametric models differ appreciably only at the tails (risk below 10% or above 90%), where little data are available to rank them. Furthermore, no parametric model can be shown to be a better representation of the non-parametric model. It is concluded that most experimental programs do not collect sufficient data to justify one parametric distribution over another. It is also concluded that a non-parametric model, while the best representation of the data at hand, is not necessarily the best representation of risk for a larger population since it underestimates injury risk at the low end and overestimates risk at the high end.
CitationKent, R. and Funk, J., "Data Censoring and Parametric Distribution Assignment in the Development of Injury Risk Functions from Biochemical Data," SAE Technical Paper 2004-01-0317, 2004, https://doi.org/10.4271/2004-01-0317.
- Allsop, D. “L”, Warner, C.Y., Wille, M.G., Schneider, D.C., Nahum, A.M. (1998) Facial impact response - A comparison of the Hybrid III dummy and human cadaver. Proceedings of the 32nd Stapp Car Crash Conference, SAE paper 881719, pp. 139-155.
- Banglmaier, R., Oniang'o, T., Haut, R. (1999a) Axially compressive impacts to the human tibiofemoral joint. American Society of Mechanical Engineers Bioengineering Conference, Big Sky, Montana.
- Banglmaier, R., Dvoracek-Driksna, D., Oniang'o, T.E., Haut, R.C. (1999b) Axially compressive load response of the 90° flexed human tibiofemoral joint. Proceedings of the 43th Stapp Car Crash Conference, SAE Paper 99SC08, pp. 127-139.
- Di Domenico, L. and Nusholtz, G. (2003) Comparison of parametric and non-parametric methods for determining injury risk. Paper 2003-01-1362, Society of Automotive Engineers, Warrendale, PA.
- Duma, S (2000) Injury Criteria for the Small Female Upper Extremity. PhD Dissertation, Department of Mechanical and Aerospace Engineering, University of Virginia.
- Duma, S.M., Crandall, J.R.(2000) Eye Injuries from Air Bags with Seamless Module Covers. Journal of Trauma, 48(4):786-9.
- Funk, J.R., Crandall, J.R., Tourret, L.J., MacMahon, C.B., Bass, C.R., Patrie, J.T., Khaewpong, N., Eppinger, R.H. (2002) The axial injury tolerance of the human foot/ankle complex and the effect of Achilles tension. ASME Journal of Biomechanical Engineering, 124(6): 750-757.
- Kaplan, E. and Meier, P. (1958) Non parametric estimation from incomplete observations. Journal of the American Statistic Association, Volume 53.
- Kent, R., Bolton, J., Crandall, J., Prasad, P., Nusholtz, G., Mertz, H., Kallieris, D. (2001) Restrained Hybrid III dummy-based criteria for thoracic hard tissue injury prediction. 2001 Conference of the International Research Council on the Biomechanics of Impact (IRCOBI), Isle of Man.
- Kent, R., Patrie, J., Poteau, F., Matsuoka, F., Mullen, C. (2003) Development of an age-dependent thoracic injury criterion for frontal impact restraint loading. Paper 72, Proc. Conference on the Enhanced Safety of Vehicles (ESV), Nagoya, Japan.
- Klopp, G.S., Crandall, J.R., Hall, G.W., Pilkey, W.D.(1997) Mechanisms of injury and injury criteria for the human foot and ankle in dynamic axial impacts to the foot. Conference of the International Research Council on the Biomechanics of Impact (IRCOBI), pp. 73-86.
- Maller, R. and Zhou, X. (1996) Survival Analysis with Long-Term Survivors Wiley and Sons, New York, NY.
- Mood, A., Graybill, F., Boes, D. (1963) Introduction to the Theory of Statistics McGraw-Hill, New York, NY.
- Nusholtz, G. and Mosier, R. (1999) Consistent threshold estimate for doubly censored biomechanical data. Paper 1999-01-0714, Society of Automotive Engineers, Warrendale, PA.
- Rupp, J., Reed, M., Jeffreys, T., Schneider, L. (2003) Effects of hip posture on the frontal impact tolerance of the human hip joint. Stapp Car Crash Journal 47:21-33.
- Stephens, M. A. (1974) EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69:730-7.
- Yoganandan, N., Pintar, F.A., Boynton, M., Begeman, P., Prasad, P., Kuppa, S.M., Morgan, R.M., Eppinger, R.H.(1996) Dynamic ankle tolerance of the human foot-ankle Complex. Proceedings of the 40th Stapp Car Crash Conference, SAE paper 962426, pp. 207-218.