Data Censoring and Parametric Distribution Assignment in the Development of Injury Risk Functions from Biochemical Data

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.