How reliable are injury risk curves

Injury risk curves are the basis for assessing automotive occupant safety. They are used in regulation, consumer test ratings, safety system design, and for the evaluation of the effectiveness of safety systems. Therefore, an injury risk curve should be accurate and credible. But how reliable is the risk prediction of an injury risk curve? The objective of this study was to identify and illustrate factors influencing the reliability of injury risk curves. Thereby, highlight the need for a more thoughtful construction and use of injury risk curves as well as the need for additional statistical measures when publishing injury risk curves. The results of this study will lead to a better understanding of injury risk curves and can also be used for a better design of experiments in biomechanical testing. Four factors affecting the reliability of injury risk predictions were evaluated exemplarily in this study: 1) The sampling, i.e. the uncertainty due to statistical inference from a sample on the population; 2) The censoring of data, i.e. the uncertainty introduced by the imprecision of the tolerance limit determination; 3) The test severities, i.e. the uncertainty in injury risk prediction as a result of test severities used in the biomechanical tests; 4) The statistical model, i.e. the bias introduced by the method used to calculate the injury risk curve. Although all of the findings presented can be explained by statistical theory, this paper demonstrates the effects of different factors on the reliability of injury risk curves in a visual manner. Statistical simulation is used to replicate biomechanical testing and injury risk curve construction. The statistical simulations comprise several steps including the definition of a distribution of the biomechanical tolerance limit in the population, the sampling and biomechanical testing of specimens as well as the construction of the injury risk curve. The statistical simulations clearly illustrate the effect of the sample size and data censoring on the uncertainty of injury risk curves. It can be concluded that the interpretation of an injury risk curve without a proper measure of confidence is meaningless. Exact data of the biomechanical tolerance limit improve the reliability of the injury risk curve – however only with the use of an appropriate statistical method. The range of criterion values used in the injury risk curve construction systematically affects the shape and reliability of the curve. Biomechanical tests should be done over a wide range of test severities in order to avoid bias in the risk estimation. It is demonstrated that the use of an unsuitable - nevertheless widely used - statistical method for constructing the injury risk curve can lead to unrealistic injury risk predictions.