Tobias Niebuhr

Pedestrian injury risk and the effect of age

Older adults and pedestrians both represent especially vulnerable groups in traffic. In the literature, hazards are usually described by the corresponding injury risks of a collision. This paper investigates the MAIS3+F risk (the risk of sustaining at least one injury of AIS 3 severity or higher, or fatal injury) for pedestrians in full-frontal pedestrian-to-passenger car collisions. Using some assumptions, a model-based approach to injury risk, allowing for the specification of individual injury risk parameters for individuals, is presented. To balance model accuracy and sample size, the GIDAS (German In-depth Accident Study) data set is divided into three age groups; children (0-14); adults (15-60); and older adults (older than 60). For each group, individual risk curves are computed. Afterwards, the curves are re-aggregated to the overall risk function. The derived model addresses the influence of age on the outcome of pedestrian-to-car accidents. The results show that older people compared with younger people have a higher MAIS3+F injury risk at all collision speeds. The injury risk for children behaves surprisingly. Compared to other age groups, their MAIS3+F injury risk is lower at lower collision speeds, but substantially higher once a threshold has been exceeded. The resulting injury risk curve obtained by re-aggregation looks surprisingly similar to the frequently used logistic regression function computed for the overall injury risk. However, for homogenous subgroups - such as the three age groups - logistic regression describes the typical risk behavior less accurately than the introduced model-based approach. Since the effect of demographic change on traffic safety is greater nowadays, there is a need to incorporate age into established models. Thus far, this is one of the first studies incorporating traffic participant age to an explicit risk function. The presented approach can be especially useful for the modeling and prediction of risks, and for the evaluation of advanced driver assistance systems.

Irregularly observed time series – some asymptotics and the block bootstrap

ABSTRACT We consider time series being observed at random time points. In addition to Parzens classical modelling by amplitude modulating sequences, we state another modelling using an integer-valued sequence as the observation times. Limiting results are presented for the sample mean and are generalized to the class of functions of smooth means. Motivated by the complicated limiting behaviour, (moving) block bootstrap possibilities are investigated. Conditional on the used modelling for the irregular spacings, one is lead to different interpretations for the block length and hence bootstrap approaches. The block length either can be interpreted as the time (resulting in an observation string of fixed length containing a random number of observations) or as the number of observations (resulting in an observation string of variable length containing a fixed number of values). Both bootstrap approaches are shown to be asymptotically valid for the sample mean. Numerical examples and an application to real-world ozone data conclude the study.

Detection of the toughest: Pedestrian injury risk as a smooth function of age

ABSTRACT Objective: Though it is common to refer to age-specific groups (e.g., children, adults, elderly), smooth trends conditional on age are mainly ignored in the literature. The present study examines the pedestrian injury risk in full-frontal pedestrian-to–passenger car accidents and incorporates age—in addition to collision speed and injury severity—as a plug-in parameter. Methods: Recent work introduced a model for pedestrian injury risk functions using explicit formulae with easily interpretable model parameters. This model is expanded by pedestrian age as another model parameter. Using the German In-Depth Accident Study (GIDAS) to obtain age-specific risk proportions, the model parameters are fitted to the raw data and then smoothed by broken-line regression. Results: The approach supplies explicit probabilities for pedestrian injury risk conditional on pedestrian age, collision speed, and injury severity under investigation. All results yield consistency to each other in the sense that risks for more severe injuries are less probable than those for less severe injuries. As a side product, the approach indicates specific ages at which the risk behavior fundamentally changes. These threshold values can be interpreted as the most robust ages for pedestrians. Conclusions: The obtained age-wise risk functions can be aggregated and adapted to any population. The presented approach is formulated in such general terms that in can be directly used for other data sets or additional parameters; for example, the pedestrians sex. Thus far, no other study using age as a plug-in parameter can be found.

Expanding Pedestrian Injury Risk to the Body Region Level: How to Model Passive Safety Systems in Pedestrian Injury Risk Functions

Objective: Assessment of the effectiveness of advanced driver assistance systems (ADAS) plays a crucial role in accident research. A common way to evaluate the effectiveness of new systems is to determine the potentials for injury severity reduction. Because injury risk functions describe the probability of an injury of a given severity conditional on a technical accident severity (closing speed, delta V, barrier equivalent speed, etc.), they are predestined for such evaluations. Methods: Recent work has stated an approach on how to model the pedestrian injury risk in pedestrian-to–passenger car accidents as a family of functions. This approach gave explicit and easily interpretable formulae for the injury risk conditional on the closing speed of the car. These results are extended to injury risk functions for pedestrian body regions. Starting with a double-checked German In-depth Accident Study (GIDAS) pedestrian-to-car accident data set (N = 444) and a functional–anatomical definition of the body regions, investigations on the influence of specific body regions on the overall injury severity will be presented. As the measure of injury severity, the ISSx, a rescaled version of the well-known Injury Severity Score (ISS), was used. Though traditional ISS is computed by summation of the squares of the 3 most severe injured body regions, ISSx is computed by the summation of the exponentials of the Abbreviated Injury Scale (AIS) severities of the 3 most severely injured body regions. The exponentials used are scaled to fit the ISS range of values between 0 and 75. Results: Three body regions (head/face/neck, thorax, hip/legs) clearly dominated abdominal and upper extremity injuries; that is, the latter 2 body regions had no influence at all on the overall injury risk over the range of technical accident severities. Thus, the ISSx is well described by use of the injury codes from the same body regions for any pedestrian injury severity. As a mathematical consequence, the ISSx becomes explicitly decomposable into the 3 body regions and so are the risk functions as body region–specific risk functions. The risk functions for each body region are stated explicitly for different injury severity levels and compared to the real-world accident data. Conclusions: The body region–specific risk functions can then be used to model the effect of improved passive safety systems. These modified body region–specific injury risk functions are aggregated to a new pedestrian injury risk function. Passive safety systems can therefore be modeled in injury risk functions for the first time. A short example on how the results can be used for assessing the effectiveness of new driver assistance systems concludes the article.