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1Executive Summary The research presented in this report deals with the joint statistical analysis of crash data and naturalistic driving data (NDD), referenced in a common spatial framework. The aim is to pro- vide a validated quantitative link between detailed measurements of naturalistic driving behav- ior, road departure crashes, and road segment characteristics. No such link exists, and therefore the goal was to develop appropriate analysis methods capable of associating crash risk with quantitative metrics (âcrash surrogatesâ) available from NDD. In this process, geographic infor- mation system (GIS) tools and other analysis tools were used. When applied to results of the future SHRP 2 naturalistic driving study (NDS), the methods should provide quantitative rela- tionships between driving and crash risk, provide validated surrogates for these types of crashes, and develop new understanding of risk factors, which can be used to improve highway safety. This work is exploratory in nature and uses preexisting driving data from southeastern Michigan to develop initial statistical models and formulate appropriate metrics. The study is based on the idea that the underlying mechanisms leading to single-vehicle road departure crashes are the same as those that create variations in normal driving, especially those involving âdisturbedâ lane-keeping control. More specifically, the study formulates the road departure crash problem according to the following set of hypotheses: 1. Single-vehicle road departure crashes occur only under conditions of disturbed control. 2. NDD contain measurable episodes of disturbed control. 3. Crash surrogates exist and are based on a combination of objective measures of disturbed control (from onboard sensors), highway geometric factors, and off-highway factors (envi- ronmental factors). 4. Crash surrogates can be related to actual crashes. Numerous research questions were formulated around this theme. The first of these questions relates to the measurement of disturbed control in naturalistic driving. A set of 14 metrics was formulated, all of them relating to the quality of lane-keeping control or the attention of the driver, or both. Since the driving data used did not contain objective variables for driver head or eye movement, not all possibilities were explored in detail. Statistical analysis was in fact restricted to three candidate metrics: ⢠Lateral deviation (LDEV): The vehicle lateral deviation from the center of the lane exceeds a threshold based on an overall frequency distribution obtained from the driving data. ⢠Lane departure warning (LDW): The onboard lane departure system used in the driving study gave an alert to the driver. ⢠Time to edge crossing (TTEC): The estimated time to departing the paved surface, on the basis of lane position and shoulder width, is less than a certain threshold (again based on an overall frequency distribution).
2A fourth candidate metric, the yaw rate error (YRE), was formulated to overcome some of the limitations of the three metrics listed above, but no statistical analysis was carried out on the YRE in this research. Further research questions were formulated around the variables and methods for performing a joint analysis of the crash data and driving data. As a starting point, a common measure of exposure was found in the form of normalized road segment traversals. The same road segment definitions were used for both data sets, though segments with zero exposure in the NDD were excluded from the study. A unified approach was adopted for the combined analysis of crash rates and surrogate events. The seemingly unrelated regression (SUR) method was adopted because it allows for the use of common explanatory variables in the two data sets and is flexible enough to include additional explanatory variables that are not available in both. This is an important property for future analysis in SHRP 2, in which driver attention variables may be included in the explanatory set for NDD (and no such quantitative information is usually avail- able for crashes). Bayesian estimation was used to determine posterior distributions of the SUR model parameters and also to estimate relative risk (RR) between surrogate and crashes. The posterior distributions of the logarithm of the relative risk (log RR) provided a set of validity tests of the surrogate used. The difference in log RR between crash and surrogate events should be zero for any particular comparison, meaning that zero should be contained within an associ- ated confidence interval. On the one hand, it was found that the simplest surrogate, LDEV, did not satisfy this criterion in the case of a curve/no-curve comparison, and therefore LDEV was not seen as acceptable for use as a crash surrogate. On the other hand, the corresponding log RR distributions for LDW and TTEC did satisfy this criterion. This analysis was not exhaustive, and was conducted as an exemplar of the method. In the future it will be important to increase the number of explanatory variables (including driver attention variables, if available) and apply multiple log RR comparisons to prioritize the wider range of metrics for lane-keeping control. Since TTEC was found to be a reasonable candidate crash surrogate, its distribution of extremes was applied to the prediction of road departure frequencies for a single example road segment. By using extreme value theory and annual average daily traffic (AADT) counts, it was possible to estimate the number of road departures. An estimate of 12 road departures per year was obtained, compared to the actual crash number of 1.8 per year (police-reported, single-vehicle road depar- ture crashes, averaged over a 5-year period). Since not every road departure is expected to result in a crash, this sample result is considered plausible at least. The crucial point is that a validated surrogate was needed for this type of analysis, and the surrogate needed be based on an underlying continuous variable. Overall, this exploratory study has demonstrated the use of the SUR analysis method for the combined analysis of crash data and naturalistic driving data. The approach provides a way to assess crash risk in a common framework and to validate or invalidate candidate surrogates. More detailed analysis of individual sites can be carried out by using extreme value theory, though it is important that surrogates be continuous and display the same RR as measured crash data. Although only a small number of surrogates were analyzed, the study demonstrates the importance of sur- rogate choice, and a new metricâthe YREâhas been defined and proposed for use in future sta- tistical analysis. When YRE is applied to data from the future SHRP 2 NDS, the increased statistical power resulting from the much larger data set will provide more definitive conclusions about surrogate validity and factors influencing overall crash risk.
