Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk (2014)

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87 C h a p t e r 8 The previous analyses have focused on crash-contributing factors in Lead-Vehicle Precrash Scenarios, including descrip- tive variables, distracting activities, glance behavior, situation kinematics, and visual cues. The focus has been on quantify- ing crash risk rather than injury risk. By developing methods to estimate both the probability of crashing and injury risk, this chapter focuses on the research question, What crash severity scale is best suited for analysis of risk? Here, we propose a method that estimates potential out- come severity (crash probability and injury risk) by using a model to simulate the effect of applying different glance dura- tions on the actual kinematics of the crashes and near crashes. These potential outcome severity scales, Model-estimated Injury Risk (MIR) and Model-estimated Crash Risk (MCR), are indices that are output as continuous values, in contrast to the approach used in previous chapters, which has two broad crash and near-crash categories. According to current common practice, safety-critical events in naturalistic driving data are grouped into categories such as crash or near crash in the SHRP 2 Event Severity variable. This approach has been used extensively in naturalistic driving studies (see Fitch et al. 2013; Klauer et al. 2010; Olson et al. 2009). However, such an approach has significant limita- tions. For example, does the categorization always treat a crash as more severe than a near crash? Why should an Event Severity variable value a very-low-velocity, stop-and-go crash (e.g., <1 mph) as more severe than a high-speed near crash on a motorway, in which the driver is just barely able to stop with full braking from 70 mph? The categorization approach cannot provide a continuous outcome variable for risk analyses across crashes and near crashes. MIR and MCR are two continuous variables that can be calculated for near crashes and crashes alike. The potential severity scales developed here were com- pared with actual outcome severity scales: (1) DeltaV, the esti- mated change in velocity for the vehicles in a crash (Kusano and Gabler 2010), and (2) minimum time to collision (minTTC) (Lee 1976). These outcome scales provide information about what actually happened in an event, are well established, and are described more in detail in Appendix A. We also compared the crashes and near crashes in the SHRP 2 sample with accident statistics, including the use of extreme value analysis (EVA) (Jonasson and Rootzén 2014). As shown in previous chapters, the mismatch between Eyes- off-Path glances and event kinematics is central to an event becoming a crash. Thus, it makes sense to ask these questions: What if the last glance duration was different in a particular event? What if the driver in the subject vehicle started his or her glance at a different point in time? Would there still be a crash? Would it turn into a near crash? Given a specific off-path glance behavior, what is the risk that this particular driving situation’s kinematics would end in a crash or result in an injury? The basic idea behind potential (model-based) severity scales is the use of mathematical simulations to provide insight into what could have happened in a specific event if the driver had behaved differently (i.e., different glance behavior). These can be called what-if simulations because they make it possi- ble to study how a change in driver glance behavior would have influenced the outcome of an individual event. An exam- ple of what-if simulations using naturalistic driving data is McLaughlin et al. (2008) in which the safety benefit of forward collision warning (FCW) systems was evaluated by applying FCW algorithms to the kinematic data of 60 near-crash events and 13 crash events in lead-vehicle conflicts. In the what-if simulations presented here, the kinematics of the subject vehi- cle are changed depending on driver off-path glance behavior to determine the effect that different glance distributions could have on the crash/near-crash outcome. These what-if simula- tions are used to calculate the following three potential severity scales: (1) Maximum Severity Delta Velocity (MSDeltaV), (2) Model-estimated Injury Risk (MIR) index, and (3) Model- estimated Crash Risk (MCR) index. A primary objective of this chapter is to demonstrate the usefulness of what-if simulations and potential (model- based) severity scales as tools for analyzing driver behavior in Actual and Potential Severity

88 naturalistic driving data. The aim is not to provide definitive answers but rather to show a proof of concept. First, we describe and show how to calculate the potential severity scales and compare them with the actual severity scales (DeltaV and minTTC). Then we present how these methods can be used to perform three types of analyses: (1) glance duration analysis, (2) secondary-task analysis, and (3) generalization analysis. The what-if method and potential severity scales are primarily demonstrated through examples. The first example, glance duration analysis, presents an application of potential severity scales to evaluate the effect of the duration of the last glance, when applied to the crashes and near crashes. The second example, secondary-task analysis, presents an evaluation procedure that can facilitate relative-risk estimates of secondary tasks (e.g., navigation entry or texting) with different off-path glance distributions. Two hypothetical tasks are evaluated. The final example, generalization analysis, evaluates the selection of near crashes and crashes in the sam- ple, with respect to accident statistics, and explores the use of extreme value theory. The what-if method is in early-stage development and needs to be validated, and the under lying assumptions and limitations need further scrutiny. A brief description of the method and results are given below. Detailed descriptions of the what-if simulations and the potential severity scales can be found in Appendix A. 8.1 the three potential Severity Scales Maximum Severity Delta Velocity (MSDeltaV) is the estimated (mass-adjusted) DeltaV of an event had the subject vehicle’s driver not performed an evasive maneuver. MSDeltaV is calcu- lated by running a what-if simulation in which any evasive brak- ing maneuver by the driver in the subject vehicle is “removed.” This removal includes the replacement of the SVspeed after the evasive maneuver with a constant speed equal to the speed just before the evasive maneuver. For crashes in which the driver did not perform an evasive maneuver, MSDeltaV is equal to the actual (original event) DeltaV. The Model-estimated Injury Risk (MIR) index is a potential severity metric that extrapolates from any event in naturalistic driving data with an evasive maneuver (e.g., crash or near crash) to a continuous injury-risk value (called MIR) of the event, given a model of driver glance-off-path behavior. This is not the risk of an injury in the actual event as it happened, but rather the risk of a serious injury in the event had it played out differ- ently according to the simulation. According to the Abbreviated Injury Scale, serious injury in this context is defined as MAIS3+ injury (Gennarelli and Wodzin 2005). The possible glance behaviors are assumed to be a sample from a probabilistic dis- tribution that can be either generic or estimated from available data. The calculation of MIR presented here is equivalent to applying all glances in a glance-off-path distribution to the kinematics of a specific event and estimating the injury risk given that distribution. That is, MIR is acquired via simulation and is related to an estimate of MAIS3+ injury risk, given the underlying assumptions. The higher the MIR index, the higher the risk of injury. The Model-estimated Crash Risk (MCR) index is based on the same concept as MIR, but the index represents the prob- ability of a crash. Here, the what-if simulation classifies an event as crash or no-crash for a specific glance duration. It is equivalent to each glance duration in the glance-off-path dis- tribution being simulated, and the outcome is classified as crash or no-crash. This is different from MIR, for which the injury risk of those crashes is calculated as well. One use for both MIR and MCR is to apply them to a sam- ple of crashes and near crashes (e.g., the data set used in this study). This is equivalent to performing all permutations of glance-off-path (in a chosen distribution) on all near crashes and crashes in the sample, producing a distribution of MIR and MCR indices for that sample. 8.2 What-If Simulation Basics and the Calculation of MIr and MCr The what-if simulations and calculations of MIR and MCR indices are based on a set of assumptions and a procedure that are briefly described below. For details and the reasoning around the choices, see Appendix A. Prerequisites • The extraction of both the subject- and lead-vehicle kinematics. • The choice of a brake profile (how the driver brakes) to be used as a hypothetical brake response in the simulations. We use a constant 8 m/s2. However, the brake profile does not have to be constant and the same across events. Future implementations should consider using (1) different brake profiles depending on scenario-specific parameters, such as the estimated coefficient of friction; and (2) different brake profiles depending on the urgency of the situation (e.g., low or high looming or looming rate). The former may use estimates of the coefficient of friction from video or quantitative data [actual acceleration and, for example, antilock braking system (ABS) engagement]. Including the coefficient of friction on the results will provide higher- fidelity results that minimize the effect of road conditions as a confounding factor. The latter (urgency-based brake response) may attenuate the effect of looming rates on the outcome, but it depends on which urgency/brake response relationship is established and used.

89 • The choice of a driver reaction time—that is, time from looking back on the road until applying full brake. Con- clusion 3 under Section 7.6 indicated that the results show that a fixed reaction time is not correct. However, we choose a fixed reaction time (0.4 second) since it pro- duces conservative estimates of risk and shows proof of concept. The value 0.4 second is the median of the reac- tion time for crashes in which the reaction is made after invTTC ≥ 0.1 s-1 is fulfilled. That is, the median reaction time for drivers when the invTTC reached at least 0.1 s-1 before the driver reaction (brake response) is 0.4 second. Alternative reaction models can be integrated into the current simulation. One implication of using a short and constant reaction time is that the MIR and MCR esti- mates will be lower on a sample level. Similar to the use of urgency-based brake profiles, if a looming-based reac- tion time were used (e.g., based on the results in Chap- ter 7) in the what-if simulation, the effect of high looming rate might be somewhat attenuated due to faster responses at high looming. • The choice and extraction of the off-path glance distribu- tion that should be used in the simulations. We choose the glance distribution from matched baseline events for most analyses but when comparing tasks, we also used the glance distributions of the individual tasks (as well as the total task time). • The choice of where (an anchor point) and how to place the glance-off-road distribution in time, in the simulation. This choice is very important for the actual outcome sever- ity estimates. We choose an anchor point at the threshold of the invTTC = 0.1 s-1 close to the crash or minTTC of the event. This is based on the assumption that the driver’s glance behavior (glance-off-road distribution) is the same as in normal driving (matched baseline) up until that point. • A choice of injury-risk function, transforming DeltaV into injury risk that is relevant for rear-end crashes. We created an injury-risk function from NASS Crashworthiness Data System (CDS) data. • Identification of the time point of start of evasive maneu- ver in the original events. We use the time of the first nega- tive derivative (deceleration) of the SVspeed after the driver reaction point. What-If Procedure The method of what-if simulations starts with the removal of the evasive maneuver in the original event from the SVspeed, substituting SVspeed at all times after the start of evasive maneuver with the speed just before the evasive maneuver. Second, a simulation is run to get the outcome of “all” pos- sible starts of an evasive maneuver by braking (Figure 8.1, Panel 1). The result is the impact speed related to the initiation of an evasive maneuver at “all” times in the event. The cyan curve in Figure 8.1, Panel 1, is the original event’s LVspeed. The red curve is the original event’s SVspeed. The green lines Figure 8.1. A short description of the main steps for calculating MIR and MCR.

90 (slopes) represent successful evasive maneuvers (where there was no crash) in the SVspeed simulations up until the first simulation ending in a crash, based on different starting points of the simulated evasive maneuvers. The blue lines (slopes) represent simulated SVspeeds where the outcome was a crash. The blue horizontal line is the simulated SVspeed until the start of each simulated evasive maneuver. The dashed black line is the evasive maneuver part of the SVspeed for the first simulation resulting in a crash. The start of the evasive maneuver corresponding to this first simulated crash is marked by a black X. The red Xs show the time instance and SVspeed value for the first and second simulations that resulted in a crash. The difference between the SVspeeds for the simulated crashes and the original LVspeed are the impact speed (shown as vertical red lines). For example, for the first crash, follow the original SVspeed, then the simulated (horizontal) SVspeed, until the black X. At that time the evasive maneuver starts. Follow the dashed line down to the red X. That is the crash point. The crash point is defined as the first time the relative distance goes below zero (integration of SVspeed and LVspeed with an initial distance). As a third step, the injury risk for each start of evasive maneu- ver is calculated (Figure 8.1, Panel 2), based on (1) the estimated impact speed in the previous step, (2) the chosen injury-risk function, and (3) estimates of SV and POV masses. That is, each simulated start of evasive maneuver has a corresponding risk of injury. The black X corresponds to the black X in Fig- ure 8.1, Panel 1—that is, the start of the evasive maneuver for the first simulated event that became a crash. As a fourth step (Figure 8.1, Panel 3), we place the glance distribution at the chosen anchor point (in this implementa- tion, invTTC = 0.1 s-1; see Appendix A). Now both the injury risks and the glance distributions are in the time domain, ready for calculating estimated injury (and crash) risk. Finally, by integrating the product of the injury risks and the glance distribution at each time point over time, an estimate of the injury risk for this event can be obtained, given (1) the glance behavior, and (2) the original lead-vehicle kinematics and simulated subject-vehicle behavior (Figure 8.1, Panel 4). This yields a value of the MIR index. The MCR index is derived by counting instances of the simulation for an event that results in a crash and relating this to the total number of instances rather than calculating the injury risk that corresponds to each such instance (i.e., MIR). This procedure to calculate MIR and MCR can now be applied to the crash and near-crash data to address different questions. In the following section, actual and potential out- come severity scales are compared as applied to the events in the present sample. Then, three analyses that may be per- formed using this approach are briefly described and results are shown. 8.3 actual Outcome Severity Versus potential Outcome Severity The comparison of actual and potential outcome severity scales is made by calculating each scale value for each of the crashes and near crashes in the present sample. Figure 8.2 shows six different outcome severity scales. When comparing the actual and potential severity scales, it is apparent that the actual severity scales are difficult to work with across crashes and near crashes because they cannot be used for both crashes and near crashes (see the three left panels in Figure 8.2). The three left panels show actual outcome severity (what actually happened) in this study’s data set. The three right panels show potential severity scales (what could have happened, created using what-if simulations) in the data set. The six scales are described in turn. The dichotomous categorization of crashes and near crashes (leftmost panel in Figure 8.2) has so far been used extensively in analysis in naturalistic driving data, but it does not provide a way to compare the two event categories (crash and near-crash) or make comparisons within each category. The minimum time to collision (second panel from the left) is well established, and although it has some drawbacks, it is one of the most readily used scales of severity for near crashes, especially as a safety-critical event trigger in natu- ralistic driving studies (Rootzén and Jonasson 2014). How- ever, even though minTTC is defined for crashes, it is not very helpful because the minTTC for crashes is by definition zero. The DeltaV (Figure 8.2, third panel from the left) is also a well-established metric of actual outcome severity (Buzeman et al. 1998; Kusano and Gabler 2010; Viano and Parenteau 2010), but it is only defined for crashes, since there is no actual crash in a near crash. Of the scales presented here, the DeltaV metric is the most relevant metric for actual outcome injury estimations. The third panel from the right in Figure 8.2 shows Maxi- mum Severity Delta Velocity (MSDeltaV), which is an esti- mate, using what-if simulations, of the DeltaV had the driver not performed an evasive maneuver. Although this is a con- tinuous potential severity metric, it does not account for any driver reaction; rather, it plays out each event to the maxi- mum possible DeltaV (excluding the following vehicle’s driver accelerating into the crash). MSDeltaV may still be used for evaluation of sample selections and for analyses that do not involve driver behavior explicitly. The difference between DeltaV (third panel from left) and MSDeltaV (third panel from right) is that DeltaV takes into account the braking of the subject vehicle after the start of the evasive maneuver, while MSDeltaV removes it. This difference is primarily created by the time headway at the start of evasive maneuver and the amplitude (brake profile) of subject-vehicle deceleration.

91 In the second panel from the right, MCR values for the indi- vidual crashes and near crashes are shown. The scale is clearly continuous for both crashes and near crashes. Thus, a high- speed near crash is rated higher than a low-speed stop-and-go crash. However, this is not what actually happened; it is what might have happened given an underlying driver behavior model. In this way, MCR is most applicable to analysis of pre- cursors of contributing factors in safety-critical events, as opposed to analysis of how drivers avoid crashes once a safety- critical event is under way. The resolution depends on the granularity of the glance distribution (fewer glances in the creation of the distribution mean lower resolution). The rightmost panel in Figure 8.2 shows the MIR values. This scale is continuous as well, for both crashes and near crashes. Although difficult to judge, comparing MIR and MCR, there seem to be only a few crashes and near crashes with high injury risk, while the probability of crashing is more uniformly distributed. This results, in part, from the matching of the matched baseline glance distribution and the specific crash and near-crash events in the sample; a different sample might produce different results. However, the results in our study seem reasonable since we would generally expect a low probability of serious injury and a higher and more uniform probability of crashing for any safety-critical event. 8.4 Glance Duration analysis To evaluate the injury risk related to a last glance of a different duration, the MIR and MCR indices can be calculated using different glance durations. A calculation of MIR was made for each last glance duration between 0.1 second and 4.0 seconds, in steps of 0.1 second. That is, instead of using the matched baseline distribution in the MIR calculations, a glance “distri- bution” with glances of only one specific duration was used for each simulation. These completely artificial distributions contained 100 glances (events) of the same duration (e.g., 0.7 second or 1.8 seconds). We call these distributions just to be coherent with the method descriptions. The single-duration distribution was applied to all crash and near-crash events respectively, producing a MIR index distribution for all near crashes and crashes (separately) for each 0.1-second step. Based on this distribution, the standard error could also be calculated. Each one-duration distribution was applied, conditioning it on overlapping the invTTC = 0.1 s-1 (see Figure 8.1). Note that in this and subsequent analyses, a number of events (crashes and near crashes) were excluded. Since this is a proof of concept, details of the exclusion criteria are not provided, but the majority were excluded because they were very-low-speed events or because there were some problems with data quality Figure 8.2. Application of six different severity scales on the crashes and near crashes used in this report. The three left plots show actual severity scales; the three right plots show potential severity scales. Left to right: dichotomous classification into crashes and near crashes, minTTC (crashes equal zero), DeltaV for crashes (no near crashes shown since DeltaV is undefined for near crashes), MSDeltaV, MCR, and MIR.

92 (e.g., availability of speed). The exclusion of very-low-speed events may affect the results, but since all analyses are relative (i.e., using the same sample of crashes and near crashes when comparisons are made), the effect is likely minor. Results from Glance Duration Analysis The MIR starts to increase more rapidly around a last glance duration of 1.25 seconds and after that is practically linearly increasing (Figure 8.3). On average, MIR for crashes seems, at least for longer durations, to reflect more severe kinematics than for near crashes, though the confidence intervals over- lap. The glance anchor point (invTTC = 0.1 s-1) can be seen as aligning the application of the glance for both crashes and near crashes to a common “start” of critical kinematics. Then, since for the same glance duration crashes have a higher MIR than near crashes, what is different is the rate at which the event is unfolding. These results indicate that crashes in the sample are, on average, developing faster than near crashes, which is consistent with the results in Chapter 7. 8.5 Secondary-task analysis The crash risk related to a visual-manual task—such as radio turning, navigation entry, or texting—can be evaluated by studying the effect of glance behavior related to these tasks (such as glance histograms collected in a separate experiment) on actual crashes and near crashes in naturalistic data (e.g., the distributions found in NHTSA 2013). Here we introduce a method that may be used to complement to such analyses. It uses what-if simulations to assess potential (model-based) injury risk, given the assumptions for the MIR index con- struction described above. This section describes the method and exemplifies its use with two hypothetical task-glance dis- tributions (Eyes off Path) with corresponding task durations (total task time). The method is based on performing simula- tions of how the duration of the last glance off path affects MIR when applied to our sample of crashes and near crashes— that is, what would happen had the glance distribution in the event been similar to the one described by the glance distribu- tion of the evaluated task. We only calculate MIR, but the same methodology can just as well be applied to MCR. In this analysis (but not all what-if analyses) it is important that the on-path glances be taken into account in the calcu- lations. In the matched baseline distributions in SHRP 2, drivers are looking on the road approximately 79% of the time. When performing a visual-manual task, however, the time of gaze on road is much smaller, say 30% of the time (NHTSA 2013). We want to compare a task of a specific length (total task time)—for example, 20 seconds—with an alternative use of that same amount of time, as in baseline driving. The top panel in Figure 8.4 shows the matched baseline distribution with what is called a point mass at a glance dura- tion of zero. This point mass corresponds to the time looking Figure 8.3. The mean MIR value for all crashes (red) and near crashes (blue) in the sample,  the standard error (dashed lines).

93 on the road. The bar at zero is 79% of the total distribution (histogram). That is, there is a 79% chance (probability of 0.79) that the driver will be looking on the road at some critical point (e.g., invTTC = 0.1 s-1). The bottom left panel in Figure 8.4 shows an example of a (hypothetical) “simple” task, off-road glance distribution. Here the point mass at zero is 30% of the total of the distribution (histogram); thus, while performing this task, there is a 30% chance that the driver is looking at the road when something occurs. To get the relative risk of engaging in different tasks, an MIR index is first calculated for each of the tasks to be compared, by applying the corresponding glance distribution to the kine- matics of all crashes and near crashes in the sample. The same is done for the matched baseline glance distribution. All the glance-off-path distributions include point masses at dura- tion zero (0) to account for the time when the driver is looking on the road (Victor et al. 2009). The resulting MIR indices for the application of each task’s glance distribution (conditioned on overlapping invTTC = 0.1 s-1) to the kinematics of each crash and near crash in the SHRP 2 sample can be compared with the corresponding distribution that results from applica- tion of the matched baseline glance distribution to the same set of crashes and near crashes. This can be done using the method outlined in Figure 8.1. Since the tasks take different amounts of time to complete, the total duration of the individual tasks is needed to calcu- late relative risk. Let us assume that the easy task takes, on average, 20 seconds to complete, while the difficult task takes Figure 8.4. Matched baseline glance distribution with a point mass at zero (78.83%) (top), the glance distribution of a hypothetical easy task with a point mass at zero (30%) (bottom left), and the glance distribution of a hypo- thetical difficult task with a point mass at zero (30%) (bottom right). Point masses correspond to the portion of the time looking on the roadway for the respective task (e.g., 0.3  30% glances on forward roadway).

94 40 seconds to complete. The RelativeRiskTask_vs_task of the two tasks can be calculated using the following equation, where the mean MIR of the matched baseline glance distribution is subtracted from the easy and difficult tasks’ mean MIRs, and the relative risk is scaled by the difference in Total Glance Time. This equation effectively assumes an alternative use (glance behavior) for the difference in total task time between the easy and difficult tasks (20 seconds), equivalent to that of the matched baseline. That is, it takes into account the MIR for the 20-second matched baseline behavior that is the dif- ference between the two tasks (total task time). ( ) ( )= − − RelativeRisk TotalTaskTime TotalTaskTime _ _ DifficultTask MatchedBaseline EasyTask MatchedBaseline DifficultTask EasyTask MIR MIR MIR MIR Task vs task i Observe that this equation would have a population interpreta- tion if the distribution of the sample of (near) accidents was representative of all the possibly dangerous situations. Since this is not entirely correct because of selection bias, a better proce- dure should incorporate weighting. Such weighting is not con- sidered here, but research on how this should be implemented would be a good next step in the method development. If only the relative risk between the task and matched base- line is desired, a simple division of mean MIRs can be per- formed (RelativeRiskTask_vs_MBL). This risk includes the point mass at zero. =RelativeRisk _ _ Task MatchedBaseline MIR MIRTask vs MBL Results from Secondary-Task Analysis The difference between the MIR index for the matched baseline glance (M = 0.267, SD = 0.372) and the simple task (M = 0.776, SD = 1.194) is significant, t256 = 9.76, p < 0.001. Similarly, the difference between the MIR for the matched baseline glance and the difficult task (M = 0.856, SD = 1.150) is significant, t256 = 11.91, p < 0.001 (see Figure 8.5). The relative risk of the difficult task and matched baseline (ratio of MIR index means; RelativeRiskDifficult_task_vs_MBL) is 3.2. The relative risk of the simple task and matched baseline (RelativeRiskEasy_task_vs_MBL) is 2.9. Now assume the difficult task’s total task time is 40 seconds, and the easy task’s total task time is 20 seconds. Using the equation for relative task risk, the relative risk is calculated to be 2.31 [RelativeRiskDifficult_ task_vs_MBL = (0.856 - 0.267)/(0.776 - 0.267) p (40/20)]. This is the relative risk of engaging in the difficult task (difficult task off-path glance distribution with a total task time of 40 sec- onds), compared with engaging in the easy task (with a total task time of 20 seconds). This relative task risk is almost the same as the relative risk that corresponds to two tasks with exactly the same glance- off-path distribution but with different durations (i.e., total task time 20 seconds and 40 seconds but same glance distri- bution), for which the relative risk would be 2.0. The small increase in relative risk (2.31 compared with 2.0) is due to the relatively minor difference in glance distributions between the two tasks. Comparing the off-path glances for the two tasks (Figure 8.4 bottom left and right), the difficult task has a few longer (>2.5-second) off-path glances than the easy task. There is also a relatively large difference in glance prob- ability in the 0.75-second and 1.25-second bins, with a higher Figure 8.5. The MIR when all the glances (glance-off-path distribution) from matched baseline (left), a hypothetical simple task (middle), and a hypothetical difficult task (right) are applied to all crash and near-crash event kinematics in the SHRP 2 data set, using what-if simulations.

95 probability of glances of 1.25-second duration in the difficult task compared with the easy task, and vice versa for 0.75 sec- onds. Longer glances in either task would increase the MIR for that task (compare with Figure 8.3). Another key component affecting the task risk is the por- tion (ratio) of time the driver looks at the forward path dur- ing task execution. In the MIR calculation this is represented as a point mass at zero duration in the glance distribution (Figure 8.4). If the two tasks had different point masses at zero, that would have had additional effects on the relative risk, increasing the risk for the task that had a lower portion of glances on road during the task. To illustrate how to evalu- ate the influence of the portion of time looking at the forward roadway, calculations of relative task risk were done for the hypothetical easy task with 11 different point masses. The point masses used were 0% to 100% glances to the forward roadway during the task, in 10% steps. Obviously, 0% and 100% glances off road during the task may not be relevant. The relative risk for the glance-off-road ratio of the matched baseline (78.83%; point mass in Figure 8.4, top) compared with the easy task with point mass of the same value (78.83%) is approximately 1.6. This is the same relative risk as if the matched baseline off-path glances had been compared with the easy tasks off-path glance distribution, without taking the glances on the forward roadway into account. Further, by simulating different glance-on-forward- roadway ratios it is possible to identify the percentage of gaze on the forward roadway that would create a risk equal to that of driving without doing the task. In our hypothetical easy task, with linear inter polation between 80% and 90%, this point is approximately 87% on-road glances during the task (as in the matched baseline). In summary, the two hypothetical tasks’ off-path glance dis- tributions shown in Figure 8.4 are similar, with a somewhat higher proportion of longer glances in the difficult task, while the total task time is longer for the difficult task. This results in a relative risk close to the one that would be obtained had only the total task time been taken into account. Note that this analy- sis assumes that drivers have the same glance behavior (1) up until invTTC = 0.1 s-1, and (2) in all contexts in our sample of crashes and near crashes. These assumptions need to be dis- cussed and the method developed further. Specifically, focus should be placed on identifying means to get the context dependency in the task-glance-off-path distributions sorted out. That is, there are likely different matched baseline glance distributions for different subscenarios and also for rear-end scenarios. Subscenarios may include highway driving with heavy and light traffic, respectively, or rural close-to-intersection scenarios. When calculating MIR for the crashes and near crashes for different tasks and baseline, to calculate relative task risk, it is likely more correct to use different matched baseline glance distributions for different scenarios. It would also be important to know if drivers would start engaging in the spe- cific task for each of the different scenarios. 8.6 Generalization analysis: Comparison of DeltaV Metrics In accident statistics, the DeltaVs of crashes are recorded. To evaluate how representative the selection of crashes is in a sam- ple (e.g., our SHRP 2 data set), a comparison of distributions of DeltaV between accident statistics and the sample of crashes can be made. Since near crashes by definition did not result in a crash, they do not have DeltaVs. Therefore, we also com- pare MSDeltaV for both crashes and near crashes to a DeltaV distribution from accident statistics. We use the National Automotive Sampling System–Crashworthiness Data System (NASS-CDS) crash database (NHTSA 2010c) to construct a distribution of DeltaV for rear-end crashes for this evaluation of representativeness. NASS-CDS is a probability sample of approximately 3,300–4,000 tow-away crashes involving a light vehicle per year. Each crash is investigated, and, when possible, DeltaV is reconstructed from measurements of damage to the vehicle. We used weights and survey techniques (Taylor Series) to estimate the distribution of DeltaV for rear-end striking crashes (frontal impacts) (see Appendix A). The distributions of DeltaV and MSDeltaV were plotted as cumulative distribu- tion functions (CDFs), and the sample means were compared with simple t-test statistics. Results from Comparison of DeltaV Metrics The actual DeltaVs in the crashes in the sample are substan- tially lower compared with the DeltaVs in the CDS accident statistics (Figure 8.6). However, this is expected, since the CDS samples tow-away crashes, which are generally the more severe 40% of police-reported crashes. The SHRP 2 sample includes crashes with very low DeltaV (even near zero), which in many cases would not be severe enough even to meet police-report criteria. These crashes have very low risk of injury and even limited property damage. There is no signifi- cant difference (t227 = 0.606, p > 0.05) between the mean MSDeltaV for crashes and near crashes in the SHRP 2 sam- ple. This means that without the just-in-time evasive maneu- ver, near crashes in this sample have the same potential for injury as the crashes. It is interesting that at their maximum severity, these crashes fall near the DeltaV distribution for tow-away crashes. The CDS crash severity is a notable land- mark, though there is no reason why these crashes should necessarily fall near that line. Interestingly, given the low actual severity of the SHRP 2 crashes, a larger sample that includes higher-severity crashes would be expected to include some very high MSDeltaV values.

96 8.7 Generalization analysis: extreme Value analysis This section discusses results of models using extreme value theory to extrapolate from crashes to high-severity (extreme) DeltaV values and from near crashes to crash risk. Like the severity modeling in Sections 8.3–8.5, this approach tries to evaluate how the sample of crashes and near crashes relates to those that appear in crash databases. Following Jonasson and Rootzén (2014), we modeled the minimum time to collision (= max {-TTC}) from the set of near crashes using a Generalized Extreme Value (GEV) distri- bution. We removed TTC values of less than 1.5 seconds, and used L-Moments estimation to obtain a fit from which we could estimate the rate of minTTC = 0 per near-crash event. The parameter estimates were µ = -1.058, σ = 0.291, and ξ = -0.244. The model fit is shown in Figure 8.7. The points gen- erally fall on the 45-degree line, indicating reasonably good fit. The return period plot is shown in Figure 8.8. Note that the observed values lie inside the confidence intervals but are tending toward the lower bound at the higher return levels. When the fit line crosses a return level of 0.0, the correspond- ing return period is the number of near crashes expected before a crash would occur. This occurs at 7,815 crashes, indi- cating a probability of 0.00013 of minTTC reaching zero. Interestingly, this value is below the confidence interval from Jonasson and Rootzén (2014), who used data from the 100-car study. Thus, using this set of near crashes, we esti- mated a greater risk of crashing than they did. Figure 8.6. Cumulative density functions (distributions) of different DeltaV scales. Figure 8.7. Empirical versus model quantiles for Generalized Extreme Value (GEV) fit to minTTC data from near crashes. Points lying on the 45-degree line indicate good fit.

97 We also used extreme value analysis (EVA) to estimate the tail of the impact-speed distribution for crashes. Since impact speed is not an extreme value, we used the points-over- threshold, or exceedance, model. This approach involves selecting a high threshold and modeling only the observations above that threshold using a Generalized Pareto (GP) distri- bution. The threshold was selected to be 4 m/s, which maxi- mizes the sample size of the exceedances while still remaining in the tail of the distribution. This is necessary because the GP model only applies to distribution tails, and thresholds that are too low tend to produce bias in the estimates. The GP model fit is shown in Figure 8.9. The points do not fall entirely on the 45-degree line, but seem to indicate that the empirical quantiles are higher than the model quantiles. This was the best fit of the available methods but indicates the weak- ness of trying to model a tail with such a small sample of points. To generalize a reasonable fit to the tail, a sample of 200 or more crashes would likely be necessary so that the tail sample (generally <1.5% of the sample) is large enough (Coles 2001). Using this GP model, we looked at the return level for impact speed, shown in Figure 8.10. Here, the return level climbs slowly but steadily (in the log of event count). Note that return levels only make sense for a return period large enough to be above threshold. Thus, only return levels of 100+ crashes are likely to be interpretable. To put these values in context, we computed the return level for return periods of 100, 200, 300, 400, and 500 events. These correspond to impact speeds of 14.4, 15.2, 15.7, 16.1, and 16.3 m/s. The CDS return periods for these impact speeds are plotted in Figure 8.11 against the GP return peri- ods for comparison. In general, the GP return periods are more spread out than those from CDS (i.e., more events are needed to see values at the next level based on the GP model compared with the CDS estimates). However, these values are generally comparable to the upper tail from CDS. In general, since CDS is only tow-away crashes, we would expect the true return period to be greater (approximately double). Figure 8.8. Return level versus return period for near-crash GEV fit. Figure 8.9. Model fit for Generalized Pareto model of impact-speed exceedances.

98 Figure 8.10. Return level graph for Generalized Pareto model of impact speed in crashes. Figure 8.11. Return periods for the Crashworthiness Data System (CDS) and GP models of SHRP 2 crashes for a sample set of impact speeds. 0 100 200 300 400 500 600 0 100 200 300 400 500 600 CD S Re tu rn P er io d Generalized Pareto Return Periods The EVA results demonstrate that crashes in this set are reasonably comparable to CDS crashes of the same type. Crashes from SHRP 2 form a small set of lower-speed events, but higher-impact-speed events would not be expected with a small sample in general. The EVA approach allows us to use the lower-speed events to estimate how many higher-speed events would be expected to occur if we had a larger sample of crashes. In addition, EVA makes it possible to estimate the correspondence between near-crash and crash events. We expect a crash to occur once per 7,815 near crashes, a number that is lower than was estimated from the 100-car study. Unlike the 100-car study, these near crashes appear to be more similar to crashes. At a minimum, the selection of rear-end-striking crashes creates a more uniform sample that might begin to correspond to a set like that described in Wu and Jovanis (2012). 8.8 General Discussion on actual and potential Severity The what-if simulations introduced in this chapter can be used to create potential severity scales that are continuous and common across crashes and near crashes (i.e., the MIR index and the MCR index), given a model of driver behavior and a set of assumptions for the simulations. These scales can, in turn, be used for many different types of analysis. We used three examples to demonstrate proof of concept but did not aim to provide definite results. Potential (Model-Estimated) Severity and Example Analyses This report introduces the MIR and MCR scales, acknowledg- ing the need for further evaluation and adjustment. However, the main aim of MIR and MCR is to establish a methodologi- cal framework and proof of concept. In particular, there is a clear need for a continuous severity scale that can be applied to both near crashes and crashes. The work described in this report shows in many ways that near crashes are not simply a less-severe version of a critical event, as the categorical meth- ods assume. Crashes and near crashes are different instan- tiations of a risk that was established earlier in the event and based on mismatches between driver behavior and the event kinematics (e.g., lead-vehicle deceleration). The scales described here provide a way to focus on the potential for damage (injury or crash) of each event, rather than the way things happened to turn out in a given case. In future analy- ses, this should help to better differentiate precursors to crashes and methods of prevention. As discussed earlier, crashes often arise from situations that change quickly,

99 resulting in higher MIR and MCR indices. It may be that rem- edies for these situations are what is needed. Analysis to that end would benefit from separating cases (whether crash or near crash) that have high MIR/MCR from those with a lower MIR/MCR. The next steps in the development of MIR and MCR and the corresponding what-if simulation focus on validation strate- gies. The validation will likely result in refinement of the method, for example, by using different reaction models or matching glance distributions with scenarios. Two different types of validations should be performed. First is the validation of the underlying assumptions in themselves. For example, how valid is it to condition the glances to overlap invTTC = 0.1 s-1? Is there a need to establish different glance distribu- tions for different scenarios (e.g., time headway) and do sepa- rate analysis for the different scenarios? The second type of validation relates to comparison of the MIR outcomes to crash statistics. For example, the MIR distributions for the present sample of crashes and near crashes can be compared with observed measures of the injury risk from accident statistics. In the glance duration analysis, the impact of the duration of a glance was evaluated. The results are in line with the results in Chapter 7 and show the potential of applying hypo- thetical ideas of glance behavior (i.e., not empirical glance distribution) on existing data. In the analyses using this method, a main assumption affecting the results is/will be the anchoring of the glances as overlapping invTTC = 0.1 s-1. This choice of anchor point was made for a few different reasons. We did want to capture the basic idea that drivers try to avoid a critical situation by adapting to the situation. In the Tijerina et al. (2004) study of eyeglance behavior during car following, it was found that drivers under normal car-following condi- tions generally do not take their eyes off the road unless both the SV and lead vehicle are traveling at approximately the same speed (i.e., at range rates close to zero). Although we want to adopt a strategy based on drivers avoiding critical situations, we want a driver model that is reasonably related to the kinematics of crashes and near crashes. In Chapter 7, Figure 7.4 shows that for matched baseline, only a few drivers started to look away at an invTTC higher than 0.1 s-1. At the same time the mean of invTTC for near crashes is just below invTTC = 0.1 s-1. This led us, for proof of concept, to choose invTTC = 0.1 s-1 as the gaze anchor point. Future application of the method can change this anchor point. Another obvious anchor point would be invTTC = 0.2 s-1 as described in Chap- ter 7 (e.g., Figure 7.3). Appendix A also includes a description of how to apply the glance distributions at the original start of last glance off path instead of conditioning on an overlap of, for example, invTTC 0.1 s-1 or invTTC 0.2 s-1. That is, the glances start at the actual start of each last glance in the origi- nal event. Further development is needed on the choice of anchor point. Should lower-value anchor points be chosen instead, in line with Tijerina et al. (2004)? Or should thresh- olds such as invTTC = 0.2 s-1 be used? If a lower-value approach is chosen, data quality may also be a limiting factor (noise at longer ranges; see Appendix A). The second example addressed the calculation of relative risk by calculating MIR for two hypothetical tasks. That is, there is a need to measure the potential risks from eyeglance characteristics of tasks that have different glance distribu- tions, total task time, and Total Eyes off Road Time (TEORT). The scales developed here present one way to incorporate these different elements of a complex glance pattern into a risk scale (MIR/MCR). More work is needed to understand whether the risks of different glance patterns are fully charac- terized by this approach. However, MIR was calculated for all crashes and near crashes (N = 256) with the two (hypotheti- cal) task-glance-off-road distributions and matched base- lines. Results showed a relative risk that was only slightly higher than the risk that only took into account exposure (20-second task versus 40-second task). However, the off- path glance distributions were only slightly different with the same ratio of eyes on road. Although this is just an example, it does show how exposure (total task time) contributes to relative task risk. The longer the total task time, the higher the risk of exposure is. Only a very large shift in the glance distri- bution toward longer glances for a task, or a different ratio of glances on the forward roadway between tasks, would create a similar risk. Further analysis should include 1. Real tasks (a larger set of task-glance distributions with real data); 2. Evaluation of how the glance anchoring affects the relative risks; 3. Evaluation of how different driver reaction models, includ- ing how the glance durations on path (between glances off path), would affect the results; 4. Categorizing events into subscenarios to extract a matched baseline for each subscenario and used it for the respective events MIR calculations; and 5. Further investigation of driver adaptation/self-pacing in initiation of tasks in different scenarios. The glance anchoring analysis is practically a sensitivity analy- sis in which the anchor point may be, for example, (a) the original last-glance off-road start, (b) a different invTTC threshold, or (c) based on a different reaction model (e.g., what is described in Chapter 7). Also, the evaluation of reac- tion models and the categorization into subscenarios can be seen as sensitivity analyses—but with the focus to enhance precision in the relative-risk estimates. Finally, the question of whether a driver would initiate a specific task in a specific situ- ation is not considered in the current model. Further work is needed to investigate how this can be integrated.

100 The third example addressed the representativeness of the sample of crashes and near crashes. This was done by com- paring DeltaV from accident statistics (NASS-CDS crash database) with the actual DeltaV of the crashes in the sample as well as the MSDeltaV for both crashes and near crashes. The results were as expected and were further corroborated by EVA analysis. Limitations The potential severity metrics developed here depend on the extent to which the underlying behavior model actually repre- sents (or is related to) driver behavior in the contexts in which it is applied. It is important to take the limitations of these metrics into account in any analysis. It is, for example, not wise to mix analysis of the behavior that actually happened in an event with the potential severity scales, unless there are strong reasons for doing so. The next step in the development of MIR, MCR, and the corresponding what-if simulations is to focus on validation strategies—that is, validation of the individual assumptions (including further refinement) and comparison with accident statistics. Since all scales rely on the underlying model, it is those that have to be validated further, in the context of use in what-if simulations. There are 15 identified assumptions related to the what-if simulations and the creation of MIR and MCR. These are described in detail in Appendix A. Of the 15, five are in need of particular scrutiny and evaluation. We believe these five (more than the others) may affect MIR/MCR index calcula- tions in a way that not only shifts the scale but also may affect conclusions without easily being about to assess why. The fol- lowing is a list of these five assumptions (details are provided in Appendix A). Note that the first four are at different levels and violate conclusions in previous chapters. Future applications of MIR and MCR should likely revise the implementation; how- ever, due to late data availability, parallel analysis (results from other chapters arrived late), and the aim only to show proof of concept, these assumptions stand and were kept for the current implementation: 1. Driver’s glance behavior (glance-off-path distribution) is the same as that in the matched baseline (or task when per- forming task analysis) up until the chosen anchor point (invTTC = 0.1 s-1); 2. Drivers respond by braking at 8 m/s2 in all situations; 3. Brake initiation is made a fixed reaction time (0.4 second) after the driver has looked back on the road; 4. The quality of data is not affecting results significantly; and 5. It is reasonable to assume that, had the event not become critical, the driver would have continued at the same speed as just before the evasive maneuver. The extreme value analysis provides a glimpse into the relationship between near crashes and crashes. It would ben- efit from a larger sample size and might be applied to a larger number of descriptors. In addition, future analysis might try the multivariate approach described in Jonasson and Rootzén (2014). Further, crashes and near crashes result from an interplay between potentially critical kinematic situations and local glance behavior. Thus, there are typically many more similar kinematic situations present in the driving data that—combined with extreme glance behavior—would have resulted in near crashes or crashes. It is of some interest to try to develop estimation methods to weight the observed crash kinetics to better represent these potentially critical situa- tions and to estimate their frequencies per driving distance or driving time. 8.9 Conclusions on actual and potential Severity This chapter has described a novel approach to analyzing driver behavior in naturalistic driving data. Specifically, we propose two potential severity scales, created using mathe- matical simulations that apply a model of driver glance behav- ior to kinematics based on actual crashes and near crashes. The two scales (MIR and MCR) are continuous and calculable for crashes and near crashes alike. These properties may be fundamental in future analysis of naturalistic driving data, but they are not present for available actual outcome severity met- rics, such as DeltaV and minTTC. We recommend that DeltaV and minTTC be calculated for all crashes and near crashes, respectively. Proof of concept of the evaluation of visual-manual task risk was established through the application of MIR to two (hypothetical) visual-manual tasks. The results of the example application of MIR (to study the effect of last glance-off-path duration between crashes and near crashes) are in line with results in Chapter 7. That is, they show that crash scenarios play out faster than near-crash scenarios—higher risks at shorter glance durations. The potential severity metrics are likely to have many uses. Those uses range from visual-manual task evaluation—by facilitating a continuous metric in advanced driver assistance systems evaluation (rather than simply count- ing instances of crashes and near crashes)—to providing a tool for further validation of driver models (e.g., reaction models). Given the inherent limitations in the metrics, assumptions must be evaluated extensively for each analysis use-case. We demonstrate how a comparable, continuous metric for crashes and near crashes can allow a more nuanced analysis of the precursor conditions, which can be worse in some near crashes than in some crashes. This approach focuses on com- mon elements of the precursor conditions and provides a way to analyze them without including the influence of actions that were taken afterwards (i.e., success or failure to avoid).

101 While success or failure to avoid is important for understand- ing avoidance itself, the outcome of an event does not, in itself, determine the inherent risk of crashing in that event. Another use of the approach is to evaluate the consequences of different task-related glance distributions on a large set of crashes and near crashes. Potential consequences of tasks depend on the inherent risk in an event, which is often related to how fast it develops. These, again, are independent of what actually happened. Finally, the EVA begins to quantify the relationship between crashes and near crashes. The similarity of precursor condi- tions for near crashes and crashes, combined with the very large number of EVA-estimated near crashes per crash, sug- gests that avoidance is common. Thus, failure to avoid may be fairly random, while avoidance of the circumstances (focus on the precursors) might be more effective in reducing crash risk. Thus, the analyses undertaken to answer the research question, What crash severity scale is best suited for analysis of risk? resulted in the formulation and proposal of two potential severity scales: Model-estimated Injury Risk (MIR) index and Model-estimated Crash Risk (MCR) index. These scales were created using mathematical simulations, applying a model of driver glance behavior to kinematics based on actual crashes and near crashes, and represent what might have happened had the event played out according to a specific driver model. The two scales (MIR and MCR) provide con- tinuous values and can be calculated for actual crash and near- crash events. However, further work is necessary to validate the scales. Note that the severity scales are simulated. Actual sever- ity scales—Delta Velocity (DeltaV) for crashes and minimum time to collision (minTTC) for near crashes—are still the most relevant metrics when analyzing actual severity (what actually happened in the event) and should be calculated for the SHRP 2 data set. The main drawback with the actual severity scales is that they cannot be used to compare both crashes and near crashes. This property—the ability to com- pare potential severity across crashes and near crashes—is enabled by our proposed MIR and MCR scales. It is impor- tant to note that these scales are also enabled by naturalistic data. Without the detailed time-series data leading up to crashes and near crashes, the MIR and MCR scales could not be computed.